TSTP Solution File: GRP167-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP167-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:10 EDT 2022
% Result : Unsatisfiable 57.53s 57.77s
% Output : CNFRefutation 57.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 110
% Number of leaves : 453
% Syntax : Number of clauses : 2115 (1073 unt; 0 nHn;1024 RR)
% Number of literals : 3611 (3610 equ;1498 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 4556 ( 53 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(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_p19,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ).
cnf(refute_0_0,plain,
multiply(multiply(inverse(X_38),X_38),X_39) = multiply(inverse(X_38),multiply(X_38,X_39)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_38))),bind(Y,$fot(X_38)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_38),X_38) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(inverse(X_38),X_38),X_39) != multiply(inverse(X_38),multiply(X_38,X_39))
| multiply(inverse(X_38),X_38) != identity
| multiply(identity,X_39) = multiply(inverse(X_38),multiply(X_38,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_38),X_38),X_39),multiply(inverse(X_38),multiply(X_38,X_39))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_38),X_38),X_39) != multiply(inverse(X_38),multiply(X_38,X_39))
| multiply(identity,X_39) = multiply(inverse(X_38),multiply(X_38,X_39)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),X_38),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_39) = multiply(inverse(X_38),multiply(X_38,X_39)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_38),X_38),X_39),multiply(inverse(X_38),multiply(X_38,X_39))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_39) = X_39,
inference(subst,[],[left_identity:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_39) != X_39
| multiply(identity,X_39) != multiply(inverse(X_38),multiply(X_38,X_39))
| X_39 = multiply(inverse(X_38),multiply(X_38,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_39),multiply(inverse(X_38),multiply(X_38,X_39))) ),[0],$fot(X_39)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_39) != multiply(inverse(X_38),multiply(X_38,X_39))
| X_39 = multiply(inverse(X_38),multiply(X_38,X_39)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_39),X_39) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_39 = multiply(inverse(X_38),multiply(X_38,X_39)),
inference(resolve,[$cnf( $equal(multiply(identity,X_39),multiply(inverse(X_38),multiply(X_38,X_39))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(X_51,inverse(multiply(X_38,X_51))) = multiply(inverse(X_38),multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51))))),
inference(subst,[],[refute_0_8:[bind(X_39,$fot(multiply(X_51,inverse(multiply(X_38,X_51)))))]]) ).
cnf(refute_0_10,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(subst,[],[associativity:[bind(Z,$fot(inverse(multiply(X,Y))))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(inverse(X_44)),inverse(X_44)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_44)))]]) ).
cnf(refute_0_12,plain,
multiply(X_40,X_41) = multiply(inverse(inverse(X_40)),multiply(inverse(X_40),multiply(X_40,X_41))),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(inverse(X_40))),bind(X_39,$fot(multiply(X_40,X_41)))]]) ).
cnf(refute_0_13,plain,
X_41 = multiply(inverse(X_40),multiply(X_40,X_41)),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(X_40)),bind(X_39,$fot(X_41))]]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( X_41 != multiply(inverse(X_40),multiply(X_40,X_41))
| multiply(inverse(X_40),multiply(X_40,X_41)) = X_41 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_41)),bind(Y0,$fot(multiply(inverse(X_40),multiply(X_40,X_41))))]]) ).
cnf(refute_0_18,plain,
multiply(inverse(X_40),multiply(X_40,X_41)) = X_41,
inference(resolve,[$cnf( $equal(X_41,multiply(inverse(X_40),multiply(X_40,X_41))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( multiply(X_40,X_41) != multiply(inverse(inverse(X_40)),multiply(inverse(X_40),multiply(X_40,X_41)))
| multiply(inverse(X_40),multiply(X_40,X_41)) != X_41
| multiply(X_40,X_41) = multiply(inverse(inverse(X_40)),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_40,X_41),multiply(inverse(inverse(X_40)),multiply(inverse(X_40),multiply(X_40,X_41)))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_20,plain,
( multiply(X_40,X_41) != multiply(inverse(inverse(X_40)),multiply(inverse(X_40),multiply(X_40,X_41)))
| multiply(X_40,X_41) = multiply(inverse(inverse(X_40)),X_41) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),multiply(X_40,X_41)),X_41) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(X_40,X_41) = multiply(inverse(inverse(X_40)),X_41),
inference(resolve,[$cnf( $equal(multiply(X_40,X_41),multiply(inverse(inverse(X_40)),multiply(inverse(X_40),multiply(X_40,X_41)))) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_44,inverse(X_44)) = multiply(inverse(inverse(X_44)),inverse(X_44)),
inference(subst,[],[refute_0_21:[bind(X_40,$fot(X_44)),bind(X_41,$fot(inverse(X_44)))]]) ).
cnf(refute_0_23,plain,
( multiply(X_44,inverse(X_44)) != multiply(inverse(inverse(X_44)),inverse(X_44))
| multiply(inverse(inverse(X_44)),inverse(X_44)) = multiply(X_44,inverse(X_44)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_44,inverse(X_44)))),bind(Y0,$fot(multiply(inverse(inverse(X_44)),inverse(X_44))))]]) ).
cnf(refute_0_24,plain,
multiply(inverse(inverse(X_44)),inverse(X_44)) = multiply(X_44,inverse(X_44)),
inference(resolve,[$cnf( $equal(multiply(X_44,inverse(X_44)),multiply(inverse(inverse(X_44)),inverse(X_44))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(inverse(inverse(X_44)),inverse(X_44)) != multiply(X_44,inverse(X_44))
| multiply(inverse(inverse(X_44)),inverse(X_44)) != identity
| multiply(X_44,inverse(X_44)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_44)),inverse(X_44)),identity) ),[0],$fot(multiply(X_44,inverse(X_44)))]]) ).
cnf(refute_0_26,plain,
( multiply(inverse(inverse(X_44)),inverse(X_44)) != identity
| multiply(X_44,inverse(X_44)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_44)),inverse(X_44)),multiply(X_44,inverse(X_44))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_44,inverse(X_44)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_44)),inverse(X_44)),identity) )],[refute_0_11,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = identity,
inference(subst,[],[refute_0_27:[bind(X_44,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_29,plain,
( multiply(multiply(X,Y),inverse(multiply(X,Y))) != multiply(X,multiply(Y,inverse(multiply(X,Y))))
| multiply(multiply(X,Y),inverse(multiply(X,Y))) != identity
| identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_30,plain,
( multiply(multiply(X,Y),inverse(multiply(X,Y))) != multiply(X,multiply(Y,inverse(multiply(X,Y))))
| identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),identity) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) )],[refute_0_10,refute_0_30]) ).
cnf(refute_0_32,plain,
identity = multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_38)),bind(Y,$fot(X_51))]]) ).
cnf(refute_0_33,plain,
( identity != multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51))))
| multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))) = identity ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51))))))]]) ).
cnf(refute_0_34,plain,
multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51))))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))) != identity
| multiply(X_51,inverse(multiply(X_38,X_51))) != multiply(inverse(X_38),multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))))
| multiply(X_51,inverse(multiply(X_38,X_51))) = multiply(inverse(X_38),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,inverse(multiply(X_38,X_51))),multiply(inverse(X_38),multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_36,plain,
( multiply(X_51,inverse(multiply(X_38,X_51))) != multiply(inverse(X_38),multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))))
| multiply(X_51,inverse(multiply(X_38,X_51))) = multiply(inverse(X_38),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))),identity) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(X_51,inverse(multiply(X_38,X_51))) = multiply(inverse(X_38),identity),
inference(resolve,[$cnf( $equal(multiply(X_51,inverse(multiply(X_38,X_51))),multiply(inverse(X_38),multiply(X_38,multiply(X_51,inverse(multiply(X_38,X_51)))))) )],[refute_0_9,refute_0_36]) ).
cnf(refute_0_38,plain,
X_41 = multiply(inverse(inverse(X_41)),multiply(inverse(X_41),X_41)),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(inverse(X_41))),bind(X_39,$fot(X_41))]]) ).
cnf(refute_0_39,plain,
multiply(inverse(X_41),X_41) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_40,plain,
( X_41 != multiply(inverse(inverse(X_41)),multiply(inverse(X_41),X_41))
| multiply(inverse(X_41),X_41) != identity
| X_41 = multiply(inverse(inverse(X_41)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_41,multiply(inverse(inverse(X_41)),multiply(inverse(X_41),X_41))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_41,plain,
( X_41 != multiply(inverse(inverse(X_41)),multiply(inverse(X_41),X_41))
| X_41 = multiply(inverse(inverse(X_41)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_41),X_41),identity) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
X_41 = multiply(inverse(inverse(X_41)),identity),
inference(resolve,[$cnf( $equal(X_41,multiply(inverse(inverse(X_41)),multiply(inverse(X_41),X_41))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( multiply(X_40,X_41) != multiply(inverse(inverse(X_40)),X_41)
| multiply(inverse(inverse(X_40)),X_41) = multiply(X_40,X_41) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_40,X_41))),bind(Y0,$fot(multiply(inverse(inverse(X_40)),X_41)))]]) ).
cnf(refute_0_44,plain,
multiply(inverse(inverse(X_40)),X_41) = multiply(X_40,X_41),
inference(resolve,[$cnf( $equal(multiply(X_40,X_41),multiply(inverse(inverse(X_40)),X_41)) )],[refute_0_21,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(inverse(inverse(X_41)),identity) = multiply(X_41,identity),
inference(subst,[],[refute_0_44:[bind(X_40,$fot(X_41)),bind(X_41,$fot(identity))]]) ).
cnf(refute_0_46,plain,
( X_41 != multiply(inverse(inverse(X_41)),identity)
| multiply(inverse(inverse(X_41)),identity) != multiply(X_41,identity)
| X_41 = multiply(X_41,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,multiply(X_41,identity)) ),[0],$fot(multiply(inverse(inverse(X_41)),identity))]]) ).
cnf(refute_0_47,plain,
( X_41 != multiply(inverse(inverse(X_41)),identity)
| X_41 = multiply(X_41,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_41)),identity),multiply(X_41,identity)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
X_41 = multiply(X_41,identity),
inference(resolve,[$cnf( $equal(X_41,multiply(inverse(inverse(X_41)),identity)) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
( X_41 != multiply(X_41,identity)
| multiply(X_41,identity) = X_41 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_41)),bind(Y0,$fot(multiply(X_41,identity)))]]) ).
cnf(refute_0_50,plain,
multiply(X_41,identity) = X_41,
inference(resolve,[$cnf( $equal(X_41,multiply(X_41,identity)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(inverse(X_38),identity) = inverse(X_38),
inference(subst,[],[refute_0_50:[bind(X_41,$fot(inverse(X_38)))]]) ).
cnf(refute_0_52,plain,
( multiply(X_51,inverse(multiply(X_38,X_51))) != multiply(inverse(X_38),identity)
| multiply(inverse(X_38),identity) != inverse(X_38)
| multiply(X_51,inverse(multiply(X_38,X_51))) = inverse(X_38) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_51,inverse(multiply(X_38,X_51))),inverse(X_38)) ),[0],$fot(multiply(inverse(X_38),identity))]]) ).
cnf(refute_0_53,plain,
( multiply(X_51,inverse(multiply(X_38,X_51))) != multiply(inverse(X_38),identity)
| multiply(X_51,inverse(multiply(X_38,X_51))) = inverse(X_38) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),identity),inverse(X_38)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(X_51,inverse(multiply(X_38,X_51))) = inverse(X_38),
inference(resolve,[$cnf( $equal(multiply(X_51,inverse(multiply(X_38,X_51))),multiply(inverse(X_38),identity)) )],[refute_0_37,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))) = inverse(inverse(X_86)),
inference(subst,[],[refute_0_54:[bind(X_38,$fot(inverse(X_86))),bind(X_51,$fot(least_upper_bound(identity,X_86)))]]) ).
cnf(refute_0_56,plain,
multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_66)),bind(Y,$fot(X_67)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_57,plain,
X_66 = multiply(X_66,identity),
inference(subst,[],[refute_0_48:[bind(X_41,$fot(X_66))]]) ).
cnf(refute_0_58,plain,
( X_66 != multiply(X_66,identity)
| multiply(X_66,identity) = X_66 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_66)),bind(Y0,$fot(multiply(X_66,identity)))]]) ).
cnf(refute_0_59,plain,
multiply(X_66,identity) = X_66,
inference(resolve,[$cnf( $equal(X_66,multiply(X_66,identity)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(X_66,identity) != X_66
| multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),X_66) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))) ),[1,1],$fot(X_66)]]) ).
cnf(refute_0_61,plain,
( multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),X_66) ),
inference(resolve,[$cnf( $equal(multiply(X_66,identity),X_66) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(multiply(X_66,X_67),X_66),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,identity))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_64,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_63]) ).
cnf(refute_0_65,plain,
least_upper_bound(multiply(X_66,X_67),X_66) = least_upper_bound(X_66,multiply(X_66,X_67)),
inference(subst,[],[refute_0_64:[bind(X,$fot(X_66)),bind(Y,$fot(multiply(X_66,X_67)))]]) ).
cnf(refute_0_66,plain,
( multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),X_66)
| least_upper_bound(multiply(X_66,X_67),X_66) != least_upper_bound(X_66,multiply(X_66,X_67))
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(X_66,multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(X_66,multiply(X_66,X_67))) ),[0],$fot(least_upper_bound(multiply(X_66,X_67),X_66))]]) ).
cnf(refute_0_67,plain,
( multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(multiply(X_66,X_67),X_66)
| multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(X_66,multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_67),X_66),least_upper_bound(X_66,multiply(X_66,X_67))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(X_66,least_upper_bound(X_67,identity)) = least_upper_bound(X_66,multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(multiply(X_66,X_67),X_66)) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = least_upper_bound(inverse(X_75),multiply(inverse(X_75),least_upper_bound(X_75,identity))),
inference(subst,[],[refute_0_68:[bind(X_66,$fot(inverse(X_75))),bind(X_67,$fot(least_upper_bound(X_75,identity)))]]) ).
cnf(refute_0_70,plain,
multiply(inverse(X_70),least_upper_bound(X_70,identity)) = least_upper_bound(inverse(X_70),multiply(inverse(X_70),X_70)),
inference(subst,[],[refute_0_68:[bind(X_66,$fot(inverse(X_70))),bind(X_67,$fot(X_70))]]) ).
cnf(refute_0_71,plain,
multiply(inverse(X_70),X_70) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_70))]]) ).
cnf(refute_0_72,plain,
( multiply(inverse(X_70),X_70) != identity
| multiply(inverse(X_70),least_upper_bound(X_70,identity)) != least_upper_bound(inverse(X_70),multiply(inverse(X_70),X_70))
| multiply(inverse(X_70),least_upper_bound(X_70,identity)) = least_upper_bound(inverse(X_70),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_70),least_upper_bound(X_70,identity)),least_upper_bound(inverse(X_70),multiply(inverse(X_70),X_70))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_73,plain,
( multiply(inverse(X_70),least_upper_bound(X_70,identity)) != least_upper_bound(inverse(X_70),multiply(inverse(X_70),X_70))
| multiply(inverse(X_70),least_upper_bound(X_70,identity)) = least_upper_bound(inverse(X_70),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_70),X_70),identity) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(X_70),least_upper_bound(X_70,identity)) = least_upper_bound(inverse(X_70),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_70),least_upper_bound(X_70,identity)),least_upper_bound(inverse(X_70),multiply(inverse(X_70),X_70))) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
least_upper_bound(inverse(X_70),identity) = least_upper_bound(identity,inverse(X_70)),
inference(subst,[],[refute_0_64:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_70)))]]) ).
cnf(refute_0_76,plain,
( multiply(inverse(X_70),least_upper_bound(X_70,identity)) != least_upper_bound(inverse(X_70),identity)
| least_upper_bound(inverse(X_70),identity) != least_upper_bound(identity,inverse(X_70))
| multiply(inverse(X_70),least_upper_bound(X_70,identity)) = least_upper_bound(identity,inverse(X_70)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_70),least_upper_bound(X_70,identity)),least_upper_bound(identity,inverse(X_70))) ),[0],$fot(least_upper_bound(inverse(X_70),identity))]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(X_70),least_upper_bound(X_70,identity)) != least_upper_bound(inverse(X_70),identity)
| multiply(inverse(X_70),least_upper_bound(X_70,identity)) = least_upper_bound(identity,inverse(X_70)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_70),identity),least_upper_bound(identity,inverse(X_70))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(inverse(X_70),least_upper_bound(X_70,identity)) = least_upper_bound(identity,inverse(X_70)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_70),least_upper_bound(X_70,identity)),least_upper_bound(inverse(X_70),identity)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(X_75),least_upper_bound(X_75,identity)) = least_upper_bound(identity,inverse(X_75)),
inference(subst,[],[refute_0_78:[bind(X_70,$fot(X_75))]]) ).
cnf(refute_0_80,plain,
( multiply(inverse(X_75),least_upper_bound(X_75,identity)) != least_upper_bound(identity,inverse(X_75))
| multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) != least_upper_bound(inverse(X_75),multiply(inverse(X_75),least_upper_bound(X_75,identity)))
| multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)),least_upper_bound(inverse(X_75),multiply(inverse(X_75),least_upper_bound(X_75,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_81,plain,
( multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) != least_upper_bound(inverse(X_75),multiply(inverse(X_75),least_upper_bound(X_75,identity)))
| multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(X_75,identity)),least_upper_bound(identity,inverse(X_75))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)),least_upper_bound(inverse(X_75),multiply(inverse(X_75),least_upper_bound(X_75,identity)))) )],[refute_0_69,refute_0_81]) ).
cnf(refute_0_83,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_84,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_85,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_88,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) = least_upper_bound(X_15,Y),
inference(subst,[],[refute_0_89:[bind(X_10,$fot(least_upper_bound(X_15,Y))),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_91,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_92,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) != X_15
| least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_93,plain,
( least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_96,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_95]) ).
cnf(refute_0_97,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_98,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(Y,X_15)))]]) ).
cnf(refute_0_99,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_94,refute_0_99]) ).
cnf(refute_0_101,plain,
least_upper_bound(identity,least_upper_bound(X_75,identity)) = least_upper_bound(identity,X_75),
inference(subst,[],[refute_0_100:[bind(Y,$fot(X_75)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_102,plain,
multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))) = multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))))]]) ).
cnf(refute_0_103,plain,
( multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))) != multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity)))
| least_upper_bound(identity,least_upper_bound(X_75,identity)) != least_upper_bound(identity,X_75)
| multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))) = multiply(inverse(X_75),least_upper_bound(identity,X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))),multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_75))]]) ).
cnf(refute_0_104,plain,
( least_upper_bound(identity,least_upper_bound(X_75,identity)) != least_upper_bound(identity,X_75)
| multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))) = multiply(inverse(X_75),least_upper_bound(identity,X_75)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))),multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity)))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))) = multiply(inverse(X_75),least_upper_bound(identity,X_75)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_75,identity)),least_upper_bound(identity,X_75)) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
least_upper_bound(X_19,least_upper_bound(X_18,X_19)) = least_upper_bound(X_19,X_18),
inference(subst,[],[refute_0_100:[bind(Y,$fot(X_18)),bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_107,plain,
least_upper_bound(X_19,X_18) = least_upper_bound(X_18,X_19),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_19)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_108,plain,
( least_upper_bound(X_19,X_18) != least_upper_bound(X_18,X_19)
| least_upper_bound(X_18,X_19) = least_upper_bound(X_19,X_18) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_19,X_18))),bind(Y0,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_109,plain,
least_upper_bound(X_18,X_19) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,X_18),least_upper_bound(X_18,X_19)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( least_upper_bound(X_18,X_19) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,X_18)) ),[0,1],$fot(least_upper_bound(X_19,X_18))]]) ).
cnf(refute_0_111,plain,
( least_upper_bound(X_19,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,X_19),least_upper_bound(X_19,X_18)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,X_18)) )],[refute_0_106,refute_0_111]) ).
cnf(refute_0_113,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_70))) = least_upper_bound(X_19,multiply(X_19,X_70)),
inference(subst,[],[refute_0_112:[bind(X_18,$fot(multiply(X_19,X_70)))]]) ).
cnf(refute_0_114,plain,
multiply(X_19,least_upper_bound(X_70,identity)) = least_upper_bound(X_19,multiply(X_19,X_70)),
inference(subst,[],[refute_0_68:[bind(X_66,$fot(X_19)),bind(X_67,$fot(X_70))]]) ).
cnf(refute_0_115,plain,
( multiply(X_19,least_upper_bound(X_70,identity)) != least_upper_bound(X_19,multiply(X_19,X_70))
| least_upper_bound(X_19,multiply(X_19,X_70)) = multiply(X_19,least_upper_bound(X_70,identity)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_19,least_upper_bound(X_70,identity)))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_19,X_70))))]]) ).
cnf(refute_0_116,plain,
least_upper_bound(X_19,multiply(X_19,X_70)) = multiply(X_19,least_upper_bound(X_70,identity)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(X_70,identity)),least_upper_bound(X_19,multiply(X_19,X_70))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( least_upper_bound(X_19,multiply(X_19,X_70)) != multiply(X_19,least_upper_bound(X_70,identity))
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_70))) != least_upper_bound(X_19,multiply(X_19,X_70))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = least_upper_bound(X_19,multiply(X_19,X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_70))),least_upper_bound(X_19,multiply(X_19,X_70))) ),[0,1],$fot(multiply(X_19,least_upper_bound(X_70,identity)))]]) ).
cnf(refute_0_118,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_70))) != least_upper_bound(X_19,multiply(X_19,X_70))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = least_upper_bound(X_19,multiply(X_19,X_70)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_70)),multiply(X_19,least_upper_bound(X_70,identity))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = least_upper_bound(X_19,multiply(X_19,X_70)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_70))),least_upper_bound(X_19,multiply(X_19,X_70))) )],[refute_0_113,refute_0_118]) ).
cnf(refute_0_120,plain,
least_upper_bound(identity,least_upper_bound(X_70,identity)) = least_upper_bound(identity,X_70),
inference(subst,[],[refute_0_100:[bind(Y,$fot(X_70)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_121,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))),
introduced(tautology,[refl,[$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))))]]) ).
cnf(refute_0_122,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))
| least_upper_bound(identity,least_upper_bound(X_70,identity)) != least_upper_bound(identity,X_70)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_70))]]) ).
cnf(refute_0_123,plain,
( least_upper_bound(identity,least_upper_bound(X_70,identity)) != least_upper_bound(identity,X_70)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,X_70)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,X_70)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_70,identity)),least_upper_bound(identity,X_70)) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| least_upper_bound(X,Y) != least_upper_bound(Y,X)
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) ),[0,1],$fot(least_upper_bound(Y,X))]]) ).
cnf(refute_0_126,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_125]) ).
cnf(refute_0_127,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) )],[glb_absorbtion,refute_0_126]) ).
cnf(refute_0_128,plain,
greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_127:[bind(X,$fot(least_upper_bound(X_18,Y)))]]) ).
cnf(refute_0_129,plain,
least_upper_bound(Y,least_upper_bound(X_18,Y)) = least_upper_bound(Y,X_18),
inference(subst,[],[refute_0_100:[bind(Y,$fot(X_18)),bind(X_15,$fot(Y))]]) ).
cnf(refute_0_130,plain,
( greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) != least_upper_bound(X_18,Y)
| least_upper_bound(Y,least_upper_bound(X_18,Y)) != least_upper_bound(Y,X_18)
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))),least_upper_bound(X_18,Y)) ),[0,1],$fot(least_upper_bound(Y,X_18))]]) ).
cnf(refute_0_131,plain,
( greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) != least_upper_bound(X_18,Y)
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))),least_upper_bound(X_18,Y)) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))) = least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),
inference(subst,[],[refute_0_132:[bind(Y,$fot(multiply(X_66,X_67))),bind(X_18,$fot(multiply(X_66,X_68)))]]) ).
cnf(refute_0_134,plain,
multiply(X_66,least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_66)),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_135,plain,
( multiply(X_66,least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))
| least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68)) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_66,least_upper_bound(X_67,X_68)))),bind(Y0,$fot(least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))))]]) ).
cnf(refute_0_136,plain,
least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68)) = multiply(X_66,least_upper_bound(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))) != least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))
| least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68)) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) = least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) ),[0,1],$fot(multiply(X_66,least_upper_bound(X_67,X_68)))]]) ).
cnf(refute_0_138,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))) != least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))
| greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) = least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68)),multiply(X_66,least_upper_bound(X_67,X_68))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) = least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),least_upper_bound(multiply(X_66,X_67),multiply(X_66,X_68))),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) )],[refute_0_133,refute_0_138]) ).
cnf(refute_0_140,plain,
greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)) = least_upper_bound(X_67,X_68),
inference(subst,[],[refute_0_132:[bind(Y,$fot(X_68)),bind(X_18,$fot(X_67))]]) ).
cnf(refute_0_141,plain,
multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))) = multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))),
introduced(tautology,[refl,[$fot(multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))))]]) ).
cnf(refute_0_142,plain,
( multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))) != multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)))
| greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)) != least_upper_bound(X_67,X_68)
| multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))),multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)))) ),[1,1],$fot(least_upper_bound(X_67,X_68))]]) ).
cnf(refute_0_143,plain,
( greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)) != least_upper_bound(X_67,X_68)
| multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))),multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)),least_upper_bound(X_67,X_68)) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_146,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_145]) ).
cnf(refute_0_147,plain,
greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) = multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))),
inference(subst,[],[refute_0_146:[bind(X,$fot(X_66)),bind(Y,$fot(least_upper_bound(X_67,X_68))),bind(Z,$fot(least_upper_bound(X_68,X_67)))]]) ).
cnf(refute_0_148,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_149,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_16,refute_0_148]) ).
cnf(refute_0_150,plain,
( multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) != multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))))),bind(Y0,$fot(multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))))),bind(Z0,$fot(multiply(X_66,least_upper_bound(X_67,X_68))))]]) ).
cnf(refute_0_151,plain,
( multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))),multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67)))) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_66,greatest_lower_bound(least_upper_bound(X_67,X_68),least_upper_bound(X_68,X_67))),multiply(X_66,least_upper_bound(X_67,X_68))) )],[refute_0_144,refute_0_151]) ).
cnf(refute_0_153,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_154,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_153]) ).
cnf(refute_0_155,plain,
least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) = multiply(X_66,least_upper_bound(X_68,X_67)),
inference(subst,[],[refute_0_154:[bind(X,$fot(X_66)),bind(Y,$fot(X_68)),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_156,plain,
greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) = greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))))]]) ).
cnf(refute_0_157,plain,
( greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) != greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)))
| least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) != multiply(X_66,least_upper_bound(X_68,X_67))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) = greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))),greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)))) ),[1,1],$fot(multiply(X_66,least_upper_bound(X_68,X_67)))]]) ).
cnf(refute_0_158,plain,
( least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) != multiply(X_66,least_upper_bound(X_68,X_67))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) = greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))),greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) = greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_68,X_67))) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
( greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) != greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67)))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))))),bind(Z0,$fot(multiply(X_66,least_upper_bound(X_67,X_68))))]]) ).
cnf(refute_0_161,plain,
( greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))),greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67)))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) = multiply(X_66,least_upper_bound(X_67,X_68)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))),multiply(X_66,least_upper_bound(X_67,X_68))) )],[refute_0_152,refute_0_161]) ).
cnf(refute_0_163,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_164,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_163]) ).
cnf(refute_0_165,plain,
greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) = greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))),
inference(subst,[],[refute_0_164:[bind(X,$fot(multiply(X_66,least_upper_bound(X_67,X_68)))),bind(Y,$fot(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))))]]) ).
cnf(refute_0_166,plain,
( greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) != greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)))
| greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))))),bind(Z0,$fot(multiply(X_66,least_upper_bound(X_67,X_68))))]]) ).
cnf(refute_0_167,plain,
( greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))),greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) = multiply(X_66,least_upper_bound(X_67,X_68)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))),multiply(X_66,least_upper_bound(X_67,X_68))) )],[refute_0_162,refute_0_167]) ).
cnf(refute_0_169,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) != multiply(X_66,least_upper_bound(X_67,X_68))
| greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) != least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))
| multiply(X_66,least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) ),[0],$fot(multiply(X_66,least_upper_bound(X_67,X_68)))]]) ).
cnf(refute_0_170,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) != least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))
| multiply(X_66,least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))),multiply(X_66,least_upper_bound(X_67,X_68))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
( multiply(X_66,least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))
| least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)) != multiply(X_66,least_upper_bound(X_68,X_67))
| multiply(X_66,least_upper_bound(X_67,X_68)) = multiply(X_66,least_upper_bound(X_68,X_67)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) ),[0],$fot(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)))]]) ).
cnf(refute_0_172,plain,
( multiply(X_66,least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))
| multiply(X_66,least_upper_bound(X_67,X_68)) = multiply(X_66,least_upper_bound(X_68,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_68,X_67))) )],[refute_0_155,refute_0_171]) ).
cnf(refute_0_173,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))) != least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))
| multiply(X_66,least_upper_bound(X_67,X_68)) = multiply(X_66,least_upper_bound(X_68,X_67)) ),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,X_68)),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) )],[refute_0_170,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(X_66,least_upper_bound(X_67,X_68)) = multiply(X_66,least_upper_bound(X_68,X_67)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67)),multiply(X_66,least_upper_bound(X_67,X_68))),least_upper_bound(multiply(X_66,X_68),multiply(X_66,X_67))) )],[refute_0_139,refute_0_173]) ).
cnf(refute_0_175,plain,
( multiply(X_66,least_upper_bound(X_67,X_68)) != multiply(X_66,least_upper_bound(X_68,X_67))
| multiply(X_66,least_upper_bound(X_68,X_67)) = multiply(X_66,least_upper_bound(X_67,X_68)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_66,least_upper_bound(X_67,X_68)))),bind(Y0,$fot(multiply(X_66,least_upper_bound(X_68,X_67))))]]) ).
cnf(refute_0_176,plain,
multiply(X_66,least_upper_bound(X_68,X_67)) = multiply(X_66,least_upper_bound(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,X_68)),multiply(X_66,least_upper_bound(X_68,X_67))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity)) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))),
inference(subst,[],[refute_0_176:[bind(X_66,$fot(X_19)),bind(X_67,$fot(identity)),bind(X_68,$fot(least_upper_bound(X_70,identity)))]]) ).
cnf(refute_0_178,plain,
( multiply(X_66,least_upper_bound(X_67,identity)) != least_upper_bound(X_66,multiply(X_66,X_67))
| least_upper_bound(X_66,multiply(X_66,X_67)) = multiply(X_66,least_upper_bound(X_67,identity)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_66,least_upper_bound(X_67,identity)))),bind(Y0,$fot(least_upper_bound(X_66,multiply(X_66,X_67))))]]) ).
cnf(refute_0_179,plain,
least_upper_bound(X_66,multiply(X_66,X_67)) = multiply(X_66,least_upper_bound(X_67,identity)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,identity)),least_upper_bound(X_66,multiply(X_66,X_67))) )],[refute_0_68,refute_0_178]) ).
cnf(refute_0_180,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity)),
inference(subst,[],[refute_0_179:[bind(X_66,$fot(X_19)),bind(X_67,$fot(least_upper_bound(X_70,identity)))]]) ).
cnf(refute_0_181,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) != multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity)))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))))]]) ).
cnf(refute_0_182,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))),multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(least_upper_bound(X_70,identity),identity)),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))) )],[refute_0_177,refute_0_182]) ).
cnf(refute_0_184,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) != multiply(X_19,least_upper_bound(identity,X_70))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,X_70)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,X_70))))]]) ).
cnf(refute_0_185,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))) != multiply(X_19,least_upper_bound(identity,X_70))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,X_70)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity)))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) = multiply(X_19,least_upper_bound(identity,X_70)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_70,identity))),multiply(X_19,least_upper_bound(identity,X_70))) )],[refute_0_124,refute_0_185]) ).
cnf(refute_0_187,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) != multiply(X_19,least_upper_bound(identity,X_70))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) != least_upper_bound(X_19,multiply(X_19,X_70))
| multiply(X_19,least_upper_bound(identity,X_70)) = least_upper_bound(X_19,multiply(X_19,X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))),least_upper_bound(X_19,multiply(X_19,X_70))) ),[0],$fot(multiply(X_19,least_upper_bound(identity,X_70)))]]) ).
cnf(refute_0_188,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) != least_upper_bound(X_19,multiply(X_19,X_70))
| multiply(X_19,least_upper_bound(identity,X_70)) = least_upper_bound(X_19,multiply(X_19,X_70)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))),multiply(X_19,least_upper_bound(identity,X_70))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( multiply(X_19,least_upper_bound(identity,X_70)) != least_upper_bound(X_19,multiply(X_19,X_70))
| least_upper_bound(X_19,multiply(X_19,X_70)) != multiply(X_19,least_upper_bound(X_70,identity))
| multiply(X_19,least_upper_bound(identity,X_70)) = multiply(X_19,least_upper_bound(X_70,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_19,least_upper_bound(identity,X_70)),multiply(X_19,least_upper_bound(X_70,identity))) ),[0],$fot(least_upper_bound(X_19,multiply(X_19,X_70)))]]) ).
cnf(refute_0_190,plain,
( multiply(X_19,least_upper_bound(identity,X_70)) != least_upper_bound(X_19,multiply(X_19,X_70))
| multiply(X_19,least_upper_bound(identity,X_70)) = multiply(X_19,least_upper_bound(X_70,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_70)),multiply(X_19,least_upper_bound(X_70,identity))) )],[refute_0_116,refute_0_189]) ).
cnf(refute_0_191,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))) != least_upper_bound(X_19,multiply(X_19,X_70))
| multiply(X_19,least_upper_bound(identity,X_70)) = multiply(X_19,least_upper_bound(X_70,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_70)),least_upper_bound(X_19,multiply(X_19,X_70))) )],[refute_0_188,refute_0_190]) ).
cnf(refute_0_192,plain,
multiply(X_19,least_upper_bound(identity,X_70)) = multiply(X_19,least_upper_bound(X_70,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_70,identity))),least_upper_bound(X_19,multiply(X_19,X_70))) )],[refute_0_119,refute_0_191]) ).
cnf(refute_0_193,plain,
( multiply(X_19,least_upper_bound(identity,X_70)) != multiply(X_19,least_upper_bound(X_70,identity))
| multiply(X_19,least_upper_bound(X_70,identity)) = multiply(X_19,least_upper_bound(identity,X_70)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_19,least_upper_bound(identity,X_70)))),bind(Y0,$fot(multiply(X_19,least_upper_bound(X_70,identity))))]]) ).
cnf(refute_0_194,plain,
multiply(X_19,least_upper_bound(X_70,identity)) = multiply(X_19,least_upper_bound(identity,X_70)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_70)),multiply(X_19,least_upper_bound(X_70,identity))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))),
inference(subst,[],[refute_0_194:[bind(X_19,$fot(inverse(X_75))),bind(X_70,$fot(least_upper_bound(X_75,identity)))]]) ).
cnf(refute_0_196,plain,
( multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))) != multiply(inverse(X_75),least_upper_bound(identity,X_75))
| multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) != multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity)))
| multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = multiply(inverse(X_75),least_upper_bound(identity,X_75)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)))),bind(Y0,$fot(multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))))),bind(Z0,$fot(multiply(inverse(X_75),least_upper_bound(identity,X_75))))]]) ).
cnf(refute_0_197,plain,
( multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))) != multiply(inverse(X_75),least_upper_bound(identity,X_75))
| multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = multiply(inverse(X_75),least_upper_bound(identity,X_75)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)),multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) = multiply(inverse(X_75),least_upper_bound(identity,X_75)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(identity,least_upper_bound(X_75,identity))),multiply(inverse(X_75),least_upper_bound(identity,X_75))) )],[refute_0_105,refute_0_197]) ).
cnf(refute_0_199,plain,
( multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) != multiply(inverse(X_75),least_upper_bound(identity,X_75))
| multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) != least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))
| multiply(inverse(X_75),least_upper_bound(identity,X_75)) = least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)),least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))) ),[0],$fot(multiply(inverse(X_75),least_upper_bound(identity,X_75)))]]) ).
cnf(refute_0_200,plain,
( multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) != least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))
| multiply(inverse(X_75),least_upper_bound(identity,X_75)) = least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)),multiply(inverse(X_75),least_upper_bound(identity,X_75))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
least_upper_bound(inverse(X_75),inverse(X_75)) = inverse(X_75),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(inverse(X_75)))]]) ).
cnf(refute_0_202,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))) = least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))))]]) ).
cnf(refute_0_203,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))) != least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75)))
| least_upper_bound(inverse(X_75),inverse(X_75)) != inverse(X_75)
| least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))) = least_upper_bound(identity,inverse(X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))),least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75)))) ),[1,1],$fot(inverse(X_75))]]) ).
cnf(refute_0_204,plain,
( least_upper_bound(inverse(X_75),inverse(X_75)) != inverse(X_75)
| least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))) = least_upper_bound(identity,inverse(X_75)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))),least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75)))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))) = least_upper_bound(identity,inverse(X_75)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_75),inverse(X_75)),inverse(X_75)) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)),Z),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(greatest_lower_bound(X_28,X_27))),bind(Y,$fot(greatest_lower_bound(X_27,X_28)))]]) ).
cnf(refute_0_207,plain,
least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))) = greatest_lower_bound(X_16,X_11),
inference(subst,[],[refute_0_89:[bind(X_10,$fot(greatest_lower_bound(X_16,X_11)))]]) ).
cnf(refute_0_208,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) = greatest_lower_bound(X_13,Y),
inference(subst,[],[refute_0_127:[bind(X,$fot(greatest_lower_bound(X_13,Y))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_209,plain,
least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) = X_13,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_210,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| least_upper_bound(X_13,greatest_lower_bound(X_13,Y)) != X_13
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_211,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,greatest_lower_bound(X_13,Y)),X_13) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),least_upper_bound(X_13,greatest_lower_bound(X_13,Y))),greatest_lower_bound(X_13,Y)) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_214,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_213]) ).
cnf(refute_0_215,plain,
greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) = greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_216,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) ),[0],$fot(greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)))]]) ).
cnf(refute_0_217,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13) != greatest_lower_bound(X_13,Y)
| greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
greatest_lower_bound(X_13,greatest_lower_bound(Y,X_13)) = greatest_lower_bound(X_13,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,Y),X_13),greatest_lower_bound(X_13,Y)) )],[refute_0_212,refute_0_217]) ).
cnf(refute_0_219,plain,
greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)) = greatest_lower_bound(X_11,X_16),
inference(subst,[],[refute_0_218:[bind(Y,$fot(X_16)),bind(X_13,$fot(X_11))]]) ).
cnf(refute_0_220,plain,
( greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)) != greatest_lower_bound(X_11,X_16)
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))) != greatest_lower_bound(X_16,X_11)
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) = greatest_lower_bound(X_16,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_16,X_11)) ),[0,1],$fot(greatest_lower_bound(X_11,X_16))]]) ).
cnf(refute_0_221,plain,
( least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))) != greatest_lower_bound(X_16,X_11)
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) = greatest_lower_bound(X_16,X_11) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)),greatest_lower_bound(X_11,X_16)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) = greatest_lower_bound(X_16,X_11),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_16,X_11)) )],[refute_0_207,refute_0_221]) ).
cnf(refute_0_223,plain,
least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)) = greatest_lower_bound(X_28,X_27),
inference(subst,[],[refute_0_222:[bind(X_11,$fot(X_27)),bind(X_16,$fot(X_28))]]) ).
cnf(refute_0_224,plain,
( least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)) != greatest_lower_bound(X_28,X_27)
| least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)),Z)
| least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)) = least_upper_bound(greatest_lower_bound(X_28,X_27),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)),Z)) ),[1,0],$fot(greatest_lower_bound(X_28,X_27))]]) ).
cnf(refute_0_225,plain,
( least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)),Z)
| least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)) = least_upper_bound(greatest_lower_bound(X_28,X_27),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)),greatest_lower_bound(X_28,X_27)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)) = least_upper_bound(greatest_lower_bound(X_28,X_27),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_28,X_27),least_upper_bound(greatest_lower_bound(X_27,X_28),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)),Z)) )],[refute_0_206,refute_0_225]) ).
cnf(refute_0_227,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_34)) = least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34),
inference(subst,[],[refute_0_226:[bind(Z,$fot(X_34)),bind(X_27,$fot(least_upper_bound(X_18,Y))),bind(X_28,$fot(least_upper_bound(Y,X_18)))]]) ).
cnf(refute_0_228,plain,
( greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_34)) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) = least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_34)),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) ),[0,1,0],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_229,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_34)) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) = least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_132,refute_0_228]) ).
cnf(refute_0_230,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) = least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),X_34)),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) )],[refute_0_227,refute_0_229]) ).
cnf(refute_0_231,plain,
least_upper_bound(least_upper_bound(X_18,Y),X_34) = least_upper_bound(X_18,least_upper_bound(Y,X_34)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_18)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_232,plain,
least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)) = least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)),X_26),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_24)),bind(Y,$fot(greatest_lower_bound(X_11,X_24))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_233,plain,
least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)) = X_24,
inference(subst,[],[refute_0_89:[bind(X_10,$fot(X_24))]]) ).
cnf(refute_0_234,plain,
( least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)) != X_24
| least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)) != least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)),X_26)
| least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)) = least_upper_bound(X_24,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)),least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)),X_26)) ),[1,0],$fot(X_24)]]) ).
cnf(refute_0_235,plain,
( least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)) != least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)),X_26)
| least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)) = least_upper_bound(X_24,X_26) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)),X_24) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)) = least_upper_bound(X_24,X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_11,X_24),X_26)),least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_11,X_24)),X_26)) )],[refute_0_232,refute_0_235]) ).
cnf(refute_0_237,plain,
least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) = least_upper_bound(least_upper_bound(X_18,Y),X_34),
inference(subst,[],[refute_0_236:[bind(X_11,$fot(least_upper_bound(Y,X_18))),bind(X_24,$fot(least_upper_bound(X_18,Y))),bind(X_26,$fot(X_34))]]) ).
cnf(refute_0_238,plain,
( least_upper_bound(least_upper_bound(X_18,Y),X_34) != least_upper_bound(X_18,least_upper_bound(Y,X_34))
| least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) != least_upper_bound(least_upper_bound(X_18,Y),X_34)
| least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,Y),X_34))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_34))))]]) ).
cnf(refute_0_239,plain,
( least_upper_bound(least_upper_bound(X_18,Y),X_34) != least_upper_bound(X_18,least_upper_bound(Y,X_34))
| least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,Y),X_34),least_upper_bound(X_18,least_upper_bound(Y,X_34))) )],[refute_0_231,refute_0_239]) ).
cnf(refute_0_241,plain,
least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(least_upper_bound(X_24,least_upper_bound(Y,X_24)),X_26),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_24)),bind(Y,$fot(least_upper_bound(Y,X_24))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_242,plain,
least_upper_bound(X_24,least_upper_bound(Y,X_24)) = least_upper_bound(X_24,Y),
inference(subst,[],[refute_0_100:[bind(X_15,$fot(X_24))]]) ).
cnf(refute_0_243,plain,
( least_upper_bound(X_24,least_upper_bound(Y,X_24)) != least_upper_bound(X_24,Y)
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(least_upper_bound(X_24,least_upper_bound(Y,X_24)),X_26)
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(least_upper_bound(X_24,Y),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(least_upper_bound(X_24,least_upper_bound(Y,X_24)),X_26)) ),[1,0],$fot(least_upper_bound(X_24,Y))]]) ).
cnf(refute_0_244,plain,
( least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(least_upper_bound(X_24,least_upper_bound(Y,X_24)),X_26)
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(least_upper_bound(X_24,Y),X_26) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(Y,X_24)),least_upper_bound(X_24,Y)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(least_upper_bound(X_24,Y),X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(least_upper_bound(X_24,least_upper_bound(Y,X_24)),X_26)) )],[refute_0_241,refute_0_244]) ).
cnf(refute_0_246,plain,
least_upper_bound(X_24,least_upper_bound(X_25,least_upper_bound(Y,X_25))) = least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(least_upper_bound(Y,X_25)))]]) ).
cnf(refute_0_247,plain,
least_upper_bound(X_25,least_upper_bound(Y,X_25)) = least_upper_bound(X_25,Y),
inference(subst,[],[refute_0_100:[bind(X_15,$fot(X_25))]]) ).
cnf(refute_0_248,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,least_upper_bound(Y,X_25))) != least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25))
| least_upper_bound(X_25,least_upper_bound(Y,X_25)) != least_upper_bound(X_25,Y)
| least_upper_bound(X_24,least_upper_bound(X_25,Y)) = least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,least_upper_bound(Y,X_25))),least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25))) ),[0,1],$fot(least_upper_bound(X_25,Y))]]) ).
cnf(refute_0_249,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,least_upper_bound(Y,X_25))) != least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25))
| least_upper_bound(X_24,least_upper_bound(X_25,Y)) = least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,least_upper_bound(Y,X_25)),least_upper_bound(X_25,Y)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
least_upper_bound(X_24,least_upper_bound(X_25,Y)) = least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,least_upper_bound(Y,X_25))),least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
least_upper_bound(least_upper_bound(X_24,X_25),Y) = least_upper_bound(X_24,least_upper_bound(X_25,Y)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_252,plain,
least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)) = least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)))]]) ).
cnf(refute_0_253,plain,
( least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)) != least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y))
| least_upper_bound(least_upper_bound(X_24,X_25),Y) != least_upper_bound(X_24,least_upper_bound(X_25,Y))
| least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)),least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y))) ),[1,1],$fot(least_upper_bound(X_24,least_upper_bound(X_25,Y)))]]) ).
cnf(refute_0_254,plain,
( least_upper_bound(least_upper_bound(X_24,X_25),Y) != least_upper_bound(X_24,least_upper_bound(X_25,Y))
| least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)),least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_24,X_25),Y),least_upper_bound(X_24,least_upper_bound(X_25,Y))) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
least_upper_bound(X,least_upper_bound(X_24,X_25)) = least_upper_bound(least_upper_bound(X_24,X_25),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_24,X_25)))]]) ).
cnf(refute_0_257,plain,
least_upper_bound(X_24,least_upper_bound(X_25,X)) = least_upper_bound(least_upper_bound(X_24,X_25),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X))]]) ).
cnf(refute_0_258,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,X)) != least_upper_bound(least_upper_bound(X_24,X_25),X)
| least_upper_bound(least_upper_bound(X_24,X_25),X) = least_upper_bound(X_24,least_upper_bound(X_25,X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_24,least_upper_bound(X_25,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_24,X_25),X)))]]) ).
cnf(refute_0_259,plain,
least_upper_bound(least_upper_bound(X_24,X_25),X) = least_upper_bound(X_24,least_upper_bound(X_25,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,X)),least_upper_bound(least_upper_bound(X_24,X_25),X)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
( least_upper_bound(X,least_upper_bound(X_24,X_25)) != least_upper_bound(least_upper_bound(X_24,X_25),X)
| least_upper_bound(least_upper_bound(X_24,X_25),X) != least_upper_bound(X_24,least_upper_bound(X_25,X))
| least_upper_bound(X,least_upper_bound(X_24,X_25)) = least_upper_bound(X_24,least_upper_bound(X_25,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_24,X_25)),least_upper_bound(X_24,least_upper_bound(X_25,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_24,X_25),X))]]) ).
cnf(refute_0_261,plain,
( least_upper_bound(X,least_upper_bound(X_24,X_25)) != least_upper_bound(least_upper_bound(X_24,X_25),X)
| least_upper_bound(X,least_upper_bound(X_24,X_25)) = least_upper_bound(X_24,least_upper_bound(X_25,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_24,X_25),X),least_upper_bound(X_24,least_upper_bound(X_25,X))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
least_upper_bound(X,least_upper_bound(X_24,X_25)) = least_upper_bound(X_24,least_upper_bound(X_25,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_24,X_25)),least_upper_bound(least_upper_bound(X_24,X_25),X)) )],[refute_0_256,refute_0_261]) ).
cnf(refute_0_263,plain,
( least_upper_bound(X,least_upper_bound(X_24,X_25)) != least_upper_bound(X_24,least_upper_bound(X_25,X))
| least_upper_bound(X_24,least_upper_bound(X_25,X)) = least_upper_bound(X,least_upper_bound(X_24,X_25)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_24,X_25)))),bind(Y0,$fot(least_upper_bound(X_24,least_upper_bound(X_25,X))))]]) ).
cnf(refute_0_264,plain,
least_upper_bound(X_24,least_upper_bound(X_25,X)) = least_upper_bound(X,least_upper_bound(X_24,X_25)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_24,X_25)),least_upper_bound(X_24,least_upper_bound(X_25,X))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) = least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)),
inference(subst,[],[refute_0_264:[bind(X,$fot(X_25)),bind(X_24,$fot(least_upper_bound(X_24,X_25))),bind(X_25,$fot(Y))]]) ).
cnf(refute_0_266,plain,
( least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)) != least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))
| least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) != least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y))
| least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)))),bind(Y0,$fot(least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)))),bind(Z0,$fot(least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))))]]) ).
cnf(refute_0_267,plain,
( least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)) != least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))
| least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)),least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,least_upper_bound(least_upper_bound(X_24,X_25),Y)),least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))) )],[refute_0_255,refute_0_267]) ).
cnf(refute_0_269,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,Y)) != least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25))
| least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)) != least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))
| least_upper_bound(X_24,least_upper_bound(X_25,Y)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_24,least_upper_bound(X_25,Y)),least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)))]]) ).
cnf(refute_0_270,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,Y)) != least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25))
| least_upper_bound(X_24,least_upper_bound(X_25,Y)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25)),least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
least_upper_bound(X_24,least_upper_bound(X_25,Y)) = least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,Y)),least_upper_bound(least_upper_bound(X_24,X_25),least_upper_bound(Y,X_25))) )],[refute_0_250,refute_0_270]) ).
cnf(refute_0_272,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,Y)) != least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))
| least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) = least_upper_bound(X_24,least_upper_bound(X_25,Y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_24,least_upper_bound(X_25,Y)))),bind(Y0,$fot(least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))))]]) ).
cnf(refute_0_273,plain,
least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y))) = least_upper_bound(X_24,least_upper_bound(X_25,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,Y)),least_upper_bound(X_25,least_upper_bound(X_24,least_upper_bound(X_25,Y)))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))) = least_upper_bound(Y,least_upper_bound(X_24,X_26)),
inference(subst,[],[refute_0_273:[bind(Y,$fot(X_26)),bind(X_24,$fot(Y)),bind(X_25,$fot(X_24))]]) ).
cnf(refute_0_275,plain,
least_upper_bound(least_upper_bound(Y,X_24),X_26) = least_upper_bound(Y,least_upper_bound(X_24,X_26)),
inference(subst,[],[refute_0_96:[bind(X,$fot(Y)),bind(Y,$fot(X_24)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_276,plain,
least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)))]]) ).
cnf(refute_0_277,plain,
( least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26))
| least_upper_bound(least_upper_bound(Y,X_24),X_26) != least_upper_bound(Y,least_upper_bound(X_24,X_26))
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_24,X_26)))]]) ).
cnf(refute_0_278,plain,
( least_upper_bound(least_upper_bound(Y,X_24),X_26) != least_upper_bound(Y,least_upper_bound(X_24,X_26))
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_24),X_26),least_upper_bound(Y,least_upper_bound(X_24,X_26))) )],[refute_0_275,refute_0_278]) ).
cnf(refute_0_280,plain,
( least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))) != least_upper_bound(Y,least_upper_bound(X_24,X_26))
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26)))
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(Y,least_upper_bound(X_24,X_26)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)))),bind(Y0,$fot(least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_24,X_26))))]]) ).
cnf(refute_0_281,plain,
( least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))) != least_upper_bound(Y,least_upper_bound(X_24,X_26))
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(Y,least_upper_bound(X_24,X_26)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26)))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) = least_upper_bound(Y,least_upper_bound(X_24,X_26)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(Y,least_upper_bound(X_24,X_26))),least_upper_bound(Y,least_upper_bound(X_24,X_26))) )],[refute_0_274,refute_0_281]) ).
cnf(refute_0_283,plain,
( least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(Y,least_upper_bound(X_24,X_26))
| least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(least_upper_bound(X_24,Y),X_26)
| least_upper_bound(Y,least_upper_bound(X_24,X_26)) = least_upper_bound(least_upper_bound(X_24,Y),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(least_upper_bound(X_24,Y),X_26)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_24,X_26)))]]) ).
cnf(refute_0_284,plain,
( least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(least_upper_bound(X_24,Y),X_26)
| least_upper_bound(Y,least_upper_bound(X_24,X_26)) = least_upper_bound(least_upper_bound(X_24,Y),X_26) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(Y,least_upper_bound(X_24,X_26))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
least_upper_bound(least_upper_bound(X_24,Y),X_26) = least_upper_bound(X_24,least_upper_bound(Y,X_26)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_24)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_286,plain,
( least_upper_bound(Y,least_upper_bound(X_24,X_26)) != least_upper_bound(least_upper_bound(X_24,Y),X_26)
| least_upper_bound(least_upper_bound(X_24,Y),X_26) != least_upper_bound(X_24,least_upper_bound(Y,X_26))
| least_upper_bound(Y,least_upper_bound(X_24,X_26)) = least_upper_bound(X_24,least_upper_bound(Y,X_26)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_24,X_26)),least_upper_bound(X_24,least_upper_bound(Y,X_26))) ),[0],$fot(least_upper_bound(least_upper_bound(X_24,Y),X_26))]]) ).
cnf(refute_0_287,plain,
( least_upper_bound(Y,least_upper_bound(X_24,X_26)) != least_upper_bound(least_upper_bound(X_24,Y),X_26)
| least_upper_bound(Y,least_upper_bound(X_24,X_26)) = least_upper_bound(X_24,least_upper_bound(Y,X_26)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_24,Y),X_26),least_upper_bound(X_24,least_upper_bound(Y,X_26))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
( least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)) != least_upper_bound(least_upper_bound(X_24,Y),X_26)
| least_upper_bound(Y,least_upper_bound(X_24,X_26)) = least_upper_bound(X_24,least_upper_bound(Y,X_26)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_24,X_26)),least_upper_bound(least_upper_bound(X_24,Y),X_26)) )],[refute_0_284,refute_0_287]) ).
cnf(refute_0_289,plain,
least_upper_bound(Y,least_upper_bound(X_24,X_26)) = least_upper_bound(X_24,least_upper_bound(Y,X_26)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(least_upper_bound(Y,X_24),X_26)),least_upper_bound(least_upper_bound(X_24,Y),X_26)) )],[refute_0_245,refute_0_288]) ).
cnf(refute_0_290,plain,
( least_upper_bound(Y,least_upper_bound(X_24,X_26)) != least_upper_bound(X_24,least_upper_bound(Y,X_26))
| least_upper_bound(X_24,least_upper_bound(Y,X_26)) = least_upper_bound(Y,least_upper_bound(X_24,X_26)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_24,X_26)))),bind(Y0,$fot(least_upper_bound(X_24,least_upper_bound(Y,X_26))))]]) ).
cnf(refute_0_291,plain,
least_upper_bound(X_24,least_upper_bound(Y,X_26)) = least_upper_bound(Y,least_upper_bound(X_24,X_26)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_24,X_26)),least_upper_bound(X_24,least_upper_bound(Y,X_26))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) = least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)),
inference(subst,[],[refute_0_291:[bind(Y,$fot(least_upper_bound(X_18,Y))),bind(X_24,$fot(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)))),bind(X_26,$fot(X_34))]]) ).
cnf(refute_0_293,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) != least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34))
| least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) != least_upper_bound(X_18,least_upper_bound(Y,X_34))
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)))),bind(Z0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_34))))]]) ).
cnf(refute_0_294,plain,
( least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) != least_upper_bound(X_18,least_upper_bound(Y,X_34))
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)),least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)),least_upper_bound(X_18,least_upper_bound(Y,X_34))) )],[refute_0_240,refute_0_294]) ).
cnf(refute_0_296,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) != least_upper_bound(X_18,least_upper_bound(Y,X_34))
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(X_18,least_upper_bound(Y,X_34)) = least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) ),[0],$fot(least_upper_bound(X_18,least_upper_bound(Y,X_34)))]]) ).
cnf(refute_0_297,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(X_18,least_upper_bound(Y,X_34)) = least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)),least_upper_bound(X_18,least_upper_bound(Y,X_34))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
least_upper_bound(least_upper_bound(Y,X_18),X_34) = least_upper_bound(Y,least_upper_bound(X_18,X_34)),
inference(subst,[],[refute_0_96:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_299,plain,
greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)) = least_upper_bound(Y,X_18),
inference(subst,[],[refute_0_132:[bind(Y,$fot(X_18)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_300,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) = least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34))]]) ).
cnf(refute_0_301,plain,
( greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)) != least_upper_bound(Y,X_18)
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) = least_upper_bound(least_upper_bound(Y,X_18),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) ),[1,0],$fot(least_upper_bound(Y,X_18))]]) ).
cnf(refute_0_302,plain,
( greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)) != least_upper_bound(Y,X_18)
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) = least_upper_bound(least_upper_bound(Y,X_18),X_34) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) = least_upper_bound(least_upper_bound(Y,X_18),X_34),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) )],[refute_0_299,refute_0_302]) ).
cnf(refute_0_304,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) != least_upper_bound(least_upper_bound(Y,X_18),X_34)
| least_upper_bound(least_upper_bound(Y,X_18),X_34) != least_upper_bound(Y,least_upper_bound(X_18,X_34))
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) = least_upper_bound(Y,least_upper_bound(X_18,X_34)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34))),bind(Y0,$fot(least_upper_bound(least_upper_bound(Y,X_18),X_34))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_34))))]]) ).
cnf(refute_0_305,plain,
( least_upper_bound(least_upper_bound(Y,X_18),X_34) != least_upper_bound(Y,least_upper_bound(X_18,X_34))
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) = least_upper_bound(Y,least_upper_bound(X_18,X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34),least_upper_bound(least_upper_bound(Y,X_18),X_34)) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) = least_upper_bound(Y,least_upper_bound(X_18,X_34)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),X_34),least_upper_bound(Y,least_upper_bound(X_18,X_34))) )],[refute_0_298,refute_0_305]) ).
cnf(refute_0_307,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_34)) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34) != least_upper_bound(Y,least_upper_bound(X_18,X_34))
| least_upper_bound(X_18,least_upper_bound(Y,X_34)) = least_upper_bound(Y,least_upper_bound(X_18,X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(Y,X_34)),least_upper_bound(Y,least_upper_bound(X_18,X_34))) ),[0],$fot(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34))]]) ).
cnf(refute_0_308,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_34)) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(X_18,least_upper_bound(Y,X_34)) = least_upper_bound(Y,least_upper_bound(X_18,X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34),least_upper_bound(Y,least_upper_bound(X_18,X_34))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)) != least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)
| least_upper_bound(X_18,least_upper_bound(Y,X_34)) = least_upper_bound(Y,least_upper_bound(X_18,X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_34)),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) )],[refute_0_297,refute_0_308]) ).
cnf(refute_0_310,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_34)) = least_upper_bound(Y,least_upper_bound(X_18,X_34)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),least_upper_bound(least_upper_bound(X_18,Y),X_34)),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_18),least_upper_bound(X_18,Y)),X_34)) )],[refute_0_230,refute_0_309]) ).
cnf(refute_0_311,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_34)) != least_upper_bound(Y,least_upper_bound(X_18,X_34))
| least_upper_bound(Y,least_upper_bound(X_18,X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_34)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_34))))]]) ).
cnf(refute_0_312,plain,
least_upper_bound(Y,least_upper_bound(X_18,X_34)) = least_upper_bound(X_18,least_upper_bound(Y,X_34)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_34)),least_upper_bound(Y,least_upper_bound(X_18,X_34))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))),
inference(subst,[],[refute_0_312:[bind(Y,$fot(inverse(X_75))),bind(X_18,$fot(identity)),bind(X_34,$fot(inverse(X_75)))]]) ).
cnf(refute_0_314,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))) != least_upper_bound(identity,inverse(X_75))
| least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) != least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75)))
| least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,inverse(X_75)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_315,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))) != least_upper_bound(identity,inverse(X_75))
| least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,inverse(X_75)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,inverse(X_75)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_75),inverse(X_75))),least_upper_bound(identity,inverse(X_75))) )],[refute_0_205,refute_0_315]) ).
cnf(refute_0_317,plain,
( multiply(inverse(X_75),least_upper_bound(identity,X_75)) != least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))
| least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))) != least_upper_bound(identity,inverse(X_75))
| multiply(inverse(X_75),least_upper_bound(identity,X_75)) = least_upper_bound(identity,inverse(X_75)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_75),least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) ),[0],$fot(least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_318,plain,
( multiply(inverse(X_75),least_upper_bound(identity,X_75)) != least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))
| multiply(inverse(X_75),least_upper_bound(identity,X_75)) = least_upper_bound(identity,inverse(X_75)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,inverse(X_75))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
( multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)) != least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))
| multiply(inverse(X_75),least_upper_bound(identity,X_75)) = least_upper_bound(identity,inverse(X_75)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(identity,X_75)),least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_200,refute_0_318]) ).
cnf(refute_0_320,plain,
multiply(inverse(X_75),least_upper_bound(identity,X_75)) = least_upper_bound(identity,inverse(X_75)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(least_upper_bound(X_75,identity),identity)),least_upper_bound(inverse(X_75),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_82,refute_0_319]) ).
cnf(refute_0_321,plain,
multiply(inverse(X_86),least_upper_bound(identity,X_86)) = least_upper_bound(identity,inverse(X_86)),
inference(subst,[],[refute_0_320:[bind(X_75,$fot(X_86))]]) ).
cnf(refute_0_322,plain,
( multiply(inverse(X_86),least_upper_bound(identity,X_86)) != least_upper_bound(identity,inverse(X_86))
| multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))) != inverse(inverse(X_86))
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = inverse(inverse(X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))),inverse(inverse(X_86))) ),[0,1,0],$fot(least_upper_bound(identity,inverse(X_86)))]]) ).
cnf(refute_0_323,plain,
( multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))) != inverse(inverse(X_86))
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = inverse(inverse(X_86)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = inverse(inverse(X_86)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))),inverse(inverse(X_86))) )],[refute_0_55,refute_0_323]) ).
cnf(refute_0_325,plain,
inverse(inverse(X_44)) = multiply(inverse(inverse(X_44)),identity),
inference(subst,[],[refute_0_48:[bind(X_41,$fot(inverse(inverse(X_44))))]]) ).
cnf(refute_0_326,plain,
multiply(X_44,identity) = multiply(inverse(inverse(X_44)),identity),
inference(subst,[],[refute_0_21:[bind(X_40,$fot(X_44)),bind(X_41,$fot(identity))]]) ).
cnf(refute_0_327,plain,
( multiply(X_44,identity) != multiply(inverse(inverse(X_44)),identity)
| multiply(inverse(inverse(X_44)),identity) = multiply(X_44,identity) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_44,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_44)),identity)))]]) ).
cnf(refute_0_328,plain,
multiply(inverse(inverse(X_44)),identity) = multiply(X_44,identity),
inference(resolve,[$cnf( $equal(multiply(X_44,identity),multiply(inverse(inverse(X_44)),identity)) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
( multiply(inverse(inverse(X_44)),identity) != multiply(X_44,identity)
| inverse(inverse(X_44)) != multiply(inverse(inverse(X_44)),identity)
| inverse(inverse(X_44)) = multiply(X_44,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_44)),multiply(inverse(inverse(X_44)),identity)) ),[1],$fot(multiply(X_44,identity))]]) ).
cnf(refute_0_330,plain,
( inverse(inverse(X_44)) != multiply(inverse(inverse(X_44)),identity)
| inverse(inverse(X_44)) = multiply(X_44,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_44)),identity),multiply(X_44,identity)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
inverse(inverse(X_44)) = multiply(X_44,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_44)),multiply(inverse(inverse(X_44)),identity)) )],[refute_0_325,refute_0_330]) ).
cnf(refute_0_332,plain,
multiply(X_44,identity) = X_44,
inference(subst,[],[refute_0_50:[bind(X_41,$fot(X_44))]]) ).
cnf(refute_0_333,plain,
( multiply(X_44,identity) != X_44
| inverse(inverse(X_44)) != multiply(X_44,identity)
| inverse(inverse(X_44)) = X_44 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_44)),multiply(X_44,identity)) ),[1],$fot(X_44)]]) ).
cnf(refute_0_334,plain,
( inverse(inverse(X_44)) != multiply(X_44,identity)
| inverse(inverse(X_44)) = X_44 ),
inference(resolve,[$cnf( $equal(multiply(X_44,identity),X_44) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
inverse(inverse(X_44)) = X_44,
inference(resolve,[$cnf( $equal(inverse(inverse(X_44)),multiply(X_44,identity)) )],[refute_0_331,refute_0_334]) ).
cnf(refute_0_336,plain,
inverse(inverse(X_86)) = X_86,
inference(subst,[],[refute_0_335:[bind(X_44,$fot(X_86))]]) ).
cnf(refute_0_337,plain,
( multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) != inverse(inverse(X_86))
| inverse(inverse(X_86)) != X_86
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = X_86 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),X_86) ),[0],$fot(inverse(inverse(X_86)))]]) ).
cnf(refute_0_338,plain,
( multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) != inverse(inverse(X_86))
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = X_86 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_86)),X_86) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = X_86,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),inverse(inverse(X_86))) )],[refute_0_324,refute_0_338]) ).
cnf(refute_0_340,plain,
inverse(inverse(greatest_lower_bound(identity,X_86))) = greatest_lower_bound(identity,X_86),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(greatest_lower_bound(identity,X_86)))]]) ).
cnf(refute_0_341,plain,
multiply(X_51,inverse(multiply(least_upper_bound(X_105,inverse(X_51)),X_51))) = inverse(least_upper_bound(X_105,inverse(X_51))),
inference(subst,[],[refute_0_54:[bind(X_38,$fot(least_upper_bound(X_105,inverse(X_51))))]]) ).
cnf(refute_0_342,plain,
multiply(least_upper_bound(X_102,inverse(X_101)),X_101) = least_upper_bound(multiply(X_102,X_101),multiply(inverse(X_101),X_101)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_101)),bind(Y,$fot(X_102)),bind(Z,$fot(inverse(X_101)))]]) ).
cnf(refute_0_343,plain,
multiply(inverse(X_101),X_101) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_101))]]) ).
cnf(refute_0_344,plain,
( multiply(inverse(X_101),X_101) != identity
| multiply(least_upper_bound(X_102,inverse(X_101)),X_101) != least_upper_bound(multiply(X_102,X_101),multiply(inverse(X_101),X_101))
| multiply(least_upper_bound(X_102,inverse(X_101)),X_101) = least_upper_bound(multiply(X_102,X_101),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(X_101)),X_101),least_upper_bound(multiply(X_102,X_101),multiply(inverse(X_101),X_101))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_345,plain,
( multiply(least_upper_bound(X_102,inverse(X_101)),X_101) != least_upper_bound(multiply(X_102,X_101),multiply(inverse(X_101),X_101))
| multiply(least_upper_bound(X_102,inverse(X_101)),X_101) = least_upper_bound(multiply(X_102,X_101),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),X_101),identity) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
multiply(least_upper_bound(X_102,inverse(X_101)),X_101) = least_upper_bound(multiply(X_102,X_101),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(X_101)),X_101),least_upper_bound(multiply(X_102,X_101),multiply(inverse(X_101),X_101))) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
least_upper_bound(multiply(X_102,X_101),identity) = least_upper_bound(identity,multiply(X_102,X_101)),
inference(subst,[],[refute_0_64:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_102,X_101)))]]) ).
cnf(refute_0_348,plain,
( multiply(least_upper_bound(X_102,inverse(X_101)),X_101) != least_upper_bound(multiply(X_102,X_101),identity)
| least_upper_bound(multiply(X_102,X_101),identity) != least_upper_bound(identity,multiply(X_102,X_101))
| multiply(least_upper_bound(X_102,inverse(X_101)),X_101) = least_upper_bound(identity,multiply(X_102,X_101)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_102,inverse(X_101)),X_101),least_upper_bound(identity,multiply(X_102,X_101))) ),[0],$fot(least_upper_bound(multiply(X_102,X_101),identity))]]) ).
cnf(refute_0_349,plain,
( multiply(least_upper_bound(X_102,inverse(X_101)),X_101) != least_upper_bound(multiply(X_102,X_101),identity)
| multiply(least_upper_bound(X_102,inverse(X_101)),X_101) = least_upper_bound(identity,multiply(X_102,X_101)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,X_101),identity),least_upper_bound(identity,multiply(X_102,X_101))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
multiply(least_upper_bound(X_102,inverse(X_101)),X_101) = least_upper_bound(identity,multiply(X_102,X_101)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(X_101)),X_101),least_upper_bound(multiply(X_102,X_101),identity)) )],[refute_0_346,refute_0_349]) ).
cnf(refute_0_351,plain,
multiply(least_upper_bound(X_105,inverse(X_51)),X_51) = least_upper_bound(identity,multiply(X_105,X_51)),
inference(subst,[],[refute_0_350:[bind(X_101,$fot(X_51)),bind(X_102,$fot(X_105))]]) ).
cnf(refute_0_352,plain,
( multiply(X_51,inverse(multiply(least_upper_bound(X_105,inverse(X_51)),X_51))) != inverse(least_upper_bound(X_105,inverse(X_51)))
| multiply(least_upper_bound(X_105,inverse(X_51)),X_51) != least_upper_bound(identity,multiply(X_105,X_51))
| multiply(X_51,inverse(least_upper_bound(identity,multiply(X_105,X_51)))) = inverse(least_upper_bound(X_105,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,inverse(multiply(least_upper_bound(X_105,inverse(X_51)),X_51))),inverse(least_upper_bound(X_105,inverse(X_51)))) ),[0,1,0],$fot(least_upper_bound(identity,multiply(X_105,X_51)))]]) ).
cnf(refute_0_353,plain,
( multiply(X_51,inverse(multiply(least_upper_bound(X_105,inverse(X_51)),X_51))) != inverse(least_upper_bound(X_105,inverse(X_51)))
| multiply(X_51,inverse(least_upper_bound(identity,multiply(X_105,X_51)))) = inverse(least_upper_bound(X_105,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_105,inverse(X_51)),X_51),least_upper_bound(identity,multiply(X_105,X_51))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
multiply(X_51,inverse(least_upper_bound(identity,multiply(X_105,X_51)))) = inverse(least_upper_bound(X_105,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(X_51,inverse(multiply(least_upper_bound(X_105,inverse(X_51)),X_51))),inverse(least_upper_bound(X_105,inverse(X_51)))) )],[refute_0_341,refute_0_353]) ).
cnf(refute_0_355,plain,
multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) = inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))),
inference(subst,[],[refute_0_354:[bind(X_105,$fot(greatest_lower_bound(identity,X_508))),bind(X_51,$fot(least_upper_bound(identity,inverse(X_508))))]]) ).
cnf(refute_0_356,plain,
multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) = least_upper_bound(X_66,multiply(X_66,greatest_lower_bound(X_94,inverse(X_66)))),
inference(subst,[],[refute_0_68:[bind(X_67,$fot(greatest_lower_bound(X_94,inverse(X_66))))]]) ).
cnf(refute_0_357,plain,
multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) = greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,inverse(X_90))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_90)),bind(Y,$fot(X_91)),bind(Z,$fot(inverse(X_90)))]]) ).
cnf(refute_0_358,plain,
multiply(X_90,inverse(X_90)) = identity,
inference(subst,[],[refute_0_27:[bind(X_44,$fot(X_90))]]) ).
cnf(refute_0_359,plain,
( multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) != greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,inverse(X_90)))
| multiply(X_90,inverse(X_90)) != identity
| multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) = greatest_lower_bound(multiply(X_90,X_91),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))),greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,inverse(X_90)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_360,plain,
( multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) != greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,inverse(X_90)))
| multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) = greatest_lower_bound(multiply(X_90,X_91),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_90,inverse(X_90)),identity) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) = greatest_lower_bound(multiply(X_90,X_91),identity),
inference(resolve,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))),greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,inverse(X_90)))) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
greatest_lower_bound(multiply(X_90,X_91),identity) = greatest_lower_bound(identity,multiply(X_90,X_91)),
inference(subst,[],[refute_0_164:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_90,X_91)))]]) ).
cnf(refute_0_363,plain,
( multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) != greatest_lower_bound(multiply(X_90,X_91),identity)
| greatest_lower_bound(multiply(X_90,X_91),identity) != greatest_lower_bound(identity,multiply(X_90,X_91))
| multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) = greatest_lower_bound(identity,multiply(X_90,X_91)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))),greatest_lower_bound(identity,multiply(X_90,X_91))) ),[0],$fot(greatest_lower_bound(multiply(X_90,X_91),identity))]]) ).
cnf(refute_0_364,plain,
( multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) != greatest_lower_bound(multiply(X_90,X_91),identity)
| multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) = greatest_lower_bound(identity,multiply(X_90,X_91)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_90,X_91),identity),greatest_lower_bound(identity,multiply(X_90,X_91))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))) = greatest_lower_bound(identity,multiply(X_90,X_91)),
inference(resolve,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,inverse(X_90))),greatest_lower_bound(multiply(X_90,X_91),identity)) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
multiply(X_66,greatest_lower_bound(X_94,inverse(X_66))) = greatest_lower_bound(identity,multiply(X_66,X_94)),
inference(subst,[],[refute_0_365:[bind(X_90,$fot(X_66)),bind(X_91,$fot(X_94))]]) ).
cnf(refute_0_367,plain,
( multiply(X_66,greatest_lower_bound(X_94,inverse(X_66))) != greatest_lower_bound(identity,multiply(X_66,X_94))
| multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) != least_upper_bound(X_66,multiply(X_66,greatest_lower_bound(X_94,inverse(X_66))))
| multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) = least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)),least_upper_bound(X_66,multiply(X_66,greatest_lower_bound(X_94,inverse(X_66))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_66,X_94)))]]) ).
cnf(refute_0_368,plain,
( multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) != least_upper_bound(X_66,multiply(X_66,greatest_lower_bound(X_94,inverse(X_66))))
| multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) = least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94))) ),
inference(resolve,[$cnf( $equal(multiply(X_66,greatest_lower_bound(X_94,inverse(X_66))),greatest_lower_bound(identity,multiply(X_66,X_94))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) = least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94))),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)),least_upper_bound(X_66,multiply(X_66,greatest_lower_bound(X_94,inverse(X_66))))) )],[refute_0_356,refute_0_368]) ).
cnf(refute_0_370,plain,
multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) = multiply(X_66,least_upper_bound(identity,greatest_lower_bound(X_94,inverse(X_66)))),
inference(subst,[],[refute_0_194:[bind(X_19,$fot(X_66)),bind(X_70,$fot(greatest_lower_bound(X_94,inverse(X_66))))]]) ).
cnf(refute_0_371,plain,
( multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) != multiply(X_66,least_upper_bound(identity,greatest_lower_bound(X_94,inverse(X_66))))
| multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) != least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94)))
| multiply(X_66,least_upper_bound(identity,greatest_lower_bound(X_94,inverse(X_66)))) = least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)),least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94)))) ),[0],$fot(multiply(X_66,least_upper_bound(identity,greatest_lower_bound(X_94,inverse(X_66)))))]]) ).
cnf(refute_0_372,plain,
( multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)) != least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94)))
| multiply(X_66,least_upper_bound(identity,greatest_lower_bound(X_94,inverse(X_66)))) = least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94))) ),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)),multiply(X_66,least_upper_bound(identity,greatest_lower_bound(X_94,inverse(X_66))))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
multiply(X_66,least_upper_bound(identity,greatest_lower_bound(X_94,inverse(X_66)))) = least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94))),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(greatest_lower_bound(X_94,inverse(X_66)),identity)),least_upper_bound(X_66,greatest_lower_bound(identity,multiply(X_66,X_94)))) )],[refute_0_369,refute_0_372]) ).
cnf(refute_0_374,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)))),
inference(subst,[],[refute_0_373:[bind(X_66,$fot(inverse(least_upper_bound(identity,inverse(X_139))))),bind(X_94,$fot(least_upper_bound(X_139,identity)))]]) ).
cnf(refute_0_375,plain,
multiply(inverse(multiply(X_52,X_38)),inverse(multiply(X_38,inverse(multiply(X_52,X_38))))) = inverse(X_38),
inference(subst,[],[refute_0_54:[bind(X_51,$fot(inverse(multiply(X_52,X_38))))]]) ).
cnf(refute_0_376,plain,
multiply(X_38,inverse(multiply(X_52,X_38))) = inverse(X_52),
inference(subst,[],[refute_0_54:[bind(X_38,$fot(X_52)),bind(X_51,$fot(X_38))]]) ).
cnf(refute_0_377,plain,
( multiply(X_38,inverse(multiply(X_52,X_38))) != inverse(X_52)
| multiply(inverse(multiply(X_52,X_38)),inverse(multiply(X_38,inverse(multiply(X_52,X_38))))) != inverse(X_38)
| multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) = inverse(X_38) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_52,X_38)),inverse(multiply(X_38,inverse(multiply(X_52,X_38))))),inverse(X_38)) ),[0,1,0],$fot(inverse(X_52))]]) ).
cnf(refute_0_378,plain,
( multiply(inverse(multiply(X_52,X_38)),inverse(multiply(X_38,inverse(multiply(X_52,X_38))))) != inverse(X_38)
| multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) = inverse(X_38) ),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(multiply(X_52,X_38))),inverse(X_52)) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) = inverse(X_38),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_52,X_38)),inverse(multiply(X_38,inverse(multiply(X_52,X_38))))),inverse(X_38)) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
inverse(inverse(X_52)) = X_52,
inference(subst,[],[refute_0_335:[bind(X_44,$fot(X_52))]]) ).
cnf(refute_0_381,plain,
multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) = multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))))]]) ).
cnf(refute_0_382,plain,
( multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) != multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52)))
| inverse(inverse(X_52)) != X_52
| multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) = multiply(inverse(multiply(X_52,X_38)),X_52) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))),multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52)))) ),[1,1],$fot(X_52)]]) ).
cnf(refute_0_383,plain,
( inverse(inverse(X_52)) != X_52
| multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) = multiply(inverse(multiply(X_52,X_38)),X_52) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))),multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52)))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) = multiply(inverse(multiply(X_52,X_38)),X_52),
inference(resolve,[$cnf( $equal(inverse(inverse(X_52)),X_52) )],[refute_0_380,refute_0_383]) ).
cnf(refute_0_385,plain,
( multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) != multiply(inverse(multiply(X_52,X_38)),X_52)
| multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) != inverse(X_38)
| multiply(inverse(multiply(X_52,X_38)),X_52) = inverse(X_38) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))),inverse(X_38)) ),[0],$fot(multiply(inverse(multiply(X_52,X_38)),X_52))]]) ).
cnf(refute_0_386,plain,
( multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))) != inverse(X_38)
| multiply(inverse(multiply(X_52,X_38)),X_52) = inverse(X_38) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))),multiply(inverse(multiply(X_52,X_38)),X_52)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
multiply(inverse(multiply(X_52,X_38)),X_52) = inverse(X_38),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_52,X_38)),inverse(inverse(X_52))),inverse(X_38)) )],[refute_0_379,refute_0_386]) ).
cnf(refute_0_388,plain,
multiply(inverse(multiply(least_upper_bound(X_139,identity),inverse(X_139))),least_upper_bound(X_139,identity)) = inverse(inverse(X_139)),
inference(subst,[],[refute_0_387:[bind(X_38,$fot(inverse(X_139))),bind(X_52,$fot(least_upper_bound(X_139,identity)))]]) ).
cnf(refute_0_389,plain,
multiply(identity,least_upper_bound(inverse(X_108),identity)) = least_upper_bound(identity,multiply(identity,inverse(X_108))),
inference(subst,[],[refute_0_68:[bind(X_66,$fot(identity)),bind(X_67,$fot(inverse(X_108)))]]) ).
cnf(refute_0_390,plain,
multiply(least_upper_bound(X_102,X_103),inverse(X_102)) = least_upper_bound(multiply(X_102,inverse(X_102)),multiply(X_103,inverse(X_102))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_102))),bind(Y,$fot(X_102)),bind(Z,$fot(X_103))]]) ).
cnf(refute_0_391,plain,
multiply(X_102,inverse(X_102)) = identity,
inference(subst,[],[refute_0_27:[bind(X_44,$fot(X_102))]]) ).
cnf(refute_0_392,plain,
( multiply(X_102,inverse(X_102)) != identity
| multiply(least_upper_bound(X_102,X_103),inverse(X_102)) != least_upper_bound(multiply(X_102,inverse(X_102)),multiply(X_103,inverse(X_102)))
| multiply(least_upper_bound(X_102,X_103),inverse(X_102)) = least_upper_bound(identity,multiply(X_103,inverse(X_102))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_102,X_103),inverse(X_102)),least_upper_bound(multiply(X_102,inverse(X_102)),multiply(X_103,inverse(X_102)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_393,plain,
( multiply(least_upper_bound(X_102,X_103),inverse(X_102)) != least_upper_bound(multiply(X_102,inverse(X_102)),multiply(X_103,inverse(X_102)))
| multiply(least_upper_bound(X_102,X_103),inverse(X_102)) = least_upper_bound(identity,multiply(X_103,inverse(X_102))) ),
inference(resolve,[$cnf( $equal(multiply(X_102,inverse(X_102)),identity) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
multiply(least_upper_bound(X_102,X_103),inverse(X_102)) = least_upper_bound(identity,multiply(X_103,inverse(X_102))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,X_103),inverse(X_102)),least_upper_bound(multiply(X_102,inverse(X_102)),multiply(X_103,inverse(X_102)))) )],[refute_0_390,refute_0_393]) ).
cnf(refute_0_395,plain,
multiply(least_upper_bound(X_108,identity),inverse(X_108)) = least_upper_bound(identity,multiply(identity,inverse(X_108))),
inference(subst,[],[refute_0_394:[bind(X_102,$fot(X_108)),bind(X_103,$fot(identity))]]) ).
cnf(refute_0_396,plain,
( multiply(least_upper_bound(X_108,identity),inverse(X_108)) != least_upper_bound(identity,multiply(identity,inverse(X_108)))
| least_upper_bound(identity,multiply(identity,inverse(X_108))) = multiply(least_upper_bound(X_108,identity),inverse(X_108)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(X_108,identity),inverse(X_108)))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,inverse(X_108)))))]]) ).
cnf(refute_0_397,plain,
least_upper_bound(identity,multiply(identity,inverse(X_108))) = multiply(least_upper_bound(X_108,identity),inverse(X_108)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),inverse(X_108)),least_upper_bound(identity,multiply(identity,inverse(X_108)))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
( multiply(identity,least_upper_bound(inverse(X_108),identity)) != least_upper_bound(identity,multiply(identity,inverse(X_108)))
| least_upper_bound(identity,multiply(identity,inverse(X_108))) != multiply(least_upper_bound(X_108,identity),inverse(X_108))
| multiply(identity,least_upper_bound(inverse(X_108),identity)) = multiply(least_upper_bound(X_108,identity),inverse(X_108)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,least_upper_bound(inverse(X_108),identity)),multiply(least_upper_bound(X_108,identity),inverse(X_108))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(X_108))))]]) ).
cnf(refute_0_399,plain,
( multiply(identity,least_upper_bound(inverse(X_108),identity)) != least_upper_bound(identity,multiply(identity,inverse(X_108)))
| multiply(identity,least_upper_bound(inverse(X_108),identity)) = multiply(least_upper_bound(X_108,identity),inverse(X_108)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(X_108))),multiply(least_upper_bound(X_108,identity),inverse(X_108))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
multiply(identity,least_upper_bound(inverse(X_108),identity)) = multiply(least_upper_bound(X_108,identity),inverse(X_108)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_108),identity)),least_upper_bound(identity,multiply(identity,inverse(X_108)))) )],[refute_0_389,refute_0_399]) ).
cnf(refute_0_401,plain,
multiply(identity,least_upper_bound(identity,inverse(X_108))) = least_upper_bound(identity,inverse(X_108)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(X_108))))]]) ).
cnf(refute_0_402,plain,
multiply(identity,least_upper_bound(inverse(X_108),identity)) = multiply(identity,least_upper_bound(identity,inverse(X_108))),
inference(subst,[],[refute_0_194:[bind(X_19,$fot(identity)),bind(X_70,$fot(inverse(X_108)))]]) ).
cnf(refute_0_403,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_108))) != least_upper_bound(identity,inverse(X_108))
| multiply(identity,least_upper_bound(inverse(X_108),identity)) != multiply(identity,least_upper_bound(identity,inverse(X_108)))
| multiply(identity,least_upper_bound(inverse(X_108),identity)) = least_upper_bound(identity,inverse(X_108)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(X_108),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(X_108))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_108))))]]) ).
cnf(refute_0_404,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_108))) != least_upper_bound(identity,inverse(X_108))
| multiply(identity,least_upper_bound(inverse(X_108),identity)) = least_upper_bound(identity,inverse(X_108)) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_108),identity)),multiply(identity,least_upper_bound(identity,inverse(X_108)))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(identity,least_upper_bound(inverse(X_108),identity)) = least_upper_bound(identity,inverse(X_108)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(X_108))),least_upper_bound(identity,inverse(X_108))) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
( multiply(identity,least_upper_bound(inverse(X_108),identity)) != multiply(least_upper_bound(X_108,identity),inverse(X_108))
| multiply(identity,least_upper_bound(inverse(X_108),identity)) != least_upper_bound(identity,inverse(X_108))
| least_upper_bound(identity,inverse(X_108)) = multiply(least_upper_bound(X_108,identity),inverse(X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_108),identity)),multiply(least_upper_bound(X_108,identity),inverse(X_108))) ),[0],$fot(least_upper_bound(identity,inverse(X_108)))]]) ).
cnf(refute_0_407,plain,
( multiply(identity,least_upper_bound(inverse(X_108),identity)) != multiply(least_upper_bound(X_108,identity),inverse(X_108))
| least_upper_bound(identity,inverse(X_108)) = multiply(least_upper_bound(X_108,identity),inverse(X_108)) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_108),identity)),least_upper_bound(identity,inverse(X_108))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
least_upper_bound(identity,inverse(X_108)) = multiply(least_upper_bound(X_108,identity),inverse(X_108)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_108),identity)),multiply(least_upper_bound(X_108,identity),inverse(X_108))) )],[refute_0_400,refute_0_407]) ).
cnf(refute_0_409,plain,
least_upper_bound(identity,inverse(X_139)) = multiply(least_upper_bound(X_139,identity),inverse(X_139)),
inference(subst,[],[refute_0_408:[bind(X_108,$fot(X_139))]]) ).
cnf(refute_0_410,plain,
( least_upper_bound(identity,inverse(X_139)) != multiply(least_upper_bound(X_139,identity),inverse(X_139))
| multiply(least_upper_bound(X_139,identity),inverse(X_139)) = least_upper_bound(identity,inverse(X_139)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(identity,inverse(X_139)))),bind(Y0,$fot(multiply(least_upper_bound(X_139,identity),inverse(X_139))))]]) ).
cnf(refute_0_411,plain,
multiply(least_upper_bound(X_139,identity),inverse(X_139)) = least_upper_bound(identity,inverse(X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_139)),multiply(least_upper_bound(X_139,identity),inverse(X_139))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
( multiply(inverse(multiply(least_upper_bound(X_139,identity),inverse(X_139))),least_upper_bound(X_139,identity)) != inverse(inverse(X_139))
| multiply(least_upper_bound(X_139,identity),inverse(X_139)) != least_upper_bound(identity,inverse(X_139))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) = inverse(inverse(X_139)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_139,identity),inverse(X_139))),least_upper_bound(X_139,identity)),inverse(inverse(X_139))) ),[0,0,0],$fot(least_upper_bound(identity,inverse(X_139)))]]) ).
cnf(refute_0_413,plain,
( multiply(inverse(multiply(least_upper_bound(X_139,identity),inverse(X_139))),least_upper_bound(X_139,identity)) != inverse(inverse(X_139))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) = inverse(inverse(X_139)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),inverse(X_139)),least_upper_bound(identity,inverse(X_139))) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) = inverse(inverse(X_139)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_139,identity),inverse(X_139))),least_upper_bound(X_139,identity)),inverse(inverse(X_139))) )],[refute_0_388,refute_0_413]) ).
cnf(refute_0_415,plain,
inverse(inverse(X_139)) = X_139,
inference(subst,[],[refute_0_335:[bind(X_44,$fot(X_139))]]) ).
cnf(refute_0_416,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) != inverse(inverse(X_139))
| inverse(inverse(X_139)) != X_139
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) = X_139 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)),X_139) ),[0],$fot(inverse(inverse(X_139)))]]) ).
cnf(refute_0_417,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) != inverse(inverse(X_139))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) = X_139 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_139)),X_139) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) = X_139,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)),inverse(inverse(X_139))) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)) != X_139
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity))))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity))))) ),[1,1,1],$fot(X_139)]]) ).
cnf(refute_0_420,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity))))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)),X_139) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity))))) )],[refute_0_374,refute_0_420]) ).
cnf(refute_0_422,plain,
multiply(X_139,identity) = X_139,
inference(subst,[],[refute_0_50:[bind(X_41,$fot(X_139))]]) ).
cnf(refute_0_423,plain,
inverse(multiply(X_139,identity)) = inverse(multiply(X_139,identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(X_139,identity)))]]) ).
cnf(refute_0_424,plain,
( multiply(X_139,identity) != X_139
| inverse(multiply(X_139,identity)) != inverse(multiply(X_139,identity))
| inverse(multiply(X_139,identity)) = inverse(X_139) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_139,identity)),inverse(multiply(X_139,identity))) ),[1,0],$fot(X_139)]]) ).
cnf(refute_0_425,plain,
( multiply(X_139,identity) != X_139
| inverse(multiply(X_139,identity)) = inverse(X_139) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_139,identity)),inverse(multiply(X_139,identity))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
inverse(multiply(X_139,identity)) = inverse(X_139),
inference(resolve,[$cnf( $equal(multiply(X_139,identity),X_139) )],[refute_0_422,refute_0_425]) ).
cnf(refute_0_427,plain,
least_upper_bound(identity,inverse(multiply(X_139,identity))) = least_upper_bound(identity,inverse(multiply(X_139,identity))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(X_139,identity))))]]) ).
cnf(refute_0_428,plain,
( inverse(multiply(X_139,identity)) != inverse(X_139)
| least_upper_bound(identity,inverse(multiply(X_139,identity))) != least_upper_bound(identity,inverse(multiply(X_139,identity)))
| least_upper_bound(identity,inverse(multiply(X_139,identity))) = least_upper_bound(identity,inverse(X_139)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_139,identity))),least_upper_bound(identity,inverse(multiply(X_139,identity)))) ),[1,1],$fot(inverse(X_139))]]) ).
cnf(refute_0_429,plain,
( inverse(multiply(X_139,identity)) != inverse(X_139)
| least_upper_bound(identity,inverse(multiply(X_139,identity))) = least_upper_bound(identity,inverse(X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_139,identity))),least_upper_bound(identity,inverse(multiply(X_139,identity)))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
least_upper_bound(identity,inverse(multiply(X_139,identity))) = least_upper_bound(identity,inverse(X_139)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_139,identity)),inverse(X_139)) )],[refute_0_426,refute_0_429]) ).
cnf(refute_0_431,plain,
inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))) = inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))))]]) ).
cnf(refute_0_432,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))) != inverse(least_upper_bound(identity,inverse(multiply(X_139,identity))))
| least_upper_bound(identity,inverse(multiply(X_139,identity))) != least_upper_bound(identity,inverse(X_139))
| inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))) = inverse(least_upper_bound(identity,inverse(X_139))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))),inverse(least_upper_bound(identity,inverse(multiply(X_139,identity))))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_139)))]]) ).
cnf(refute_0_433,plain,
( least_upper_bound(identity,inverse(multiply(X_139,identity))) != least_upper_bound(identity,inverse(X_139))
| inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))) = inverse(least_upper_bound(identity,inverse(X_139))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))),inverse(least_upper_bound(identity,inverse(multiply(X_139,identity))))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))) = inverse(least_upper_bound(identity,inverse(X_139))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_139,identity))),least_upper_bound(identity,inverse(X_139))) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
inverse(multiply(X_52,X_38)) = multiply(inverse(X_38),multiply(X_38,inverse(multiply(X_52,X_38)))),
inference(subst,[],[refute_0_8:[bind(X_39,$fot(inverse(multiply(X_52,X_38))))]]) ).
cnf(refute_0_436,plain,
( multiply(X_38,inverse(multiply(X_52,X_38))) != inverse(X_52)
| inverse(multiply(X_52,X_38)) != multiply(inverse(X_38),multiply(X_38,inverse(multiply(X_52,X_38))))
| inverse(multiply(X_52,X_38)) = multiply(inverse(X_38),inverse(X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_52,X_38)),multiply(inverse(X_38),multiply(X_38,inverse(multiply(X_52,X_38))))) ),[1,1],$fot(inverse(X_52))]]) ).
cnf(refute_0_437,plain,
( inverse(multiply(X_52,X_38)) != multiply(inverse(X_38),multiply(X_38,inverse(multiply(X_52,X_38))))
| inverse(multiply(X_52,X_38)) = multiply(inverse(X_38),inverse(X_52)) ),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(multiply(X_52,X_38))),inverse(X_52)) )],[refute_0_376,refute_0_436]) ).
cnf(refute_0_438,plain,
inverse(multiply(X_52,X_38)) = multiply(inverse(X_38),inverse(X_52)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_52,X_38)),multiply(inverse(X_38),multiply(X_38,inverse(multiply(X_52,X_38))))) )],[refute_0_435,refute_0_437]) ).
cnf(refute_0_439,plain,
inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(least_upper_bound(X_78,X_79))),bind(X_52,$fot(inverse(X_78)))]]) ).
cnf(refute_0_440,plain,
multiply(inverse(X_67),least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(inverse(X_67),X_67),multiply(inverse(X_67),X_68)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_67))),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_441,plain,
multiply(inverse(X_67),X_67) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_442,plain,
( multiply(inverse(X_67),X_67) != identity
| multiply(inverse(X_67),least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(inverse(X_67),X_67),multiply(inverse(X_67),X_68))
| multiply(inverse(X_67),least_upper_bound(X_67,X_68)) = least_upper_bound(identity,multiply(inverse(X_67),X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_67),least_upper_bound(X_67,X_68)),least_upper_bound(multiply(inverse(X_67),X_67),multiply(inverse(X_67),X_68))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_443,plain,
( multiply(inverse(X_67),least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(inverse(X_67),X_67),multiply(inverse(X_67),X_68))
| multiply(inverse(X_67),least_upper_bound(X_67,X_68)) = least_upper_bound(identity,multiply(inverse(X_67),X_68)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_67),X_67),identity) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
multiply(inverse(X_67),least_upper_bound(X_67,X_68)) = least_upper_bound(identity,multiply(inverse(X_67),X_68)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_67),least_upper_bound(X_67,X_68)),least_upper_bound(multiply(inverse(X_67),X_67),multiply(inverse(X_67),X_68))) )],[refute_0_440,refute_0_443]) ).
cnf(refute_0_445,plain,
multiply(inverse(X_78),least_upper_bound(X_78,X_79)) = least_upper_bound(identity,multiply(inverse(X_78),X_79)),
inference(subst,[],[refute_0_444:[bind(X_67,$fot(X_78)),bind(X_68,$fot(X_79))]]) ).
cnf(refute_0_446,plain,
( multiply(inverse(X_78),least_upper_bound(X_78,X_79)) != least_upper_bound(identity,multiply(inverse(X_78),X_79))
| inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))) != multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))
| inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))),multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))) ),[0,0],$fot(least_upper_bound(identity,multiply(inverse(X_78),X_79)))]]) ).
cnf(refute_0_447,plain,
( inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))) != multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))
| inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_78),least_upper_bound(X_78,X_79)),least_upper_bound(identity,multiply(inverse(X_78),X_79))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))),multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))) )],[refute_0_439,refute_0_447]) ).
cnf(refute_0_449,plain,
multiply(inverse(multiply(X_55,multiply(inverse(X_55),X_39))),X_55) = inverse(multiply(inverse(X_55),X_39)),
inference(subst,[],[refute_0_387:[bind(X_38,$fot(multiply(inverse(X_55),X_39))),bind(X_52,$fot(X_55))]]) ).
cnf(refute_0_450,plain,
X_39 = multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39)),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(inverse(X_44)))]]) ).
cnf(refute_0_451,plain,
multiply(X_44,multiply(inverse(X_44),X_39)) = multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39)),
inference(subst,[],[refute_0_21:[bind(X_40,$fot(X_44)),bind(X_41,$fot(multiply(inverse(X_44),X_39)))]]) ).
cnf(refute_0_452,plain,
( multiply(X_44,multiply(inverse(X_44),X_39)) != multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39))
| multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39)) = multiply(X_44,multiply(inverse(X_44),X_39)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_44,multiply(inverse(X_44),X_39)))),bind(Y0,$fot(multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39))))]]) ).
cnf(refute_0_453,plain,
multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39)) = multiply(X_44,multiply(inverse(X_44),X_39)),
inference(resolve,[$cnf( $equal(multiply(X_44,multiply(inverse(X_44),X_39)),multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39))) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
( X_39 != multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39))
| multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39)) != multiply(X_44,multiply(inverse(X_44),X_39))
| X_39 = multiply(X_44,multiply(inverse(X_44),X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_39,multiply(X_44,multiply(inverse(X_44),X_39))) ),[0],$fot(multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39)))]]) ).
cnf(refute_0_455,plain,
( X_39 != multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39))
| X_39 = multiply(X_44,multiply(inverse(X_44),X_39)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39)),multiply(X_44,multiply(inverse(X_44),X_39))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
X_39 = multiply(X_44,multiply(inverse(X_44),X_39)),
inference(resolve,[$cnf( $equal(X_39,multiply(inverse(inverse(X_44)),multiply(inverse(X_44),X_39))) )],[refute_0_450,refute_0_455]) ).
cnf(refute_0_457,plain,
X_39 = multiply(X_55,multiply(inverse(X_55),X_39)),
inference(subst,[],[refute_0_456:[bind(X_44,$fot(X_55))]]) ).
cnf(refute_0_458,plain,
( X_39 != multiply(X_55,multiply(inverse(X_55),X_39))
| multiply(X_55,multiply(inverse(X_55),X_39)) = X_39 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_39)),bind(Y0,$fot(multiply(X_55,multiply(inverse(X_55),X_39))))]]) ).
cnf(refute_0_459,plain,
multiply(X_55,multiply(inverse(X_55),X_39)) = X_39,
inference(resolve,[$cnf( $equal(X_39,multiply(X_55,multiply(inverse(X_55),X_39))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
( multiply(X_55,multiply(inverse(X_55),X_39)) != X_39
| multiply(inverse(multiply(X_55,multiply(inverse(X_55),X_39))),X_55) != inverse(multiply(inverse(X_55),X_39))
| multiply(inverse(X_39),X_55) = inverse(multiply(inverse(X_55),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_55,multiply(inverse(X_55),X_39))),X_55),inverse(multiply(inverse(X_55),X_39))) ),[0,0,0],$fot(X_39)]]) ).
cnf(refute_0_461,plain,
( multiply(inverse(multiply(X_55,multiply(inverse(X_55),X_39))),X_55) != inverse(multiply(inverse(X_55),X_39))
| multiply(inverse(X_39),X_55) = inverse(multiply(inverse(X_55),X_39)) ),
inference(resolve,[$cnf( $equal(multiply(X_55,multiply(inverse(X_55),X_39)),X_39) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
multiply(inverse(X_39),X_55) = inverse(multiply(inverse(X_55),X_39)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_55,multiply(inverse(X_55),X_39))),X_55),inverse(multiply(inverse(X_55),X_39))) )],[refute_0_449,refute_0_461]) ).
cnf(refute_0_463,plain,
( multiply(inverse(X_39),X_55) != inverse(multiply(inverse(X_55),X_39))
| inverse(multiply(inverse(X_55),X_39)) = multiply(inverse(X_39),X_55) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(inverse(X_39),X_55))),bind(Y0,$fot(inverse(multiply(inverse(X_55),X_39))))]]) ).
cnf(refute_0_464,plain,
inverse(multiply(inverse(X_55),X_39)) = multiply(inverse(X_39),X_55),
inference(resolve,[$cnf( $equal(multiply(inverse(X_39),X_55),inverse(multiply(inverse(X_55),X_39))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),X_78),
inference(subst,[],[refute_0_464:[bind(X_39,$fot(least_upper_bound(X_78,X_79))),bind(X_55,$fot(X_78))]]) ).
cnf(refute_0_466,plain,
( inverse(multiply(X_52,X_38)) != multiply(inverse(X_38),inverse(X_52))
| multiply(inverse(X_38),inverse(X_52)) = inverse(multiply(X_52,X_38)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(multiply(X_52,X_38)))),bind(Y0,$fot(multiply(inverse(X_38),inverse(X_52))))]]) ).
cnf(refute_0_467,plain,
multiply(inverse(X_38),inverse(X_52)) = inverse(multiply(X_52,X_38)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_52,X_38)),multiply(inverse(X_38),inverse(X_52))) )],[refute_0_438,refute_0_466]) ).
cnf(refute_0_468,plain,
multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) = inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(least_upper_bound(X_78,X_79))),bind(X_52,$fot(inverse(X_78)))]]) ).
cnf(refute_0_469,plain,
( multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) != inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79)))
| inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))) != multiply(inverse(least_upper_bound(X_78,X_79)),X_78)
| multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) = multiply(inverse(least_upper_bound(X_78,X_79)),X_78) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))))),bind(Y0,$fot(inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_78,X_79)),X_78)))]]) ).
cnf(refute_0_470,plain,
( inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))) != multiply(inverse(least_upper_bound(X_78,X_79)),X_78)
| multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) = multiply(inverse(least_upper_bound(X_78,X_79)),X_78) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))),inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79)))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) = multiply(inverse(least_upper_bound(X_78,X_79)),X_78),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79))),multiply(inverse(least_upper_bound(X_78,X_79)),X_78)) )],[refute_0_465,refute_0_470]) ).
cnf(refute_0_472,plain,
( multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))) != multiply(inverse(least_upper_bound(X_78,X_79)),X_78)
| inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) != multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))
| inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),X_78) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))),multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_78,X_79)),X_78))]]) ).
cnf(refute_0_473,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) != multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))
| inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),X_78) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78))),multiply(inverse(least_upper_bound(X_78,X_79)),X_78)) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))) = multiply(inverse(least_upper_bound(X_78,X_79)),X_78),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79))),multiply(inverse(least_upper_bound(X_78,X_79)),inverse(inverse(X_78)))) )],[refute_0_448,refute_0_473]) ).
cnf(refute_0_475,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_248),inverse(X_52)))) = multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248),
inference(subst,[],[refute_0_474:[bind(X_78,$fot(X_248)),bind(X_79,$fot(inverse(X_52)))]]) ).
cnf(refute_0_476,plain,
inverse(multiply(X_52,X_248)) = multiply(inverse(X_248),inverse(X_52)),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(X_248))]]) ).
cnf(refute_0_477,plain,
( inverse(multiply(X_52,X_248)) != multiply(inverse(X_248),inverse(X_52))
| multiply(inverse(X_248),inverse(X_52)) = inverse(multiply(X_52,X_248)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(multiply(X_52,X_248)))),bind(Y0,$fot(multiply(inverse(X_248),inverse(X_52))))]]) ).
cnf(refute_0_478,plain,
multiply(inverse(X_248),inverse(X_52)) = inverse(multiply(X_52,X_248)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_52,X_248)),multiply(inverse(X_248),inverse(X_52))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
( multiply(inverse(X_248),inverse(X_52)) != inverse(multiply(X_52,X_248))
| inverse(least_upper_bound(identity,multiply(inverse(X_248),inverse(X_52)))) != multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248)
| inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))) = multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_248),inverse(X_52)))),multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248)) ),[0,0,1],$fot(inverse(multiply(X_52,X_248)))]]) ).
cnf(refute_0_480,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_248),inverse(X_52)))) != multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248)
| inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))) = multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_248),inverse(X_52)),inverse(multiply(X_52,X_248))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))) = multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_248),inverse(X_52)))),multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248)) )],[refute_0_475,refute_0_480]) ).
cnf(refute_0_482,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))) != multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248)
| multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248) = inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248)))]]) ).
cnf(refute_0_483,plain,
multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248) = inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X_52,X_248)))),multiply(inverse(least_upper_bound(X_248,inverse(X_52))),X_248)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) = inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))),
inference(subst,[],[refute_0_483:[bind(X_248,$fot(identity)),bind(X_52,$fot(X_139))]]) ).
cnf(refute_0_485,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) != inverse(least_upper_bound(identity,inverse(multiply(X_139,identity))))
| inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))) != inverse(least_upper_bound(identity,inverse(X_139)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) = inverse(least_upper_bound(identity,inverse(X_139))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_139)))))]]) ).
cnf(refute_0_486,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))) != inverse(least_upper_bound(identity,inverse(X_139)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) = inverse(least_upper_bound(identity,inverse(X_139))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity),inverse(least_upper_bound(identity,inverse(multiply(X_139,identity))))) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) = inverse(least_upper_bound(identity,inverse(X_139))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X_139,identity)))),inverse(least_upper_bound(identity,inverse(X_139)))) )],[refute_0_434,refute_0_486]) ).
cnf(refute_0_488,plain,
least_upper_bound(identity,greatest_lower_bound(X_139,identity)) = identity,
inference(subst,[],[refute_0_89:[bind(X_10,$fot(identity)),bind(X_11,$fot(X_139))]]) ).
cnf(refute_0_489,plain,
multiply(greatest_lower_bound(X_139,identity),identity) = greatest_lower_bound(X_139,identity),
inference(subst,[],[refute_0_50:[bind(X_41,$fot(greatest_lower_bound(X_139,identity)))]]) ).
cnf(refute_0_490,plain,
multiply(greatest_lower_bound(X_111,identity),X_110) = greatest_lower_bound(multiply(X_111,X_110),multiply(identity,X_110)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_491,plain,
multiply(identity,X_110) = X_110,
inference(subst,[],[left_identity:[bind(X,$fot(X_110))]]) ).
cnf(refute_0_492,plain,
( multiply(greatest_lower_bound(X_111,identity),X_110) != greatest_lower_bound(multiply(X_111,X_110),multiply(identity,X_110))
| multiply(identity,X_110) != X_110
| multiply(greatest_lower_bound(X_111,identity),X_110) = greatest_lower_bound(multiply(X_111,X_110),X_110) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_111,identity),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(identity,X_110))) ),[1,1],$fot(X_110)]]) ).
cnf(refute_0_493,plain,
( multiply(greatest_lower_bound(X_111,identity),X_110) != greatest_lower_bound(multiply(X_111,X_110),multiply(identity,X_110))
| multiply(greatest_lower_bound(X_111,identity),X_110) = greatest_lower_bound(multiply(X_111,X_110),X_110) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_110),X_110) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
multiply(greatest_lower_bound(X_111,identity),X_110) = greatest_lower_bound(multiply(X_111,X_110),X_110),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,identity),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(identity,X_110))) )],[refute_0_490,refute_0_493]) ).
cnf(refute_0_495,plain,
greatest_lower_bound(multiply(X_111,X_110),X_110) = greatest_lower_bound(X_110,multiply(X_111,X_110)),
inference(subst,[],[refute_0_164:[bind(X,$fot(X_110)),bind(Y,$fot(multiply(X_111,X_110)))]]) ).
cnf(refute_0_496,plain,
( multiply(greatest_lower_bound(X_111,identity),X_110) != greatest_lower_bound(multiply(X_111,X_110),X_110)
| greatest_lower_bound(multiply(X_111,X_110),X_110) != greatest_lower_bound(X_110,multiply(X_111,X_110))
| multiply(greatest_lower_bound(X_111,identity),X_110) = greatest_lower_bound(X_110,multiply(X_111,X_110)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_111,identity),X_110),greatest_lower_bound(X_110,multiply(X_111,X_110))) ),[0],$fot(greatest_lower_bound(multiply(X_111,X_110),X_110))]]) ).
cnf(refute_0_497,plain,
( multiply(greatest_lower_bound(X_111,identity),X_110) != greatest_lower_bound(multiply(X_111,X_110),X_110)
| multiply(greatest_lower_bound(X_111,identity),X_110) = greatest_lower_bound(X_110,multiply(X_111,X_110)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,X_110),X_110),greatest_lower_bound(X_110,multiply(X_111,X_110))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
multiply(greatest_lower_bound(X_111,identity),X_110) = greatest_lower_bound(X_110,multiply(X_111,X_110)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,identity),X_110),greatest_lower_bound(multiply(X_111,X_110),X_110)) )],[refute_0_494,refute_0_497]) ).
cnf(refute_0_499,plain,
( multiply(greatest_lower_bound(X_111,identity),X_110) != greatest_lower_bound(X_110,multiply(X_111,X_110))
| greatest_lower_bound(X_110,multiply(X_111,X_110)) = multiply(greatest_lower_bound(X_111,identity),X_110) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(X_111,identity),X_110))),bind(Y0,$fot(greatest_lower_bound(X_110,multiply(X_111,X_110))))]]) ).
cnf(refute_0_500,plain,
greatest_lower_bound(X_110,multiply(X_111,X_110)) = multiply(greatest_lower_bound(X_111,identity),X_110),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,identity),X_110),greatest_lower_bound(X_110,multiply(X_111,X_110))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
greatest_lower_bound(identity,multiply(X_139,identity)) = multiply(greatest_lower_bound(X_139,identity),identity),
inference(subst,[],[refute_0_500:[bind(X_110,$fot(identity)),bind(X_111,$fot(X_139))]]) ).
cnf(refute_0_502,plain,
( multiply(greatest_lower_bound(X_139,identity),identity) != greatest_lower_bound(X_139,identity)
| greatest_lower_bound(identity,multiply(X_139,identity)) != multiply(greatest_lower_bound(X_139,identity),identity)
| greatest_lower_bound(identity,multiply(X_139,identity)) = greatest_lower_bound(X_139,identity) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_139,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_139,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_139,identity)))]]) ).
cnf(refute_0_503,plain,
( multiply(greatest_lower_bound(X_139,identity),identity) != greatest_lower_bound(X_139,identity)
| greatest_lower_bound(identity,multiply(X_139,identity)) = greatest_lower_bound(X_139,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_139,identity)),multiply(greatest_lower_bound(X_139,identity),identity)) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
greatest_lower_bound(identity,multiply(X_139,identity)) = greatest_lower_bound(X_139,identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_139,identity),identity),greatest_lower_bound(X_139,identity)) )],[refute_0_489,refute_0_503]) ).
cnf(refute_0_505,plain,
multiply(X_139,greatest_lower_bound(identity,inverse(X_139))) = greatest_lower_bound(identity,multiply(X_139,identity)),
inference(subst,[],[refute_0_365:[bind(X_90,$fot(X_139)),bind(X_91,$fot(identity))]]) ).
cnf(refute_0_506,plain,
( multiply(X_139,greatest_lower_bound(identity,inverse(X_139))) != greatest_lower_bound(identity,multiply(X_139,identity))
| greatest_lower_bound(identity,multiply(X_139,identity)) != greatest_lower_bound(X_139,identity)
| multiply(X_139,greatest_lower_bound(identity,inverse(X_139))) = greatest_lower_bound(X_139,identity) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(X_139,greatest_lower_bound(identity,inverse(X_139))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_139,identity)))),bind(Z0,$fot(greatest_lower_bound(X_139,identity)))]]) ).
cnf(refute_0_507,plain,
( greatest_lower_bound(identity,multiply(X_139,identity)) != greatest_lower_bound(X_139,identity)
| multiply(X_139,greatest_lower_bound(identity,inverse(X_139))) = greatest_lower_bound(X_139,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_139,greatest_lower_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(X_139,identity))) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
multiply(X_139,greatest_lower_bound(identity,inverse(X_139))) = greatest_lower_bound(X_139,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_139,identity)),greatest_lower_bound(X_139,identity)) )],[refute_0_504,refute_0_507]) ).
cnf(refute_0_509,plain,
least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) = least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))))]]) ).
cnf(refute_0_510,plain,
( multiply(X_139,greatest_lower_bound(identity,inverse(X_139))) != greatest_lower_bound(X_139,identity)
| least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) != least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139))))
| least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) = least_upper_bound(identity,greatest_lower_bound(X_139,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))),least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139))))) ),[1,1],$fot(greatest_lower_bound(X_139,identity))]]) ).
cnf(refute_0_511,plain,
( multiply(X_139,greatest_lower_bound(identity,inverse(X_139))) != greatest_lower_bound(X_139,identity)
| least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) = least_upper_bound(identity,greatest_lower_bound(X_139,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))),least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139))))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) = least_upper_bound(identity,greatest_lower_bound(X_139,identity)),
inference(resolve,[$cnf( $equal(multiply(X_139,greatest_lower_bound(identity,inverse(X_139))),greatest_lower_bound(X_139,identity)) )],[refute_0_508,refute_0_511]) ).
cnf(refute_0_513,plain,
( least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) != least_upper_bound(identity,greatest_lower_bound(X_139,identity))
| least_upper_bound(identity,greatest_lower_bound(X_139,identity)) != identity
| least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) = identity ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(X_139,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_514,plain,
( least_upper_bound(identity,greatest_lower_bound(X_139,identity)) != identity
| least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))),least_upper_bound(identity,greatest_lower_bound(X_139,identity))) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_139,identity)),identity) )],[refute_0_488,refute_0_514]) ).
cnf(refute_0_516,plain,
least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)) = least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_24,Y)),X_26),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_24)),bind(Y,$fot(greatest_lower_bound(X_24,Y))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_517,plain,
least_upper_bound(X_24,greatest_lower_bound(X_24,Y)) = X_24,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_518,plain,
( least_upper_bound(X_24,greatest_lower_bound(X_24,Y)) != X_24
| least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)) != least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_24,Y)),X_26)
| least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)) = least_upper_bound(X_24,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)),least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_24,Y)),X_26)) ),[1,0],$fot(X_24)]]) ).
cnf(refute_0_519,plain,
( least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)) != least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_24,Y)),X_26)
| least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)) = least_upper_bound(X_24,X_26) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,greatest_lower_bound(X_24,Y)),X_24) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)) = least_upper_bound(X_24,X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),X_26)),least_upper_bound(least_upper_bound(X_24,greatest_lower_bound(X_24,Y)),X_26)) )],[refute_0_516,refute_0_519]) ).
cnf(refute_0_521,plain,
least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))) = least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y))),
inference(subst,[],[refute_0_520:[bind(X_26,$fot(multiply(X_447,greatest_lower_bound(X_24,Y))))]]) ).
cnf(refute_0_522,plain,
multiply(least_upper_bound(X_102,identity),X_101) = least_upper_bound(multiply(X_102,X_101),multiply(identity,X_101)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_101)),bind(Y,$fot(X_102)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_523,plain,
multiply(identity,X_101) = X_101,
inference(subst,[],[left_identity:[bind(X,$fot(X_101))]]) ).
cnf(refute_0_524,plain,
( multiply(identity,X_101) != X_101
| multiply(least_upper_bound(X_102,identity),X_101) != least_upper_bound(multiply(X_102,X_101),multiply(identity,X_101))
| multiply(least_upper_bound(X_102,identity),X_101) = least_upper_bound(multiply(X_102,X_101),X_101) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_102,identity),X_101),least_upper_bound(multiply(X_102,X_101),multiply(identity,X_101))) ),[1,1],$fot(X_101)]]) ).
cnf(refute_0_525,plain,
( multiply(least_upper_bound(X_102,identity),X_101) != least_upper_bound(multiply(X_102,X_101),multiply(identity,X_101))
| multiply(least_upper_bound(X_102,identity),X_101) = least_upper_bound(multiply(X_102,X_101),X_101) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_101),X_101) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
multiply(least_upper_bound(X_102,identity),X_101) = least_upper_bound(multiply(X_102,X_101),X_101),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,identity),X_101),least_upper_bound(multiply(X_102,X_101),multiply(identity,X_101))) )],[refute_0_522,refute_0_525]) ).
cnf(refute_0_527,plain,
least_upper_bound(multiply(X_102,X_101),X_101) = least_upper_bound(X_101,multiply(X_102,X_101)),
inference(subst,[],[refute_0_64:[bind(X,$fot(X_101)),bind(Y,$fot(multiply(X_102,X_101)))]]) ).
cnf(refute_0_528,plain,
( multiply(least_upper_bound(X_102,identity),X_101) != least_upper_bound(multiply(X_102,X_101),X_101)
| least_upper_bound(multiply(X_102,X_101),X_101) != least_upper_bound(X_101,multiply(X_102,X_101))
| multiply(least_upper_bound(X_102,identity),X_101) = least_upper_bound(X_101,multiply(X_102,X_101)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_102,identity),X_101),least_upper_bound(X_101,multiply(X_102,X_101))) ),[0],$fot(least_upper_bound(multiply(X_102,X_101),X_101))]]) ).
cnf(refute_0_529,plain,
( multiply(least_upper_bound(X_102,identity),X_101) != least_upper_bound(multiply(X_102,X_101),X_101)
| multiply(least_upper_bound(X_102,identity),X_101) = least_upper_bound(X_101,multiply(X_102,X_101)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,X_101),X_101),least_upper_bound(X_101,multiply(X_102,X_101))) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
multiply(least_upper_bound(X_102,identity),X_101) = least_upper_bound(X_101,multiply(X_102,X_101)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,identity),X_101),least_upper_bound(multiply(X_102,X_101),X_101)) )],[refute_0_526,refute_0_529]) ).
cnf(refute_0_531,plain,
multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y)) = least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y))),
inference(subst,[],[refute_0_530:[bind(X_101,$fot(greatest_lower_bound(X_24,Y))),bind(X_102,$fot(X_447))]]) ).
cnf(refute_0_532,plain,
( multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y)) != least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))
| least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y))) = multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))))]]) ).
cnf(refute_0_533,plain,
least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y))) = multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y)),least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
( least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))) != least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y)))
| least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y))) != multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y))
| least_upper_bound(X_24,multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y))) = least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))),least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y)))) ),[0,1],$fot(multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y)))]]) ).
cnf(refute_0_535,plain,
( least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))) != least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y)))
| least_upper_bound(X_24,multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y))) = least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y))),multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y))) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
least_upper_bound(X_24,multiply(least_upper_bound(X_447,identity),greatest_lower_bound(X_24,Y))) = least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(greatest_lower_bound(X_24,Y),multiply(X_447,greatest_lower_bound(X_24,Y)))),least_upper_bound(X_24,multiply(X_447,greatest_lower_bound(X_24,Y)))) )],[refute_0_521,refute_0_535]) ).
cnf(refute_0_537,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) = least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))),
inference(subst,[],[refute_0_536:[bind(Y,$fot(inverse(X_139))),bind(X_24,$fot(identity)),bind(X_447,$fot(X_139))]]) ).
cnf(refute_0_538,plain,
( least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) != identity
| least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) != least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139))))
| least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) = identity ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_539,plain,
( least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))) != identity
| least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))),least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139))))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_139,greatest_lower_bound(identity,inverse(X_139)))),identity) )],[refute_0_515,refute_0_539]) ).
cnf(refute_0_541,plain,
multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) = greatest_lower_bound(least_upper_bound(X_70,identity),multiply(inverse(X_70),least_upper_bound(X_70,identity))),
inference(subst,[],[refute_0_498:[bind(X_110,$fot(least_upper_bound(X_70,identity))),bind(X_111,$fot(inverse(X_70)))]]) ).
cnf(refute_0_542,plain,
( multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) != greatest_lower_bound(least_upper_bound(X_70,identity),multiply(inverse(X_70),least_upper_bound(X_70,identity)))
| multiply(inverse(X_70),least_upper_bound(X_70,identity)) != least_upper_bound(identity,inverse(X_70))
| multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)),greatest_lower_bound(least_upper_bound(X_70,identity),multiply(inverse(X_70),least_upper_bound(X_70,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_70)))]]) ).
cnf(refute_0_543,plain,
( multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) != greatest_lower_bound(least_upper_bound(X_70,identity),multiply(inverse(X_70),least_upper_bound(X_70,identity)))
| multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_70),least_upper_bound(X_70,identity)),least_upper_bound(identity,inverse(X_70))) )],[refute_0_78,refute_0_542]) ).
cnf(refute_0_544,plain,
multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)),greatest_lower_bound(least_upper_bound(X_70,identity),multiply(inverse(X_70),least_upper_bound(X_70,identity)))) )],[refute_0_541,refute_0_543]) ).
cnf(refute_0_545,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_17,X_16),
inference(subst,[],[refute_0_218:[bind(Y,$fot(X_16)),bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_546,plain,
greatest_lower_bound(X_17,X_16) = greatest_lower_bound(X_16,X_17),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_547,plain,
( greatest_lower_bound(X_17,X_16) != greatest_lower_bound(X_16,X_17)
| greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X_17,X_16))),bind(Y0,$fot(greatest_lower_bound(X_16,X_17)))]]) ).
cnf(refute_0_548,plain,
greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_16),greatest_lower_bound(X_16,X_17)) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
( greatest_lower_bound(X_16,X_17) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_17,X_16)) ),[0,1],$fot(greatest_lower_bound(X_17,X_16))]]) ).
cnf(refute_0_550,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,X_17),greatest_lower_bound(X_17,X_16)) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_17,X_16)) )],[refute_0_545,refute_0_550]) ).
cnf(refute_0_552,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = greatest_lower_bound(X_17,multiply(X_191,X_17)),
inference(subst,[],[refute_0_551:[bind(X_16,$fot(multiply(X_191,X_17)))]]) ).
cnf(refute_0_553,plain,
multiply(greatest_lower_bound(X_191,identity),X_17) = greatest_lower_bound(X_17,multiply(X_191,X_17)),
inference(subst,[],[refute_0_498:[bind(X_110,$fot(X_17)),bind(X_111,$fot(X_191))]]) ).
cnf(refute_0_554,plain,
( multiply(greatest_lower_bound(X_191,identity),X_17) != greatest_lower_bound(X_17,multiply(X_191,X_17))
| greatest_lower_bound(X_17,multiply(X_191,X_17)) = multiply(greatest_lower_bound(X_191,identity),X_17) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(X_191,identity),X_17))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(X_191,X_17))))]]) ).
cnf(refute_0_555,plain,
greatest_lower_bound(X_17,multiply(X_191,X_17)) = multiply(greatest_lower_bound(X_191,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_191,identity),X_17),greatest_lower_bound(X_17,multiply(X_191,X_17))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
( greatest_lower_bound(X_17,multiply(X_191,X_17)) != multiply(greatest_lower_bound(X_191,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) != greatest_lower_bound(X_17,multiply(X_191,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(X_191,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))),greatest_lower_bound(X_17,multiply(X_191,X_17))) ),[1],$fot(multiply(greatest_lower_bound(X_191,identity),X_17))]]) ).
cnf(refute_0_557,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) != greatest_lower_bound(X_17,multiply(X_191,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(X_191,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_191,X_17)),multiply(greatest_lower_bound(X_191,identity),X_17)) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(X_191,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))),greatest_lower_bound(X_17,multiply(X_191,X_17))) )],[refute_0_552,refute_0_557]) ).
cnf(refute_0_559,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)) = greatest_lower_bound(identity,X_191),
inference(subst,[],[refute_0_218:[bind(Y,$fot(X_191)),bind(X_13,$fot(identity))]]) ).
cnf(refute_0_560,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17))]]) ).
cnf(refute_0_561,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)
| greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)) != greatest_lower_bound(identity,X_191)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) = multiply(greatest_lower_bound(identity,X_191),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)) ),[1,0],$fot(greatest_lower_bound(identity,X_191))]]) ).
cnf(refute_0_562,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)) != greatest_lower_bound(identity,X_191)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) = multiply(greatest_lower_bound(identity,X_191),X_17) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)) )],[refute_0_560,refute_0_561]) ).
cnf(refute_0_563,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) = multiply(greatest_lower_bound(identity,X_191),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),greatest_lower_bound(identity,X_191)) )],[refute_0_559,refute_0_562]) ).
cnf(refute_0_564,plain,
least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),
inference(subst,[],[refute_0_222:[bind(X_11,$fot(multiply(X_111,X_110))),bind(X_16,$fot(multiply(X_112,X_110)))]]) ).
cnf(refute_0_565,plain,
multiply(greatest_lower_bound(X_111,X_112),X_110) = greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(X_112))]]) ).
cnf(refute_0_566,plain,
( multiply(greatest_lower_bound(X_111,X_112),X_110) != greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))
| greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(X_111,X_112),X_110))),bind(Y0,$fot(greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))))]]) ).
cnf(refute_0_567,plain,
greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
( greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) != greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))
| least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) = greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))) ),[0,1],$fot(multiply(greatest_lower_bound(X_111,X_112),X_110))]]) ).
cnf(refute_0_569,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) != greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))
| least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) = greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) = greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))) )],[refute_0_564,refute_0_569]) ).
cnf(refute_0_571,plain,
least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)) = greatest_lower_bound(X_111,X_112),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(greatest_lower_bound(X_111,X_112)))]]) ).
cnf(refute_0_572,plain,
multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110) = multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110))]]) ).
cnf(refute_0_573,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110) != multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110)
| least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)) != greatest_lower_bound(X_111,X_112)
| multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110),multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110)) ),[1,0],$fot(greatest_lower_bound(X_111,X_112))]]) ).
cnf(refute_0_574,plain,
( least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)) != greatest_lower_bound(X_111,X_112)
| multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110),multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110)) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110) = multiply(greatest_lower_bound(X_111,X_112),X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),greatest_lower_bound(X_111,X_112)) )],[refute_0_571,refute_0_574]) ).
cnf(refute_0_576,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_577,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_576]) ).
cnf(refute_0_578,plain,
least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) = multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110),
inference(subst,[],[refute_0_577:[bind(X,$fot(X_110)),bind(Y,$fot(greatest_lower_bound(X_111,X_112))),bind(Z,$fot(greatest_lower_bound(X_111,X_112)))]]) ).
cnf(refute_0_579,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) != multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110)
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110))),bind(Z0,$fot(multiply(greatest_lower_bound(X_111,X_112),X_110)))]]) ).
cnf(refute_0_580,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)),multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110)) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_111,X_112),greatest_lower_bound(X_111,X_112)),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) )],[refute_0_575,refute_0_580]) ).
cnf(refute_0_582,plain,
least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))))]]) ).
cnf(refute_0_583,plain,
( greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) != least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)))
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_111,X_112),X_110))]]) ).
cnf(refute_0_584,plain,
( greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)))) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) )],[refute_0_567,refute_0_584]) ).
cnf(refute_0_586,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) != least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110))
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_111,X_112),X_110)))]]) ).
cnf(refute_0_587,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) = multiply(greatest_lower_bound(X_111,X_112),X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_111,X_112),X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) )],[refute_0_581,refute_0_587]) ).
cnf(refute_0_589,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),
inference(subst,[],[refute_0_100:[bind(Y,$fot(greatest_lower_bound(X_36,X_35))),bind(X_15,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))]]) ).
cnf(refute_0_590,plain,
least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),
inference(subst,[],[refute_0_226:[bind(Z,$fot(X_34)),bind(X_27,$fot(X_35)),bind(X_28,$fot(X_36))]]) ).
cnf(refute_0_591,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))]]) ).
cnf(refute_0_592,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) )],[refute_0_589,refute_0_592]) ).
cnf(refute_0_594,plain,
least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),
inference(subst,[],[refute_0_100:[bind(Y,$fot(greatest_lower_bound(X_35,X_36))),bind(X_15,$fot(X_34))]]) ).
cnf(refute_0_595,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),
inference(subst,[],[associativity_of_lub:[bind(Y,$fot(greatest_lower_bound(X_36,X_35))),bind(Z,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))]]) ).
cnf(refute_0_596,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))]]) ).
cnf(refute_0_597,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_590,refute_0_596]) ).
cnf(refute_0_598,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) )],[refute_0_595,refute_0_597]) ).
cnf(refute_0_599,plain,
least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),
inference(subst,[],[refute_0_96:[bind(Y,$fot(greatest_lower_bound(X_36,X_35))),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_600,plain,
least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)))]]) ).
cnf(refute_0_601,plain,
( least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))
| least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34))) ),[1,1],$fot(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))]]) ).
cnf(refute_0_602,plain,
( least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))
| least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) )],[refute_0_599,refute_0_602]) ).
cnf(refute_0_604,plain,
least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)),
inference(subst,[],[refute_0_291:[bind(Y,$fot(greatest_lower_bound(X_35,X_36))),bind(X_24,$fot(least_upper_bound(X,greatest_lower_bound(X_36,X_35)))),bind(X_26,$fot(X_34))]]) ).
cnf(refute_0_605,plain,
( least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))))]]) ).
cnf(refute_0_606,plain,
( least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),X_34)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))) )],[refute_0_603,refute_0_606]) ).
cnf(refute_0_608,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))
| least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))) ),[0],$fot(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))]]) ).
cnf(refute_0_609,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) )],[refute_0_598,refute_0_609]) ).
cnf(refute_0_611,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))
| least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))))]]) ).
cnf(refute_0_612,plain,
least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) = least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),
inference(subst,[],[refute_0_612:[bind(X,$fot(X_34)),bind(X_35,$fot(X_36)),bind(X_36,$fot(X_35))]]) ).
cnf(refute_0_614,plain,
( least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))))),bind(Y0,$fot(least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))),bind(Z0,$fot(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))))]]) ).
cnf(refute_0_615,plain,
( least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))) )],[refute_0_594,refute_0_615]) ).
cnf(refute_0_617,plain,
least_upper_bound(X_24,least_upper_bound(X_25,X_26)) = least_upper_bound(least_upper_bound(X_24,X_25),X_26),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_618,plain,
least_upper_bound(X_26,X_25) = least_upper_bound(X_25,X_26),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(X_25))]]) ).
cnf(refute_0_619,plain,
( least_upper_bound(X_26,X_25) != least_upper_bound(X_25,X_26)
| least_upper_bound(X_25,X_26) = least_upper_bound(X_26,X_25) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_26,X_25))),bind(Y0,$fot(least_upper_bound(X_25,X_26)))]]) ).
cnf(refute_0_620,plain,
least_upper_bound(X_25,X_26) = least_upper_bound(X_26,X_25),
inference(resolve,[$cnf( $equal(least_upper_bound(X_26,X_25),least_upper_bound(X_25,X_26)) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,X_26)) != least_upper_bound(least_upper_bound(X_24,X_25),X_26)
| least_upper_bound(X_25,X_26) != least_upper_bound(X_26,X_25)
| least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(least_upper_bound(X_24,X_25),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,X_26)),least_upper_bound(least_upper_bound(X_24,X_25),X_26)) ),[0,1],$fot(least_upper_bound(X_26,X_25))]]) ).
cnf(refute_0_622,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,X_26)) != least_upper_bound(least_upper_bound(X_24,X_25),X_26)
| least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(least_upper_bound(X_24,X_25),X_26) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),least_upper_bound(X_26,X_25)) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(least_upper_bound(X_24,X_25),X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,X_26)),least_upper_bound(least_upper_bound(X_24,X_25),X_26)) )],[refute_0_617,refute_0_622]) ).
cnf(refute_0_624,plain,
least_upper_bound(least_upper_bound(X_24,X_25),X_26) = least_upper_bound(X_24,least_upper_bound(X_25,X_26)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_625,plain,
( least_upper_bound(X_24,least_upper_bound(X_26,X_25)) != least_upper_bound(least_upper_bound(X_24,X_25),X_26)
| least_upper_bound(least_upper_bound(X_24,X_25),X_26) != least_upper_bound(X_24,least_upper_bound(X_25,X_26))
| least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(X_24,least_upper_bound(X_25,X_26)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_24,least_upper_bound(X_26,X_25)),least_upper_bound(X_24,least_upper_bound(X_25,X_26))) ),[0],$fot(least_upper_bound(least_upper_bound(X_24,X_25),X_26))]]) ).
cnf(refute_0_626,plain,
( least_upper_bound(X_24,least_upper_bound(X_26,X_25)) != least_upper_bound(least_upper_bound(X_24,X_25),X_26)
| least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(X_24,least_upper_bound(X_25,X_26)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_24,X_25),X_26),least_upper_bound(X_24,least_upper_bound(X_25,X_26))) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(X_24,least_upper_bound(X_25,X_26)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_26,X_25)),least_upper_bound(least_upper_bound(X_24,X_25),X_26)) )],[refute_0_623,refute_0_626]) ).
cnf(refute_0_628,plain,
( least_upper_bound(X_24,least_upper_bound(X_26,X_25)) != least_upper_bound(X_24,least_upper_bound(X_25,X_26))
| least_upper_bound(X_24,least_upper_bound(X_25,X_26)) = least_upper_bound(X_24,least_upper_bound(X_26,X_25)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_24,least_upper_bound(X_26,X_25)))),bind(Y0,$fot(least_upper_bound(X_24,least_upper_bound(X_25,X_26))))]]) ).
cnf(refute_0_629,plain,
least_upper_bound(X_24,least_upper_bound(X_25,X_26)) = least_upper_bound(X_24,least_upper_bound(X_26,X_25)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_26,X_25)),least_upper_bound(X_24,least_upper_bound(X_25,X_26))) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),
inference(subst,[],[refute_0_629:[bind(X_24,$fot(greatest_lower_bound(X_36,X_35))),bind(X_25,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),bind(X_26,$fot(X_34))]]) ).
cnf(refute_0_631,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))))),bind(Z0,$fot(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))))]]) ).
cnf(refute_0_632,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(X_34,least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))) )],[refute_0_616,refute_0_632]) ).
cnf(refute_0_634,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)),
inference(subst,[],[refute_0_291:[bind(Y,$fot(greatest_lower_bound(X_36,X_35))),bind(X_24,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),bind(X_26,$fot(X_34))]]) ).
cnf(refute_0_635,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)) != least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)))),bind(Z0,$fot(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))))]]) ).
cnf(refute_0_636,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)) != least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34))) )],[refute_0_634,refute_0_635]) ).
cnf(refute_0_637,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),X_34)),least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))) )],[refute_0_633,refute_0_636]) ).
cnf(refute_0_638,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) ),[0],$fot(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)))]]) ).
cnf(refute_0_639,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(X_34,greatest_lower_bound(X_35,X_36))) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),
inference(subst,[],[refute_0_132:[bind(Y,$fot(greatest_lower_bound(X_36,X_35))),bind(X_18,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))]]) ).
cnf(refute_0_641,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))]]) ).
cnf(refute_0_642,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_590,refute_0_641]) ).
cnf(refute_0_643,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) )],[refute_0_640,refute_0_642]) ).
cnf(refute_0_644,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),
inference(subst,[],[refute_0_132:[bind(Y,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))),bind(X_18,$fot(greatest_lower_bound(X_36,X_35)))]]) ).
cnf(refute_0_645,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) ),[0,0],$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))]]) ).
cnf(refute_0_646,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_590,refute_0_645]) ).
cnf(refute_0_647,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) )],[refute_0_644,refute_0_646]) ).
cnf(refute_0_648,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))),
inference(subst,[],[refute_0_96:[bind(X,$fot(greatest_lower_bound(X_35,X_36))),bind(Y,$fot(X_34)),bind(Z,$fot(greatest_lower_bound(X_36,X_35)))]]) ).
cnf(refute_0_649,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))))]]) ).
cnf(refute_0_650,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))) ),[1,1],$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))))]]) ).
cnf(refute_0_651,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) )],[refute_0_648,refute_0_651]) ).
cnf(refute_0_653,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) ),[0],$fot(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))))]]) ).
cnf(refute_0_654,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) = least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)))]]) ).
cnf(refute_0_656,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_590,refute_0_655]) ).
cnf(refute_0_657,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) )],[refute_0_654,refute_0_656]) ).
cnf(refute_0_658,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),least_upper_bound(greatest_lower_bound(X_36,X_35),least_upper_bound(greatest_lower_bound(X_35,X_36),X_34))) )],[refute_0_647,refute_0_657]) ).
cnf(refute_0_659,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))))
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))]]) ).
cnf(refute_0_660,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))))) )],[refute_0_652,refute_0_659]) ).
cnf(refute_0_661,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_658,refute_0_660]) ).
cnf(refute_0_662,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),
inference(subst,[],[refute_0_164:[bind(X,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))),bind(Y,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))))]]) ).
cnf(refute_0_663,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))
| greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))]]) ).
cnf(refute_0_664,plain,
( greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))]]) ).
cnf(refute_0_667,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))
| least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))]]) ).
cnf(refute_0_669,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) )],[refute_0_648,refute_0_668]) ).
cnf(refute_0_670,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) )],[refute_0_667,refute_0_669]) ).
cnf(refute_0_671,plain,
least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) )],[refute_0_643,refute_0_670]) ).
cnf(refute_0_672,plain,
( least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))
| least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))))]]) ).
cnf(refute_0_673,plain,
least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
( least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) != least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))]]) ).
cnf(refute_0_675,plain,
( least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35)))) )],[refute_0_648,refute_0_674]) ).
cnf(refute_0_676,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,X_36),least_upper_bound(X_34,greatest_lower_bound(X_36,X_35))),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_673,refute_0_675]) ).
cnf(refute_0_677,plain,
( least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)))]]) ).
cnf(refute_0_678,plain,
( least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))
| least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) )],[refute_0_639,refute_0_678]) ).
cnf(refute_0_680,plain,
least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) = least_upper_bound(greatest_lower_bound(X_36,X_35),X_34),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)),least_upper_bound(least_upper_bound(greatest_lower_bound(X_35,X_36),X_34),greatest_lower_bound(X_36,X_35))) )],[refute_0_593,refute_0_679]) ).
cnf(refute_0_681,plain,
( least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) != least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)
| least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)))]]) ).
cnf(refute_0_682,plain,
least_upper_bound(greatest_lower_bound(X_36,X_35),X_34) = least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_34,greatest_lower_bound(X_35,X_36)),least_upper_bound(greatest_lower_bound(X_36,X_35),X_34)) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) = least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),
inference(subst,[],[refute_0_682:[bind(X_34,$fot(multiply(greatest_lower_bound(X_111,X_112),X_110))),bind(X_35,$fot(multiply(X_111,X_110))),bind(X_36,$fot(multiply(X_112,X_110)))]]) ).
cnf(refute_0_684,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) != least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)))
| least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_111,X_112),X_110)))]]) ).
cnf(refute_0_685,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)),least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110)))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) = multiply(greatest_lower_bound(X_111,X_112),X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(X_112,X_110))),multiply(greatest_lower_bound(X_111,X_112),X_110)) )],[refute_0_588,refute_0_685]) ).
cnf(refute_0_687,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) != multiply(greatest_lower_bound(X_111,X_112),X_110)
| least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) != greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))
| multiply(greatest_lower_bound(X_111,X_112),X_110) = greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)),greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))) ),[0],$fot(multiply(greatest_lower_bound(X_111,X_112),X_110))]]) ).
cnf(refute_0_688,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) != greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))
| multiply(greatest_lower_bound(X_111,X_112),X_110) = greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_690,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_689]) ).
cnf(refute_0_691,plain,
greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)) = multiply(greatest_lower_bound(X_112,X_111),X_110),
inference(subst,[],[refute_0_690:[bind(X,$fot(X_110)),bind(Y,$fot(X_112)),bind(Z,$fot(X_111))]]) ).
cnf(refute_0_692,plain,
( multiply(greatest_lower_bound(X_111,X_112),X_110) != greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))
| greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != multiply(greatest_lower_bound(X_112,X_111),X_110)
| multiply(greatest_lower_bound(X_111,X_112),X_110) = multiply(greatest_lower_bound(X_112,X_111),X_110) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_112,X_111),X_110)) ),[0],$fot(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)))]]) ).
cnf(refute_0_693,plain,
( multiply(greatest_lower_bound(X_111,X_112),X_110) != greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))
| multiply(greatest_lower_bound(X_111,X_112),X_110) = multiply(greatest_lower_bound(X_112,X_111),X_110) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_112,X_111),X_110)) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)) != greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))
| multiply(greatest_lower_bound(X_111,X_112),X_110) = multiply(greatest_lower_bound(X_112,X_111),X_110) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),X_110),greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))) )],[refute_0_688,refute_0_693]) ).
cnf(refute_0_695,plain,
multiply(greatest_lower_bound(X_111,X_112),X_110) = multiply(greatest_lower_bound(X_112,X_111),X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(greatest_lower_bound(X_111,X_112),X_110)),greatest_lower_bound(multiply(X_112,X_110),multiply(X_111,X_110))) )],[refute_0_570,refute_0_694]) ).
cnf(refute_0_696,plain,
( multiply(greatest_lower_bound(X_111,X_112),X_110) != multiply(greatest_lower_bound(X_112,X_111),X_110)
| multiply(greatest_lower_bound(X_112,X_111),X_110) = multiply(greatest_lower_bound(X_111,X_112),X_110) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(X_111,X_112),X_110))),bind(Y0,$fot(multiply(greatest_lower_bound(X_112,X_111),X_110)))]]) ).
cnf(refute_0_697,plain,
multiply(greatest_lower_bound(X_112,X_111),X_110) = multiply(greatest_lower_bound(X_111,X_112),X_110),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),X_110),multiply(greatest_lower_bound(X_112,X_111),X_110)) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17),
inference(subst,[],[refute_0_697:[bind(X_110,$fot(X_17)),bind(X_111,$fot(identity)),bind(X_112,$fot(greatest_lower_bound(X_191,identity)))]]) ).
cnf(refute_0_699,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)) = multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17),
inference(subst,[],[refute_0_500:[bind(X_110,$fot(X_17)),bind(X_111,$fot(greatest_lower_bound(X_191,identity)))]]) ).
cnf(refute_0_700,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)) != multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)))),bind(Y0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)))]]) ).
cnf(refute_0_701,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)),multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17)) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_191,identity),identity),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)) )],[refute_0_698,refute_0_701]) ).
cnf(refute_0_703,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)),X_33),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(greatest_lower_bound(Y,X_31))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_704,plain,
greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)) = greatest_lower_bound(X_31,Y),
inference(subst,[],[refute_0_218:[bind(X_13,$fot(X_31))]]) ).
cnf(refute_0_705,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)) != greatest_lower_bound(X_31,Y)
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)),X_33)
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)),X_33)) ),[1,0],$fot(greatest_lower_bound(X_31,Y))]]) ).
cnf(refute_0_706,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)),X_33)
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)),greatest_lower_bound(X_31,Y)) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(greatest_lower_bound(X_31,greatest_lower_bound(Y,X_31)),X_33)) )],[refute_0_703,refute_0_706]) ).
cnf(refute_0_708,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(greatest_lower_bound(Y,X_32)))]]) ).
cnf(refute_0_709,plain,
greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,Y),
inference(subst,[],[refute_0_218:[bind(X_13,$fot(X_32))]]) ).
cnf(refute_0_710,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32)) != greatest_lower_bound(X_32,Y)
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))),greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))) ),[0,1],$fot(greatest_lower_bound(X_32,Y))]]) ).
cnf(refute_0_711,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32)),greatest_lower_bound(X_32,Y)) )],[refute_0_709,refute_0_710]) ).
cnf(refute_0_712,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,greatest_lower_bound(Y,X_32))),greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))) )],[refute_0_708,refute_0_711]) ).
cnf(refute_0_713,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_714,plain,
greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)))]]) ).
cnf(refute_0_715,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) != greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))
| greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))) ),[1,1],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))]]) ).
cnf(refute_0_716,plain,
( greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))
| greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y),greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) )],[refute_0_713,refute_0_716]) ).
cnf(refute_0_718,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_31,X_32)))]]) ).
cnf(refute_0_719,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X))]]) ).
cnf(refute_0_720,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),X) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)))]]) ).
cnf(refute_0_721,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),X) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)),greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),X) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X))]]) ).
cnf(refute_0_723,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),X),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))) )],[refute_0_721,refute_0_722]) ).
cnf(refute_0_724,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(greatest_lower_bound(X_31,X_32),X)) )],[refute_0_718,refute_0_723]) ).
cnf(refute_0_725,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)))),bind(Y0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))))]]) ).
cnf(refute_0_726,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))) )],[refute_0_724,refute_0_725]) ).
cnf(refute_0_727,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),
inference(subst,[],[refute_0_726:[bind(X,$fot(X_32)),bind(X_31,$fot(greatest_lower_bound(X_31,X_32))),bind(X_32,$fot(Y))]]) ).
cnf(refute_0_728,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) != greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)))),bind(Y0,$fot(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)))),bind(Z0,$fot(greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))))]]) ).
cnf(refute_0_729,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y))) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X_31,X_32),Y)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) )],[refute_0_717,refute_0_729]) ).
cnf(refute_0_731,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)))]]) ).
cnf(refute_0_732,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),greatest_lower_bound(greatest_lower_bound(X_31,X_32),greatest_lower_bound(Y,X_32))) )],[refute_0_712,refute_0_732]) ).
cnf(refute_0_734,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))
| greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))),bind(Y0,$fot(greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))))]]) ).
cnf(refute_0_735,plain,
greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y))) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,greatest_lower_bound(X_32,Y)))) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) = greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)),
inference(subst,[],[refute_0_735:[bind(Y,$fot(X_33)),bind(X_31,$fot(Y)),bind(X_32,$fot(X_31))]]) ).
cnf(refute_0_737,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33) = greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)),
inference(subst,[],[refute_0_214:[bind(X,$fot(Y)),bind(Y,$fot(X_31)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_738,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)))]]) ).
cnf(refute_0_739,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33))
| greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33) != greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)))]]) ).
cnf(refute_0_740,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33) != greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33))) )],[refute_0_738,refute_0_739]) ).
cnf(refute_0_741,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33),greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) )],[refute_0_737,refute_0_740]) ).
cnf(refute_0_742,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) != greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)))),bind(Y0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))))]]) ).
cnf(refute_0_743,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) != greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) = greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))),greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) )],[refute_0_736,refute_0_743]) ).
cnf(refute_0_745,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)
| greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) = greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)))]]) ).
cnf(refute_0_746,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)
| greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) = greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33) = greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33)),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_31)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_748,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)
| greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33) != greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33))
| greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)),greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33))]]) ).
cnf(refute_0_749,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)
| greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33),greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)) != greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)
| greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)),greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)) )],[refute_0_746,refute_0_749]) ).
cnf(refute_0_751,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_31,X_33)) = greatest_lower_bound(X_31,greatest_lower_bound(Y,X_33)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(Y,X_31),X_33)),greatest_lower_bound(greatest_lower_bound(X_31,Y),X_33)) )],[refute_0_707,refute_0_750]) ).
cnf(refute_0_752,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))) = greatest_lower_bound(X_31,greatest_lower_bound(Y,multiply(X_191,Y))),
inference(subst,[],[refute_0_751:[bind(X_33,$fot(multiply(X_191,Y)))]]) ).
cnf(refute_0_753,plain,
multiply(greatest_lower_bound(X_191,identity),Y) = greatest_lower_bound(Y,multiply(X_191,Y)),
inference(subst,[],[refute_0_498:[bind(X_110,$fot(Y)),bind(X_111,$fot(X_191))]]) ).
cnf(refute_0_754,plain,
( multiply(greatest_lower_bound(X_191,identity),Y) != greatest_lower_bound(Y,multiply(X_191,Y))
| greatest_lower_bound(Y,multiply(X_191,Y)) = multiply(greatest_lower_bound(X_191,identity),Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(X_191,identity),Y))),bind(Y0,$fot(greatest_lower_bound(Y,multiply(X_191,Y))))]]) ).
cnf(refute_0_755,plain,
greatest_lower_bound(Y,multiply(X_191,Y)) = multiply(greatest_lower_bound(X_191,identity),Y),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_191,identity),Y),greatest_lower_bound(Y,multiply(X_191,Y))) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
( greatest_lower_bound(Y,multiply(X_191,Y)) != multiply(greatest_lower_bound(X_191,identity),Y)
| greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))) != greatest_lower_bound(X_31,greatest_lower_bound(Y,multiply(X_191,Y)))
| greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))) = greatest_lower_bound(X_31,multiply(greatest_lower_bound(X_191,identity),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))),greatest_lower_bound(X_31,greatest_lower_bound(Y,multiply(X_191,Y)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_191,identity),Y))]]) ).
cnf(refute_0_757,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))) != greatest_lower_bound(X_31,greatest_lower_bound(Y,multiply(X_191,Y)))
| greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))) = greatest_lower_bound(X_31,multiply(greatest_lower_bound(X_191,identity),Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,multiply(X_191,Y)),multiply(greatest_lower_bound(X_191,identity),Y)) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))) = greatest_lower_bound(X_31,multiply(greatest_lower_bound(X_191,identity),Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_31,multiply(X_191,Y))),greatest_lower_bound(X_31,greatest_lower_bound(Y,multiply(X_191,Y)))) )],[refute_0_752,refute_0_757]) ).
cnf(refute_0_759,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)),
inference(subst,[],[refute_0_758:[bind(Y,$fot(X_17)),bind(X_31,$fot(X_17))]]) ).
cnf(refute_0_760,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) != greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)))]]) ).
cnf(refute_0_761,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))),greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_191,identity),X_17)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)) )],[refute_0_702,refute_0_761]) ).
cnf(refute_0_763,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) != multiply(greatest_lower_bound(identity,X_191),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(identity,X_191),X_17) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_191),X_17)))]]) ).
cnf(refute_0_764,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17) != multiply(greatest_lower_bound(identity,X_191),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(identity,X_191),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17)) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) = multiply(greatest_lower_bound(identity,X_191),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_191,identity)),X_17),multiply(greatest_lower_bound(identity,X_191),X_17)) )],[refute_0_563,refute_0_764]) ).
cnf(refute_0_766,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) != multiply(greatest_lower_bound(X_191,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) != multiply(greatest_lower_bound(identity,X_191),X_17)
| multiply(greatest_lower_bound(identity,X_191),X_17) = multiply(greatest_lower_bound(X_191,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))),multiply(greatest_lower_bound(X_191,identity),X_17)) ),[0],$fot(multiply(greatest_lower_bound(identity,X_191),X_17))]]) ).
cnf(refute_0_767,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))) != multiply(greatest_lower_bound(X_191,identity),X_17)
| multiply(greatest_lower_bound(identity,X_191),X_17) = multiply(greatest_lower_bound(X_191,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))),multiply(greatest_lower_bound(identity,X_191),X_17)) )],[refute_0_765,refute_0_766]) ).
cnf(refute_0_768,plain,
multiply(greatest_lower_bound(identity,X_191),X_17) = multiply(greatest_lower_bound(X_191,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_191,X_17))),multiply(greatest_lower_bound(X_191,identity),X_17)) )],[refute_0_558,refute_0_767]) ).
cnf(refute_0_769,plain,
( multiply(greatest_lower_bound(identity,X_191),X_17) != multiply(greatest_lower_bound(X_191,identity),X_17)
| multiply(greatest_lower_bound(X_191,identity),X_17) = multiply(greatest_lower_bound(identity,X_191),X_17) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_191),X_17))),bind(Y0,$fot(multiply(greatest_lower_bound(X_191,identity),X_17)))]]) ).
cnf(refute_0_770,plain,
multiply(greatest_lower_bound(X_191,identity),X_17) = multiply(greatest_lower_bound(identity,X_191),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_191),X_17),multiply(greatest_lower_bound(X_191,identity),X_17)) )],[refute_0_768,refute_0_769]) ).
cnf(refute_0_771,plain,
multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) = multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)),
inference(subst,[],[refute_0_770:[bind(X_17,$fot(least_upper_bound(X_70,identity))),bind(X_191,$fot(inverse(X_70)))]]) ).
cnf(refute_0_772,plain,
( multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) != multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity))
| multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) != greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))
| multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)),greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)))]]) ).
cnf(refute_0_773,plain,
( multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)) != greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))
| multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)),multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity))) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_70),identity),least_upper_bound(X_70,identity)),greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))) )],[refute_0_544,refute_0_773]) ).
cnf(refute_0_775,plain,
multiply(X_90,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_90)),bind(Y,$fot(X_91)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_776,plain,
X_90 = multiply(X_90,identity),
inference(subst,[],[refute_0_48:[bind(X_41,$fot(X_90))]]) ).
cnf(refute_0_777,plain,
( X_90 != multiply(X_90,identity)
| multiply(X_90,identity) = X_90 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_90)),bind(Y0,$fot(multiply(X_90,identity)))]]) ).
cnf(refute_0_778,plain,
multiply(X_90,identity) = X_90,
inference(resolve,[$cnf( $equal(X_90,multiply(X_90,identity)) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
( multiply(X_90,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,identity))
| multiply(X_90,identity) != X_90
| multiply(X_90,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(multiply(X_90,X_91),X_90) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,identity)),greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,identity))) ),[1,1],$fot(X_90)]]) ).
cnf(refute_0_780,plain,
( multiply(X_90,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,identity))
| multiply(X_90,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(multiply(X_90,X_91),X_90) ),
inference(resolve,[$cnf( $equal(multiply(X_90,identity),X_90) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
multiply(X_90,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(multiply(X_90,X_91),X_90),
inference(resolve,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,identity)),greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,identity))) )],[refute_0_775,refute_0_780]) ).
cnf(refute_0_782,plain,
greatest_lower_bound(multiply(X_90,X_91),X_90) = greatest_lower_bound(X_90,multiply(X_90,X_91)),
inference(subst,[],[refute_0_164:[bind(X,$fot(X_90)),bind(Y,$fot(multiply(X_90,X_91)))]]) ).
cnf(refute_0_783,plain,
( multiply(X_90,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(multiply(X_90,X_91),X_90)
| greatest_lower_bound(multiply(X_90,X_91),X_90) != greatest_lower_bound(X_90,multiply(X_90,X_91))
| multiply(X_90,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(X_90,multiply(X_90,X_91)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_90,greatest_lower_bound(X_91,identity)),greatest_lower_bound(X_90,multiply(X_90,X_91))) ),[0],$fot(greatest_lower_bound(multiply(X_90,X_91),X_90))]]) ).
cnf(refute_0_784,plain,
( multiply(X_90,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(multiply(X_90,X_91),X_90)
| multiply(X_90,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(X_90,multiply(X_90,X_91)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_90,X_91),X_90),greatest_lower_bound(X_90,multiply(X_90,X_91))) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
multiply(X_90,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(X_90,multiply(X_90,X_91)),
inference(resolve,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,identity)),greatest_lower_bound(multiply(X_90,X_91),X_90)) )],[refute_0_781,refute_0_784]) ).
cnf(refute_0_786,plain,
multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) = greatest_lower_bound(least_upper_bound(X_108,identity),multiply(least_upper_bound(X_108,identity),inverse(X_108))),
inference(subst,[],[refute_0_785:[bind(X_90,$fot(least_upper_bound(X_108,identity))),bind(X_91,$fot(inverse(X_108)))]]) ).
cnf(refute_0_787,plain,
( least_upper_bound(identity,inverse(X_108)) != multiply(least_upper_bound(X_108,identity),inverse(X_108))
| multiply(least_upper_bound(X_108,identity),inverse(X_108)) = least_upper_bound(identity,inverse(X_108)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(identity,inverse(X_108)))),bind(Y0,$fot(multiply(least_upper_bound(X_108,identity),inverse(X_108))))]]) ).
cnf(refute_0_788,plain,
multiply(least_upper_bound(X_108,identity),inverse(X_108)) = least_upper_bound(identity,inverse(X_108)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_108)),multiply(least_upper_bound(X_108,identity),inverse(X_108))) )],[refute_0_408,refute_0_787]) ).
cnf(refute_0_789,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) != greatest_lower_bound(least_upper_bound(X_108,identity),multiply(least_upper_bound(X_108,identity),inverse(X_108)))
| multiply(least_upper_bound(X_108,identity),inverse(X_108)) != least_upper_bound(identity,inverse(X_108))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) = greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)),greatest_lower_bound(least_upper_bound(X_108,identity),multiply(least_upper_bound(X_108,identity),inverse(X_108)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_108)))]]) ).
cnf(refute_0_790,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) != greatest_lower_bound(least_upper_bound(X_108,identity),multiply(least_upper_bound(X_108,identity),inverse(X_108)))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) = greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),inverse(X_108)),least_upper_bound(identity,inverse(X_108))) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) = greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)),greatest_lower_bound(least_upper_bound(X_108,identity),multiply(least_upper_bound(X_108,identity),inverse(X_108)))) )],[refute_0_786,refute_0_790]) ).
cnf(refute_0_792,plain,
least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),greatest_lower_bound(X_11,multiply(X_11,X_438))) = greatest_lower_bound(multiply(X_11,X_438),X_11),
inference(subst,[],[refute_0_222:[bind(X_16,$fot(multiply(X_11,X_438)))]]) ).
cnf(refute_0_793,plain,
multiply(X_11,greatest_lower_bound(X_438,identity)) = greatest_lower_bound(X_11,multiply(X_11,X_438)),
inference(subst,[],[refute_0_785:[bind(X_90,$fot(X_11)),bind(X_91,$fot(X_438))]]) ).
cnf(refute_0_794,plain,
( multiply(X_11,greatest_lower_bound(X_438,identity)) != greatest_lower_bound(X_11,multiply(X_11,X_438))
| greatest_lower_bound(X_11,multiply(X_11,X_438)) = multiply(X_11,greatest_lower_bound(X_438,identity)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_11,greatest_lower_bound(X_438,identity)))),bind(Y0,$fot(greatest_lower_bound(X_11,multiply(X_11,X_438))))]]) ).
cnf(refute_0_795,plain,
greatest_lower_bound(X_11,multiply(X_11,X_438)) = multiply(X_11,greatest_lower_bound(X_438,identity)),
inference(resolve,[$cnf( $equal(multiply(X_11,greatest_lower_bound(X_438,identity)),greatest_lower_bound(X_11,multiply(X_11,X_438))) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
( greatest_lower_bound(X_11,multiply(X_11,X_438)) != multiply(X_11,greatest_lower_bound(X_438,identity))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),greatest_lower_bound(X_11,multiply(X_11,X_438))) != greatest_lower_bound(multiply(X_11,X_438),X_11)
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = greatest_lower_bound(multiply(X_11,X_438),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),greatest_lower_bound(X_11,multiply(X_11,X_438))),greatest_lower_bound(multiply(X_11,X_438),X_11)) ),[0,1],$fot(multiply(X_11,greatest_lower_bound(X_438,identity)))]]) ).
cnf(refute_0_797,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),greatest_lower_bound(X_11,multiply(X_11,X_438))) != greatest_lower_bound(multiply(X_11,X_438),X_11)
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = greatest_lower_bound(multiply(X_11,X_438),X_11) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,multiply(X_11,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = greatest_lower_bound(multiply(X_11,X_438),X_11),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),greatest_lower_bound(X_11,multiply(X_11,X_438))),greatest_lower_bound(multiply(X_11,X_438),X_11)) )],[refute_0_792,refute_0_797]) ).
cnf(refute_0_799,plain,
least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)) = greatest_lower_bound(identity,X_438),
inference(subst,[],[refute_0_222:[bind(X_11,$fot(X_438)),bind(X_16,$fot(identity))]]) ).
cnf(refute_0_800,plain,
multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))) = multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))),
introduced(tautology,[refl,[$fot(multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))))]]) ).
cnf(refute_0_801,plain,
( multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))) != multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)))
| least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)) != greatest_lower_bound(identity,X_438)
| multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))),multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_438))]]) ).
cnf(refute_0_802,plain,
( least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)) != greatest_lower_bound(identity,X_438)
| multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(resolve,[$cnf( $equal(multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))),multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)))) )],[refute_0_800,refute_0_801]) ).
cnf(refute_0_803,plain,
multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)),greatest_lower_bound(identity,X_438)) )],[refute_0_799,refute_0_802]) ).
cnf(refute_0_804,plain,
least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) = multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))),
inference(subst,[],[refute_0_154:[bind(X,$fot(X_11)),bind(Y,$fot(greatest_lower_bound(identity,X_438))),bind(Z,$fot(greatest_lower_bound(X_438,identity)))]]) ).
cnf(refute_0_805,plain,
( multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))) != multiply(X_11,greatest_lower_bound(identity,X_438))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) != multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))))),bind(Y0,$fot(multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))))),bind(Z0,$fot(multiply(X_11,greatest_lower_bound(identity,X_438))))]]) ).
cnf(refute_0_806,plain,
( multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))) != multiply(X_11,greatest_lower_bound(identity,X_438))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))),multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity)))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)),
inference(resolve,[$cnf( $equal(multiply(X_11,least_upper_bound(greatest_lower_bound(identity,X_438),greatest_lower_bound(X_438,identity))),multiply(X_11,greatest_lower_bound(identity,X_438))) )],[refute_0_803,refute_0_806]) ).
cnf(refute_0_808,plain,
least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))))]]) ).
cnf(refute_0_809,plain,
( greatest_lower_bound(X_11,multiply(X_11,X_438)) != multiply(X_11,greatest_lower_bound(X_438,identity))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) != least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))),least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))) ),[1,1],$fot(multiply(X_11,greatest_lower_bound(X_438,identity)))]]) ).
cnf(refute_0_810,plain,
( greatest_lower_bound(X_11,multiply(X_11,X_438)) != multiply(X_11,greatest_lower_bound(X_438,identity))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))),least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))) )],[refute_0_808,refute_0_809]) ).
cnf(refute_0_811,plain,
least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,multiply(X_11,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) )],[refute_0_795,refute_0_810]) ).
cnf(refute_0_812,plain,
( least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) != multiply(X_11,greatest_lower_bound(identity,X_438))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) != least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity)))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))))),bind(Y0,$fot(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))))),bind(Z0,$fot(multiply(X_11,greatest_lower_bound(identity,X_438))))]]) ).
cnf(refute_0_813,plain,
( least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) != multiply(X_11,greatest_lower_bound(identity,X_438))
| least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))),least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity)))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) = multiply(X_11,greatest_lower_bound(identity,X_438)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))),multiply(X_11,greatest_lower_bound(identity,X_438))) )],[refute_0_807,refute_0_813]) ).
cnf(refute_0_815,plain,
multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))) = least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(multiply(X_38,X_66)))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_66)),bind(Y,$fot(X_67)),bind(Z,$fot(inverse(multiply(X_38,X_66))))]]) ).
cnf(refute_0_816,plain,
multiply(X_66,inverse(multiply(X_38,X_66))) = inverse(X_38),
inference(subst,[],[refute_0_54:[bind(X_51,$fot(X_66))]]) ).
cnf(refute_0_817,plain,
( multiply(X_66,inverse(multiply(X_38,X_66))) != inverse(X_38)
| multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(multiply(X_38,X_66))))
| multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))) = least_upper_bound(multiply(X_66,X_67),inverse(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))),least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(multiply(X_38,X_66))))) ),[1,1],$fot(inverse(X_38))]]) ).
cnf(refute_0_818,plain,
( multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(multiply(X_38,X_66))))
| multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))) = least_upper_bound(multiply(X_66,X_67),inverse(X_38)) ),
inference(resolve,[$cnf( $equal(multiply(X_66,inverse(multiply(X_38,X_66))),inverse(X_38)) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))) = least_upper_bound(multiply(X_66,X_67),inverse(X_38)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,inverse(multiply(X_38,X_66)))),least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(multiply(X_38,X_66))))) )],[refute_0_815,refute_0_818]) ).
cnf(refute_0_820,plain,
multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))),
inference(subst,[],[refute_0_819:[bind(X_38,$fot(inverse(greatest_lower_bound(X_433,X_100)))),bind(X_66,$fot(X_433)),bind(X_67,$fot(X_434))]]) ).
cnf(refute_0_821,plain,
inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(greatest_lower_bound(X_99,X_100))),bind(X_52,$fot(inverse(X_99)))]]) ).
cnf(refute_0_822,plain,
multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(multiply(inverse(X_91),X_91),multiply(inverse(X_91),X_92)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_91))),bind(Y,$fot(X_91)),bind(Z,$fot(X_92))]]) ).
cnf(refute_0_823,plain,
multiply(inverse(X_91),X_91) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_91))]]) ).
cnf(refute_0_824,plain,
( multiply(inverse(X_91),X_91) != identity
| multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)) != greatest_lower_bound(multiply(inverse(X_91),X_91),multiply(inverse(X_91),X_92))
| multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(identity,multiply(inverse(X_91),X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)),greatest_lower_bound(multiply(inverse(X_91),X_91),multiply(inverse(X_91),X_92))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_825,plain,
( multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)) != greatest_lower_bound(multiply(inverse(X_91),X_91),multiply(inverse(X_91),X_92))
| multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(identity,multiply(inverse(X_91),X_92)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),X_91),identity) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(identity,multiply(inverse(X_91),X_92)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),greatest_lower_bound(X_91,X_92)),greatest_lower_bound(multiply(inverse(X_91),X_91),multiply(inverse(X_91),X_92))) )],[refute_0_822,refute_0_825]) ).
cnf(refute_0_827,plain,
multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) = greatest_lower_bound(identity,multiply(inverse(X_99),X_100)),
inference(subst,[],[refute_0_826:[bind(X_91,$fot(X_99)),bind(X_92,$fot(X_100))]]) ).
cnf(refute_0_828,plain,
( multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) != greatest_lower_bound(identity,multiply(inverse(X_99),X_100))
| inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))) != multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))),multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_99),X_100)))]]) ).
cnf(refute_0_829,plain,
( inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))) != multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)),greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))),multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))) )],[refute_0_821,refute_0_829]) ).
cnf(refute_0_831,plain,
inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99),
inference(subst,[],[refute_0_464:[bind(X_39,$fot(greatest_lower_bound(X_99,X_100))),bind(X_55,$fot(X_99))]]) ).
cnf(refute_0_832,plain,
multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) = inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(greatest_lower_bound(X_99,X_100))),bind(X_52,$fot(inverse(X_99)))]]) ).
cnf(refute_0_833,plain,
( multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) != inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)))
| inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))) != multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99)
| multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))))),bind(Y0,$fot(inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99)))]]) ).
cnf(refute_0_834,plain,
( inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))) != multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99)
| multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))),inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)))) )],[refute_0_832,refute_0_833]) ).
cnf(refute_0_835,plain,
multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100))),multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99)) )],[refute_0_831,refute_0_834]) ).
cnf(refute_0_836,plain,
( multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))) != multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) != multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))),multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99))]]) ).
cnf(refute_0_837,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) != multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99))),multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99)) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))) = multiply(inverse(greatest_lower_bound(X_99,X_100)),X_99),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_99),X_100))),multiply(inverse(greatest_lower_bound(X_99,X_100)),inverse(inverse(X_99)))) )],[refute_0_830,refute_0_837]) ).
cnf(refute_0_839,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))) = multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433),
inference(subst,[],[refute_0_838:[bind(X_99,$fot(X_433))]]) ).
cnf(refute_0_840,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))) != multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)
| multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433) = inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)))]]) ).
cnf(refute_0_841,plain,
multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433) = inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))),multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433) != inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))) ),[0,1,1,0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))]]) ).
cnf(refute_0_843,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433),inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) )],[refute_0_841,refute_0_842]) ).
cnf(refute_0_844,plain,
multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_433,X_100)),X_433)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))) )],[refute_0_820,refute_0_843]) ).
cnf(refute_0_845,plain,
multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))),
inference(subst,[],[refute_0_819:[bind(X_38,$fot(inverse(greatest_lower_bound(X_97,X_433)))),bind(X_66,$fot(X_433)),bind(X_67,$fot(X_434))]]) ).
cnf(refute_0_846,plain,
inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(greatest_lower_bound(X_97,X_98))),bind(X_52,$fot(inverse(X_98)))]]) ).
cnf(refute_0_847,plain,
multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(multiply(inverse(X_92),X_91),multiply(inverse(X_92),X_92)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_92))),bind(Y,$fot(X_91)),bind(Z,$fot(X_92))]]) ).
cnf(refute_0_848,plain,
multiply(inverse(X_92),X_92) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_92))]]) ).
cnf(refute_0_849,plain,
( multiply(inverse(X_92),X_92) != identity
| multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) != greatest_lower_bound(multiply(inverse(X_92),X_91),multiply(inverse(X_92),X_92))
| multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(multiply(inverse(X_92),X_91),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)),greatest_lower_bound(multiply(inverse(X_92),X_91),multiply(inverse(X_92),X_92))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_850,plain,
( multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) != greatest_lower_bound(multiply(inverse(X_92),X_91),multiply(inverse(X_92),X_92))
| multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(multiply(inverse(X_92),X_91),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_92),X_92),identity) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(multiply(inverse(X_92),X_91),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)),greatest_lower_bound(multiply(inverse(X_92),X_91),multiply(inverse(X_92),X_92))) )],[refute_0_847,refute_0_850]) ).
cnf(refute_0_852,plain,
greatest_lower_bound(multiply(inverse(X_92),X_91),identity) = greatest_lower_bound(identity,multiply(inverse(X_92),X_91)),
inference(subst,[],[refute_0_164:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_92),X_91)))]]) ).
cnf(refute_0_853,plain,
( multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) != greatest_lower_bound(multiply(inverse(X_92),X_91),identity)
| greatest_lower_bound(multiply(inverse(X_92),X_91),identity) != greatest_lower_bound(identity,multiply(inverse(X_92),X_91))
| multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(identity,multiply(inverse(X_92),X_91)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_92),X_91),identity))]]) ).
cnf(refute_0_854,plain,
( multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) != greatest_lower_bound(multiply(inverse(X_92),X_91),identity)
| multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(identity,multiply(inverse(X_92),X_91)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_92),X_91),identity),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) = greatest_lower_bound(identity,multiply(inverse(X_92),X_91)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)),greatest_lower_bound(multiply(inverse(X_92),X_91),identity)) )],[refute_0_851,refute_0_854]) ).
cnf(refute_0_856,plain,
multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)) = greatest_lower_bound(identity,multiply(inverse(X_98),X_97)),
inference(subst,[],[refute_0_855:[bind(X_91,$fot(X_97)),bind(X_92,$fot(X_98))]]) ).
cnf(refute_0_857,plain,
( multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)) != greatest_lower_bound(identity,multiply(inverse(X_98),X_97))
| inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))) != multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))),multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))]]) ).
cnf(refute_0_858,plain,
( inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))) != multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))),multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))) )],[refute_0_846,refute_0_858]) ).
cnf(refute_0_860,plain,
inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98),
inference(subst,[],[refute_0_464:[bind(X_39,$fot(greatest_lower_bound(X_97,X_98))),bind(X_55,$fot(X_98))]]) ).
cnf(refute_0_861,plain,
multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) = inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(greatest_lower_bound(X_97,X_98))),bind(X_52,$fot(inverse(X_98)))]]) ).
cnf(refute_0_862,plain,
( multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) != inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)))
| inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))) != multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98)
| multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))))),bind(Y0,$fot(inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98)))]]) ).
cnf(refute_0_863,plain,
( inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))) != multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98)
| multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))),inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)))) )],[refute_0_861,refute_0_862]) ).
cnf(refute_0_864,plain,
multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))),multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98)) )],[refute_0_860,refute_0_863]) ).
cnf(refute_0_865,plain,
( multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))) != multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) != multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))),multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98))]]) ).
cnf(refute_0_866,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) != multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98))),multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98)) )],[refute_0_864,refute_0_865]) ).
cnf(refute_0_867,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(greatest_lower_bound(X_97,X_98)),X_98),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_98),X_97))),multiply(inverse(greatest_lower_bound(X_97,X_98)),inverse(inverse(X_98)))) )],[refute_0_859,refute_0_866]) ).
cnf(refute_0_868,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))) = multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433),
inference(subst,[],[refute_0_867:[bind(X_98,$fot(X_433))]]) ).
cnf(refute_0_869,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))) != multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)
| multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433) = inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)))]]) ).
cnf(refute_0_870,plain,
multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433) = inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))),multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)) )],[refute_0_868,refute_0_869]) ).
cnf(refute_0_871,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433) != inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))) ),[0,1,1,0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))]]) ).
cnf(refute_0_872,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433),inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(multiply(inverse(greatest_lower_bound(X_97,X_433)),X_433)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))) )],[refute_0_845,refute_0_872]) ).
cnf(refute_0_874,plain,
inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) = greatest_lower_bound(identity,multiply(inverse(X_433),X_97)),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))]]) ).
cnf(refute_0_875,plain,
least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) = least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))))]]) ).
cnf(refute_0_876,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) != greatest_lower_bound(identity,multiply(inverse(X_433),X_97))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) != least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) = least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))),least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))]]) ).
cnf(refute_0_877,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) != greatest_lower_bound(identity,multiply(inverse(X_433),X_97))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) = least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))),least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) = least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97))),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))),greatest_lower_bound(identity,multiply(inverse(X_433),X_97))) )],[refute_0_874,refute_0_877]) ).
cnf(refute_0_879,plain,
multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) = multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))),
introduced(tautology,[refl,[$fot(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))))]]) ).
cnf(refute_0_880,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) != multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) != least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) = multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))),multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))))) ),[1,1],$fot(least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))]]) ).
cnf(refute_0_881,plain,
( least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) != least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) = multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) ),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))),multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))))) )],[refute_0_879,refute_0_880]) ).
cnf(refute_0_882,plain,
multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) = multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))),least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) )],[refute_0_878,refute_0_881]) ).
cnf(refute_0_883,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) != multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))) ),[0],$fot(multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))]]) ).
cnf(refute_0_884,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) ),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))),multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97))))) )],[refute_0_882,refute_0_883]) ).
cnf(refute_0_885,plain,
inverse(inverse(greatest_lower_bound(X_97,X_433))) = greatest_lower_bound(X_97,X_433),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(greatest_lower_bound(X_97,X_433)))]]) ).
cnf(refute_0_886,plain,
least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))))]]) ).
cnf(refute_0_887,plain,
( inverse(inverse(greatest_lower_bound(X_97,X_433))) != greatest_lower_bound(X_97,X_433)
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))) ),[1,1],$fot(greatest_lower_bound(X_97,X_433))]]) ).
cnf(refute_0_888,plain,
( inverse(inverse(greatest_lower_bound(X_97,X_433))) != greatest_lower_bound(X_97,X_433)
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))) )],[refute_0_886,refute_0_887]) ).
cnf(refute_0_889,plain,
least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_97,X_433))),greatest_lower_bound(X_97,X_433)) )],[refute_0_885,refute_0_888]) ).
cnf(refute_0_890,plain,
( multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))) != least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433))
| multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))),least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433))) ),[0],$fot(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))))]]) ).
cnf(refute_0_891,plain,
( multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433)))),least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433))) )],[refute_0_889,refute_0_890]) ).
cnf(refute_0_892,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))
| multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433)) ),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))) )],[refute_0_884,refute_0_891]) ).
cnf(refute_0_893,plain,
multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_97,X_433)),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_97)))))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_97,X_433))))) )],[refute_0_873,refute_0_892]) ).
cnf(refute_0_894,plain,
multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)),
inference(subst,[],[refute_0_893:[bind(X_97,$fot(X_100))]]) ).
cnf(refute_0_895,plain,
inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) = greatest_lower_bound(identity,multiply(inverse(X_433),X_100)),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))]]) ).
cnf(refute_0_896,plain,
least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) = least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))))]]) ).
cnf(refute_0_897,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) != greatest_lower_bound(identity,multiply(inverse(X_433),X_100))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) != least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) = least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))),least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))]]) ).
cnf(refute_0_898,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) != greatest_lower_bound(identity,multiply(inverse(X_433),X_100))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) = least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))),least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) = least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100))),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))),greatest_lower_bound(identity,multiply(inverse(X_433),X_100))) )],[refute_0_895,refute_0_898]) ).
cnf(refute_0_900,plain,
multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),
introduced(tautology,[refl,[$fot(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))))]]) ).
cnf(refute_0_901,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) != multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))))
| least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) != least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))))) ),[1,1],$fot(least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))]]) ).
cnf(refute_0_902,plain,
( least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) != least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) ),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))))) )],[refute_0_900,refute_0_901]) ).
cnf(refute_0_903,plain,
multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))),least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) )],[refute_0_899,refute_0_902]) ).
cnf(refute_0_904,plain,
( multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) != least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) != multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))))),bind(Y0,$fot(multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),bind(Z0,$fot(least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433))))]]) ).
cnf(refute_0_905,plain,
( multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))) != least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) ),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100))))) )],[refute_0_903,refute_0_904]) ).
cnf(refute_0_906,plain,
multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))),least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433))) )],[refute_0_894,refute_0_905]) ).
cnf(refute_0_907,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) != least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433))
| multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))) ),[0],$fot(least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)))]]) ).
cnf(refute_0_908,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) ),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433))) )],[refute_0_906,refute_0_907]) ).
cnf(refute_0_909,plain,
inverse(inverse(greatest_lower_bound(X_433,X_100))) = greatest_lower_bound(X_433,X_100),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(greatest_lower_bound(X_433,X_100)))]]) ).
cnf(refute_0_910,plain,
least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) = least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))))]]) ).
cnf(refute_0_911,plain,
( inverse(inverse(greatest_lower_bound(X_433,X_100))) != greatest_lower_bound(X_433,X_100)
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))) ),[1,1],$fot(greatest_lower_bound(X_433,X_100))]]) ).
cnf(refute_0_912,plain,
( inverse(inverse(greatest_lower_bound(X_433,X_100))) != greatest_lower_bound(X_433,X_100)
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_433,X_100))),greatest_lower_bound(X_433,X_100)) )],[refute_0_909,refute_0_912]) ).
cnf(refute_0_914,plain,
( least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))) != least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100))
| least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)),least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100))) ),[0],$fot(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))))]]) ).
cnf(refute_0_915,plain,
( least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100)))),least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100))) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
( multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))) != least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))
| least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))) )],[refute_0_908,refute_0_915]) ).
cnf(refute_0_917,plain,
least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_100,X_433)) = least_upper_bound(multiply(X_433,X_434),greatest_lower_bound(X_433,X_100)),
inference(resolve,[$cnf( $equal(multiply(X_433,least_upper_bound(X_434,inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_433),X_100)))))),least_upper_bound(multiply(X_433,X_434),inverse(inverse(greatest_lower_bound(X_433,X_100))))) )],[refute_0_844,refute_0_916]) ).
cnf(refute_0_918,plain,
least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11)) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))),
inference(subst,[],[refute_0_917:[bind(X_100,$fot(multiply(X_11,X_438))),bind(X_433,$fot(X_11)),bind(X_434,$fot(greatest_lower_bound(identity,X_438)))]]) ).
cnf(refute_0_919,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),
inference(subst,[],[refute_0_671:[bind(X_34,$fot(X_297)),bind(X_35,$fot(multiply(X,Y))),bind(X_36,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_920,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) != least_upper_bound(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),least_upper_bound(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) ),[1,0],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_921,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) != least_upper_bound(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_146,refute_0_920]) ).
cnf(refute_0_922,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),least_upper_bound(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) )],[refute_0_919,refute_0_921]) ).
cnf(refute_0_923,plain,
greatest_lower_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(subst,[],[refute_0_146:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_924,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297))]]) ).
cnf(refute_0_925,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) != least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297)
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297)) ),[1,0],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_926,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297)) )],[refute_0_924,refute_0_925]) ).
cnf(refute_0_927,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_923,refute_0_926]) ).
cnf(refute_0_928,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) != least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297)
| least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) ),[0],$fot(least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297))]]) ).
cnf(refute_0_929,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297)) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) = greatest_lower_bound(Y,Z),
inference(subst,[],[refute_0_222:[bind(X_11,$fot(Z)),bind(X_16,$fot(Y))]]) ).
cnf(refute_0_931,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_932,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_933,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( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_930,refute_0_933]) ).
cnf(refute_0_935,plain,
least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))))]]) ).
cnf(refute_0_936,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(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) != least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))
| least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))),least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_937,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(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))),least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_934,refute_0_937]) ).
cnf(refute_0_939,plain,
least_upper_bound(X_239,least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z))),
inference(subst,[],[refute_0_289:[bind(Y,$fot(X_239)),bind(X_24,$fot(multiply(X,Y))),bind(X_26,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_940,plain,
( least_upper_bound(X_239,least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z)))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_239,least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z)))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_941,plain,
( least_upper_bound(X_239,least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z)))
| least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_154,refute_0_940]) ).
cnf(refute_0_942,plain,
least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_239,least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z)))) )],[refute_0_939,refute_0_941]) ).
cnf(refute_0_943,plain,
( least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z)))
| least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z))) = least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z)))))]]) ).
cnf(refute_0_944,plain,
least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z))) = least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_239,multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Y),least_upper_bound(X_239,multiply(X,Z)))) )],[refute_0_942,refute_0_943]) ).
cnf(refute_0_945,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))),
inference(subst,[],[refute_0_944:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y))),bind(X_239,$fot(X_297))]]) ).
cnf(refute_0_946,plain,
( least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) != least_upper_bound(X_297,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)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))))),bind(Y0,$fot(least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))))),bind(Z0,$fot(least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))))]]) ).
cnf(refute_0_947,plain,
( least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))),least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))) )],[refute_0_945,refute_0_946]) ).
cnf(refute_0_948,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))) )],[refute_0_938,refute_0_947]) ).
cnf(refute_0_949,plain,
least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_950,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_951,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_949,refute_0_950]) ).
cnf(refute_0_952,plain,
least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_923,refute_0_951]) ).
cnf(refute_0_953,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))))]]) ).
cnf(refute_0_954,plain,
( least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) ),[1,1],$fot(least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_955,plain,
( least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) )],[refute_0_952,refute_0_955]) ).
cnf(refute_0_957,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y))))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))))),bind(Z0,$fot(least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))))]]) ).
cnf(refute_0_958,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y))))) )],[refute_0_956,refute_0_957]) ).
cnf(refute_0_959,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Z,Y)))),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))) )],[refute_0_948,refute_0_958]) ).
cnf(refute_0_960,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))
| least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) ),[1],$fot(least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_961,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))
| least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) )],[refute_0_929,refute_0_961]) ).
cnf(refute_0_963,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) = least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),X_297),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),least_upper_bound(X_297,greatest_lower_bound(multiply(X,Z),multiply(X,Y))))) )],[refute_0_922,refute_0_962]) ).
cnf(refute_0_964,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) != least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))
| least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) = least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297))),bind(Y0,$fot(least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))))]]) ).
cnf(refute_0_965,plain,
least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z))) = least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Z,Y)),X_297),least_upper_bound(X_297,multiply(X,greatest_lower_bound(Y,Z)))) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11)),
inference(subst,[],[refute_0_965:[bind(X,$fot(X_11)),bind(Y,$fot(X_438)),bind(Z,$fot(identity)),bind(X_297,$fot(greatest_lower_bound(multiply(X_11,X_438),X_11)))]]) ).
cnf(refute_0_967,plain,
( least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11)) != least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) != least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))))),bind(Y0,$fot(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11)))),bind(Z0,$fot(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))))]]) ).
cnf(refute_0_968,plain,
( least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11)) != least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))),least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11))) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11)),least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))) )],[refute_0_918,refute_0_968]) ).
cnf(refute_0_970,plain,
( least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) != multiply(X_11,greatest_lower_bound(identity,X_438))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) != least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))))),bind(Y0,$fot(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))))),bind(Z0,$fot(multiply(X_11,greatest_lower_bound(identity,X_438))))]]) ).
cnf(refute_0_971,plain,
( least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))) != multiply(X_11,greatest_lower_bound(identity,X_438))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))),least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438)))) )],[refute_0_969,refute_0_970]) ).
cnf(refute_0_972,plain,
least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) = multiply(X_11,greatest_lower_bound(identity,X_438)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(X_11,multiply(X_11,X_438))),multiply(X_11,greatest_lower_bound(identity,X_438))) )],[refute_0_814,refute_0_971]) ).
cnf(refute_0_973,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) != multiply(X_11,greatest_lower_bound(identity,X_438))
| least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) != greatest_lower_bound(multiply(X_11,X_438),X_11)
| multiply(X_11,greatest_lower_bound(identity,X_438)) = greatest_lower_bound(multiply(X_11,X_438),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))),greatest_lower_bound(multiply(X_11,X_438),X_11)) ),[0],$fot(multiply(X_11,greatest_lower_bound(identity,X_438)))]]) ).
cnf(refute_0_974,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) != greatest_lower_bound(multiply(X_11,X_438),X_11)
| multiply(X_11,greatest_lower_bound(identity,X_438)) = greatest_lower_bound(multiply(X_11,X_438),X_11) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))),multiply(X_11,greatest_lower_bound(identity,X_438))) )],[refute_0_972,refute_0_973]) ).
cnf(refute_0_975,plain,
X_39 = multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),multiply(greatest_lower_bound(inverse(X_39),X_116),X_39)),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(greatest_lower_bound(inverse(X_39),X_116)))]]) ).
cnf(refute_0_976,plain,
multiply(greatest_lower_bound(inverse(X_110),X_112),X_110) = greatest_lower_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_110)),bind(Y,$fot(inverse(X_110))),bind(Z,$fot(X_112))]]) ).
cnf(refute_0_977,plain,
multiply(inverse(X_110),X_110) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_110))]]) ).
cnf(refute_0_978,plain,
( multiply(greatest_lower_bound(inverse(X_110),X_112),X_110) != greatest_lower_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))
| multiply(inverse(X_110),X_110) != identity
| multiply(greatest_lower_bound(inverse(X_110),X_112),X_110) = greatest_lower_bound(identity,multiply(X_112,X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_110),X_112),X_110),greatest_lower_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_979,plain,
( multiply(greatest_lower_bound(inverse(X_110),X_112),X_110) != greatest_lower_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))
| multiply(greatest_lower_bound(inverse(X_110),X_112),X_110) = greatest_lower_bound(identity,multiply(X_112,X_110)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_110),X_110),identity) )],[refute_0_977,refute_0_978]) ).
cnf(refute_0_980,plain,
multiply(greatest_lower_bound(inverse(X_110),X_112),X_110) = greatest_lower_bound(identity,multiply(X_112,X_110)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_110),X_112),X_110),greatest_lower_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))) )],[refute_0_976,refute_0_979]) ).
cnf(refute_0_981,plain,
multiply(greatest_lower_bound(inverse(X_39),X_116),X_39) = greatest_lower_bound(identity,multiply(X_116,X_39)),
inference(subst,[],[refute_0_980:[bind(X_110,$fot(X_39)),bind(X_112,$fot(X_116))]]) ).
cnf(refute_0_982,plain,
( X_39 != multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),multiply(greatest_lower_bound(inverse(X_39),X_116),X_39))
| multiply(greatest_lower_bound(inverse(X_39),X_116),X_39) != greatest_lower_bound(identity,multiply(X_116,X_39))
| X_39 = multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),greatest_lower_bound(identity,multiply(X_116,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(X_39,multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),multiply(greatest_lower_bound(inverse(X_39),X_116),X_39))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_116,X_39)))]]) ).
cnf(refute_0_983,plain,
( X_39 != multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),multiply(greatest_lower_bound(inverse(X_39),X_116),X_39))
| X_39 = multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),greatest_lower_bound(identity,multiply(X_116,X_39))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_39),X_116),X_39),greatest_lower_bound(identity,multiply(X_116,X_39))) )],[refute_0_981,refute_0_982]) ).
cnf(refute_0_984,plain,
X_39 = multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),greatest_lower_bound(identity,multiply(X_116,X_39))),
inference(resolve,[$cnf( $equal(X_39,multiply(inverse(greatest_lower_bound(inverse(X_39),X_116)),multiply(greatest_lower_bound(inverse(X_39),X_116),X_39))) )],[refute_0_975,refute_0_983]) ).
cnf(refute_0_985,plain,
greatest_lower_bound(X_91,X_92) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)))),
inference(subst,[],[refute_0_984:[bind(X_116,$fot(inverse(X_92))),bind(X_39,$fot(greatest_lower_bound(X_91,X_92)))]]) ).
cnf(refute_0_986,plain,
( multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)) != greatest_lower_bound(identity,multiply(inverse(X_92),X_91))
| greatest_lower_bound(X_91,X_92) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,multiply(inverse(X_92),greatest_lower_bound(X_91,X_92))))
| greatest_lower_bound(X_91,X_92) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_91,X_92),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,multiply(inverse(X_92),greatest_lower_bound(X_91,X_92))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))]]) ).
cnf(refute_0_987,plain,
( greatest_lower_bound(X_91,X_92) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,multiply(inverse(X_92),greatest_lower_bound(X_91,X_92))))
| greatest_lower_bound(X_91,X_92) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_92),greatest_lower_bound(X_91,X_92)),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) )],[refute_0_855,refute_0_986]) ).
cnf(refute_0_988,plain,
greatest_lower_bound(X_91,X_92) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_91,X_92),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,multiply(inverse(X_92),greatest_lower_bound(X_91,X_92))))) )],[refute_0_985,refute_0_987]) ).
cnf(refute_0_989,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(identity,multiply(inverse(X_92),X_91)),
inference(subst,[],[refute_0_551:[bind(X_16,$fot(multiply(inverse(X_92),X_91))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_990,plain,
multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))))]]) ).
cnf(refute_0_991,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))
| greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != greatest_lower_bound(identity,multiply(inverse(X_92),X_91))
| multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))]]) ).
cnf(refute_0_992,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != greatest_lower_bound(identity,multiply(inverse(X_92),X_91))
| multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))) )],[refute_0_990,refute_0_991]) ).
cnf(refute_0_993,plain,
multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) )],[refute_0_989,refute_0_992]) ).
cnf(refute_0_994,plain,
multiply(inverse(X_126),inverse(multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)))) = inverse(greatest_lower_bound(X_126,X_127)),
inference(subst,[],[refute_0_54:[bind(X_38,$fot(greatest_lower_bound(X_126,X_127))),bind(X_51,$fot(inverse(X_126)))]]) ).
cnf(refute_0_995,plain,
multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)) = greatest_lower_bound(multiply(X_111,inverse(X_111)),multiply(X_112,inverse(X_111))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_111))),bind(Y,$fot(X_111)),bind(Z,$fot(X_112))]]) ).
cnf(refute_0_996,plain,
multiply(X_111,inverse(X_111)) = identity,
inference(subst,[],[refute_0_27:[bind(X_44,$fot(X_111))]]) ).
cnf(refute_0_997,plain,
( multiply(X_111,inverse(X_111)) != identity
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)) != greatest_lower_bound(multiply(X_111,inverse(X_111)),multiply(X_112,inverse(X_111)))
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)) = greatest_lower_bound(identity,multiply(X_112,inverse(X_111))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)),greatest_lower_bound(multiply(X_111,inverse(X_111)),multiply(X_112,inverse(X_111)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_998,plain,
( multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)) != greatest_lower_bound(multiply(X_111,inverse(X_111)),multiply(X_112,inverse(X_111)))
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)) = greatest_lower_bound(identity,multiply(X_112,inverse(X_111))) ),
inference(resolve,[$cnf( $equal(multiply(X_111,inverse(X_111)),identity) )],[refute_0_996,refute_0_997]) ).
cnf(refute_0_999,plain,
multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)) = greatest_lower_bound(identity,multiply(X_112,inverse(X_111))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),inverse(X_111)),greatest_lower_bound(multiply(X_111,inverse(X_111)),multiply(X_112,inverse(X_111)))) )],[refute_0_995,refute_0_998]) ).
cnf(refute_0_1000,plain,
multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)) = greatest_lower_bound(identity,multiply(X_127,inverse(X_126))),
inference(subst,[],[refute_0_999:[bind(X_111,$fot(X_126)),bind(X_112,$fot(X_127))]]) ).
cnf(refute_0_1001,plain,
( multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)) != greatest_lower_bound(identity,multiply(X_127,inverse(X_126)))
| multiply(inverse(X_126),inverse(multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)))) != inverse(greatest_lower_bound(X_126,X_127))
| multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) = inverse(greatest_lower_bound(X_126,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_126),inverse(multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)))),inverse(greatest_lower_bound(X_126,X_127))) ),[0,1,0],$fot(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))]]) ).
cnf(refute_0_1002,plain,
( multiply(inverse(X_126),inverse(multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)))) != inverse(greatest_lower_bound(X_126,X_127))
| multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) = inverse(greatest_lower_bound(X_126,X_127)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)),greatest_lower_bound(identity,multiply(X_127,inverse(X_126)))) )],[refute_0_1000,refute_0_1001]) ).
cnf(refute_0_1003,plain,
multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) = inverse(greatest_lower_bound(X_126,X_127)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_126),inverse(multiply(greatest_lower_bound(X_126,X_127),inverse(X_126)))),inverse(greatest_lower_bound(X_126,X_127))) )],[refute_0_994,refute_0_1002]) ).
cnf(refute_0_1004,plain,
inverse(inverse(X_126)) = X_126,
inference(subst,[],[refute_0_335:[bind(X_44,$fot(X_126))]]) ).
cnf(refute_0_1005,plain,
greatest_lower_bound(X_127,inverse(inverse(X_126))) = greatest_lower_bound(X_127,inverse(inverse(X_126))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_127,inverse(inverse(X_126))))]]) ).
cnf(refute_0_1006,plain,
( greatest_lower_bound(X_127,inverse(inverse(X_126))) != greatest_lower_bound(X_127,inverse(inverse(X_126)))
| inverse(inverse(X_126)) != X_126
| greatest_lower_bound(X_127,inverse(inverse(X_126))) = greatest_lower_bound(X_127,X_126) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_127,inverse(inverse(X_126))),greatest_lower_bound(X_127,inverse(inverse(X_126)))) ),[1,1],$fot(X_126)]]) ).
cnf(refute_0_1007,plain,
( inverse(inverse(X_126)) != X_126
| greatest_lower_bound(X_127,inverse(inverse(X_126))) = greatest_lower_bound(X_127,X_126) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_127,inverse(inverse(X_126))),greatest_lower_bound(X_127,inverse(inverse(X_126)))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
greatest_lower_bound(X_127,inverse(inverse(X_126))) = greatest_lower_bound(X_127,X_126),
inference(resolve,[$cnf( $equal(inverse(inverse(X_126)),X_126) )],[refute_0_1004,refute_0_1007]) ).
cnf(refute_0_1009,plain,
inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))) = inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))))]]) ).
cnf(refute_0_1010,plain,
( greatest_lower_bound(X_127,inverse(inverse(X_126))) != greatest_lower_bound(X_127,X_126)
| inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))) != inverse(greatest_lower_bound(X_127,inverse(inverse(X_126))))
| inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))) = inverse(greatest_lower_bound(X_127,X_126)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))),inverse(greatest_lower_bound(X_127,inverse(inverse(X_126))))) ),[1,0],$fot(greatest_lower_bound(X_127,X_126))]]) ).
cnf(refute_0_1011,plain,
( greatest_lower_bound(X_127,inverse(inverse(X_126))) != greatest_lower_bound(X_127,X_126)
| inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))) = inverse(greatest_lower_bound(X_127,X_126)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))),inverse(greatest_lower_bound(X_127,inverse(inverse(X_126))))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))) = inverse(greatest_lower_bound(X_127,X_126)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_127,inverse(inverse(X_126))),greatest_lower_bound(X_127,X_126)) )],[refute_0_1008,refute_0_1011]) ).
cnf(refute_0_1013,plain,
multiply(X_51,inverse(multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51))) = inverse(greatest_lower_bound(X_114,inverse(X_51))),
inference(subst,[],[refute_0_54:[bind(X_38,$fot(greatest_lower_bound(X_114,inverse(X_51))))]]) ).
cnf(refute_0_1014,plain,
multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) = greatest_lower_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(inverse(X_110)))]]) ).
cnf(refute_0_1015,plain,
( multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) != greatest_lower_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))
| multiply(inverse(X_110),X_110) != identity
| multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) = greatest_lower_bound(multiply(X_111,X_110),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1016,plain,
( multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) != greatest_lower_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))
| multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) = greatest_lower_bound(multiply(X_111,X_110),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_110),X_110),identity) )],[refute_0_977,refute_0_1015]) ).
cnf(refute_0_1017,plain,
multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) = greatest_lower_bound(multiply(X_111,X_110),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110),greatest_lower_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))) )],[refute_0_1014,refute_0_1016]) ).
cnf(refute_0_1018,plain,
greatest_lower_bound(multiply(X_111,X_110),identity) = greatest_lower_bound(identity,multiply(X_111,X_110)),
inference(subst,[],[refute_0_164:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_111,X_110)))]]) ).
cnf(refute_0_1019,plain,
( multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) != greatest_lower_bound(multiply(X_111,X_110),identity)
| greatest_lower_bound(multiply(X_111,X_110),identity) != greatest_lower_bound(identity,multiply(X_111,X_110))
| multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) = greatest_lower_bound(identity,multiply(X_111,X_110)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110),greatest_lower_bound(identity,multiply(X_111,X_110))) ),[0],$fot(greatest_lower_bound(multiply(X_111,X_110),identity))]]) ).
cnf(refute_0_1020,plain,
( multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) != greatest_lower_bound(multiply(X_111,X_110),identity)
| multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) = greatest_lower_bound(identity,multiply(X_111,X_110)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,X_110),identity),greatest_lower_bound(identity,multiply(X_111,X_110))) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110) = greatest_lower_bound(identity,multiply(X_111,X_110)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,inverse(X_110)),X_110),greatest_lower_bound(multiply(X_111,X_110),identity)) )],[refute_0_1017,refute_0_1020]) ).
cnf(refute_0_1022,plain,
multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51) = greatest_lower_bound(identity,multiply(X_114,X_51)),
inference(subst,[],[refute_0_1021:[bind(X_110,$fot(X_51)),bind(X_111,$fot(X_114))]]) ).
cnf(refute_0_1023,plain,
( multiply(X_51,inverse(multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51))) != inverse(greatest_lower_bound(X_114,inverse(X_51)))
| multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51) != greatest_lower_bound(identity,multiply(X_114,X_51))
| multiply(X_51,inverse(greatest_lower_bound(identity,multiply(X_114,X_51)))) = inverse(greatest_lower_bound(X_114,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,inverse(multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51))),inverse(greatest_lower_bound(X_114,inverse(X_51)))) ),[0,1,0],$fot(greatest_lower_bound(identity,multiply(X_114,X_51)))]]) ).
cnf(refute_0_1024,plain,
( multiply(X_51,inverse(multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51))) != inverse(greatest_lower_bound(X_114,inverse(X_51)))
| multiply(X_51,inverse(greatest_lower_bound(identity,multiply(X_114,X_51)))) = inverse(greatest_lower_bound(X_114,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51),greatest_lower_bound(identity,multiply(X_114,X_51))) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
multiply(X_51,inverse(greatest_lower_bound(identity,multiply(X_114,X_51)))) = inverse(greatest_lower_bound(X_114,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(X_51,inverse(multiply(greatest_lower_bound(X_114,inverse(X_51)),X_51))),inverse(greatest_lower_bound(X_114,inverse(X_51)))) )],[refute_0_1013,refute_0_1024]) ).
cnf(refute_0_1026,plain,
multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) = inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))),
inference(subst,[],[refute_0_1025:[bind(X_114,$fot(X_127)),bind(X_51,$fot(inverse(X_126)))]]) ).
cnf(refute_0_1027,plain,
( multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) != inverse(greatest_lower_bound(X_127,inverse(inverse(X_126))))
| inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))) != inverse(greatest_lower_bound(X_127,X_126))
| multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) = inverse(greatest_lower_bound(X_127,X_126)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))))),bind(Y0,$fot(inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_127,X_126))))]]) ).
cnf(refute_0_1028,plain,
( inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))) != inverse(greatest_lower_bound(X_127,X_126))
| multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) = inverse(greatest_lower_bound(X_127,X_126)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))),inverse(greatest_lower_bound(X_127,inverse(inverse(X_126))))) )],[refute_0_1026,refute_0_1027]) ).
cnf(refute_0_1029,plain,
multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) = inverse(greatest_lower_bound(X_127,X_126)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_127,inverse(inverse(X_126)))),inverse(greatest_lower_bound(X_127,X_126))) )],[refute_0_1012,refute_0_1028]) ).
cnf(refute_0_1030,plain,
( multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) != inverse(greatest_lower_bound(X_126,X_127))
| multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) != inverse(greatest_lower_bound(X_127,X_126))
| inverse(greatest_lower_bound(X_127,X_126)) = inverse(greatest_lower_bound(X_126,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))),inverse(greatest_lower_bound(X_126,X_127))) ),[0],$fot(inverse(greatest_lower_bound(X_127,X_126)))]]) ).
cnf(refute_0_1031,plain,
( multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))) != inverse(greatest_lower_bound(X_126,X_127))
| inverse(greatest_lower_bound(X_127,X_126)) = inverse(greatest_lower_bound(X_126,X_127)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))),inverse(greatest_lower_bound(X_127,X_126))) )],[refute_0_1029,refute_0_1030]) ).
cnf(refute_0_1032,plain,
inverse(greatest_lower_bound(X_127,X_126)) = inverse(greatest_lower_bound(X_126,X_127)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_126),inverse(greatest_lower_bound(identity,multiply(X_127,inverse(X_126))))),inverse(greatest_lower_bound(X_126,X_127))) )],[refute_0_1003,refute_0_1031]) ).
cnf(refute_0_1033,plain,
( inverse(greatest_lower_bound(X_127,X_126)) != inverse(greatest_lower_bound(X_126,X_127))
| inverse(greatest_lower_bound(X_126,X_127)) = inverse(greatest_lower_bound(X_127,X_126)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(greatest_lower_bound(X_127,X_126)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_126,X_127))))]]) ).
cnf(refute_0_1034,plain,
inverse(greatest_lower_bound(X_126,X_127)) = inverse(greatest_lower_bound(X_127,X_126)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_127,X_126)),inverse(greatest_lower_bound(X_126,X_127))) )],[refute_0_1032,refute_0_1033]) ).
cnf(refute_0_1035,plain,
inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))) = inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),
inference(subst,[],[refute_0_1034:[bind(X_126,$fot(inverse(greatest_lower_bound(X_91,X_92)))),bind(X_127,$fot(inverse(X_92)))]]) ).
cnf(refute_0_1036,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))))]]) ).
cnf(refute_0_1037,plain,
( multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))
| inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))) != inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))) ),[1,0],$fot(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))))]]) ).
cnf(refute_0_1038,plain,
( inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))) != inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))) )],[refute_0_1036,refute_0_1037]) ).
cnf(refute_0_1039,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92))))) )],[refute_0_1035,refute_0_1038]) ).
cnf(refute_0_1040,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))))]]) ).
cnf(refute_0_1041,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))) )],[refute_0_1039,refute_0_1040]) ).
cnf(refute_0_1042,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) )],[refute_0_993,refute_0_1041]) ).
cnf(refute_0_1043,plain,
( multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))
| greatest_lower_bound(X_91,X_92) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))
| greatest_lower_bound(X_91,X_92) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_91,X_92),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))) ),[1],$fot(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))]]) ).
cnf(refute_0_1044,plain,
( greatest_lower_bound(X_91,X_92) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))
| greatest_lower_bound(X_91,X_92) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) )],[refute_0_1042,refute_0_1043]) ).
cnf(refute_0_1045,plain,
greatest_lower_bound(X_91,X_92) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_91,X_92),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_91,X_92)),inverse(X_92))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))) )],[refute_0_988,refute_0_1044]) ).
cnf(refute_0_1046,plain,
multiply(X_92,identity) = X_92,
inference(subst,[],[refute_0_50:[bind(X_41,$fot(X_92))]]) ).
cnf(refute_0_1047,plain,
greatest_lower_bound(multiply(X_92,identity),X_91) = greatest_lower_bound(multiply(X_92,identity),X_91),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_92,identity),X_91))]]) ).
cnf(refute_0_1048,plain,
( multiply(X_92,identity) != X_92
| greatest_lower_bound(multiply(X_92,identity),X_91) != greatest_lower_bound(multiply(X_92,identity),X_91)
| greatest_lower_bound(multiply(X_92,identity),X_91) = greatest_lower_bound(X_92,X_91) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_92,identity),X_91),greatest_lower_bound(multiply(X_92,identity),X_91)) ),[1,0],$fot(X_92)]]) ).
cnf(refute_0_1049,plain,
( multiply(X_92,identity) != X_92
| greatest_lower_bound(multiply(X_92,identity),X_91) = greatest_lower_bound(X_92,X_91) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_92,identity),X_91),greatest_lower_bound(multiply(X_92,identity),X_91)) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
greatest_lower_bound(multiply(X_92,identity),X_91) = greatest_lower_bound(X_92,X_91),
inference(resolve,[$cnf( $equal(multiply(X_92,identity),X_92) )],[refute_0_1046,refute_0_1049]) ).
cnf(refute_0_1051,plain,
multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))) = greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,multiply(inverse(X_90),X_39))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_90)),bind(Y,$fot(X_91)),bind(Z,$fot(multiply(inverse(X_90),X_39)))]]) ).
cnf(refute_0_1052,plain,
X_39 = multiply(X_90,multiply(inverse(X_90),X_39)),
inference(subst,[],[refute_0_456:[bind(X_44,$fot(X_90))]]) ).
cnf(refute_0_1053,plain,
( X_39 != multiply(X_90,multiply(inverse(X_90),X_39))
| multiply(X_90,multiply(inverse(X_90),X_39)) = X_39 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_39)),bind(Y0,$fot(multiply(X_90,multiply(inverse(X_90),X_39))))]]) ).
cnf(refute_0_1054,plain,
multiply(X_90,multiply(inverse(X_90),X_39)) = X_39,
inference(resolve,[$cnf( $equal(X_39,multiply(X_90,multiply(inverse(X_90),X_39))) )],[refute_0_1052,refute_0_1053]) ).
cnf(refute_0_1055,plain,
( multiply(X_90,multiply(inverse(X_90),X_39)) != X_39
| multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))) != greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,multiply(inverse(X_90),X_39)))
| multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))) = greatest_lower_bound(multiply(X_90,X_91),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))),greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,multiply(inverse(X_90),X_39)))) ),[1,1],$fot(X_39)]]) ).
cnf(refute_0_1056,plain,
( multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))) != greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,multiply(inverse(X_90),X_39)))
| multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))) = greatest_lower_bound(multiply(X_90,X_91),X_39) ),
inference(resolve,[$cnf( $equal(multiply(X_90,multiply(inverse(X_90),X_39)),X_39) )],[refute_0_1054,refute_0_1055]) ).
cnf(refute_0_1057,plain,
multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))) = greatest_lower_bound(multiply(X_90,X_91),X_39),
inference(resolve,[$cnf( $equal(multiply(X_90,greatest_lower_bound(X_91,multiply(inverse(X_90),X_39))),greatest_lower_bound(multiply(X_90,X_91),multiply(X_90,multiply(inverse(X_90),X_39)))) )],[refute_0_1051,refute_0_1056]) ).
cnf(refute_0_1058,plain,
multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(multiply(X_92,identity),X_91),
inference(subst,[],[refute_0_1057:[bind(X_39,$fot(X_91)),bind(X_90,$fot(X_92)),bind(X_91,$fot(identity))]]) ).
cnf(refute_0_1059,plain,
( multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != greatest_lower_bound(multiply(X_92,identity),X_91)
| greatest_lower_bound(multiply(X_92,identity),X_91) != greatest_lower_bound(X_92,X_91)
| multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(X_92,X_91) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_92,identity),X_91))),bind(Z0,$fot(greatest_lower_bound(X_92,X_91)))]]) ).
cnf(refute_0_1060,plain,
( greatest_lower_bound(multiply(X_92,identity),X_91) != greatest_lower_bound(X_92,X_91)
| multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(X_92,X_91) ),
inference(resolve,[$cnf( $equal(multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),greatest_lower_bound(multiply(X_92,identity),X_91)) )],[refute_0_1058,refute_0_1059]) ).
cnf(refute_0_1061,plain,
multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(X_92,X_91),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_92,identity),X_91),greatest_lower_bound(X_92,X_91)) )],[refute_0_1050,refute_0_1060]) ).
cnf(refute_0_1062,plain,
multiply(inverse(multiply(X_52,greatest_lower_bound(X_94,inverse(X_52)))),X_52) = inverse(greatest_lower_bound(X_94,inverse(X_52))),
inference(subst,[],[refute_0_387:[bind(X_38,$fot(greatest_lower_bound(X_94,inverse(X_52))))]]) ).
cnf(refute_0_1063,plain,
multiply(X_52,greatest_lower_bound(X_94,inverse(X_52))) = greatest_lower_bound(identity,multiply(X_52,X_94)),
inference(subst,[],[refute_0_365:[bind(X_90,$fot(X_52)),bind(X_91,$fot(X_94))]]) ).
cnf(refute_0_1064,plain,
( multiply(X_52,greatest_lower_bound(X_94,inverse(X_52))) != greatest_lower_bound(identity,multiply(X_52,X_94))
| multiply(inverse(multiply(X_52,greatest_lower_bound(X_94,inverse(X_52)))),X_52) != inverse(greatest_lower_bound(X_94,inverse(X_52)))
| multiply(inverse(greatest_lower_bound(identity,multiply(X_52,X_94))),X_52) = inverse(greatest_lower_bound(X_94,inverse(X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_52,greatest_lower_bound(X_94,inverse(X_52)))),X_52),inverse(greatest_lower_bound(X_94,inverse(X_52)))) ),[0,0,0],$fot(greatest_lower_bound(identity,multiply(X_52,X_94)))]]) ).
cnf(refute_0_1065,plain,
( multiply(inverse(multiply(X_52,greatest_lower_bound(X_94,inverse(X_52)))),X_52) != inverse(greatest_lower_bound(X_94,inverse(X_52)))
| multiply(inverse(greatest_lower_bound(identity,multiply(X_52,X_94))),X_52) = inverse(greatest_lower_bound(X_94,inverse(X_52))) ),
inference(resolve,[$cnf( $equal(multiply(X_52,greatest_lower_bound(X_94,inverse(X_52))),greatest_lower_bound(identity,multiply(X_52,X_94))) )],[refute_0_1063,refute_0_1064]) ).
cnf(refute_0_1066,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(X_52,X_94))),X_52) = inverse(greatest_lower_bound(X_94,inverse(X_52))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_52,greatest_lower_bound(X_94,inverse(X_52)))),X_52),inverse(greatest_lower_bound(X_94,inverse(X_52)))) )],[refute_0_1062,refute_0_1065]) ).
cnf(refute_0_1067,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)))),greatest_lower_bound(X_111,X_112)) = inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))),
inference(subst,[],[refute_0_1066:[bind(X_52,$fot(greatest_lower_bound(X_111,X_112))),bind(X_94,$fot(inverse(X_112)))]]) ).
cnf(refute_0_1068,plain,
multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) = greatest_lower_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_112))),bind(Y,$fot(X_111)),bind(Z,$fot(X_112))]]) ).
cnf(refute_0_1069,plain,
multiply(X_112,inverse(X_112)) = identity,
inference(subst,[],[refute_0_27:[bind(X_44,$fot(X_112))]]) ).
cnf(refute_0_1070,plain,
( multiply(X_112,inverse(X_112)) != identity
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) != greatest_lower_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) = greatest_lower_bound(multiply(X_111,inverse(X_112)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)),greatest_lower_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1071,plain,
( multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) != greatest_lower_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) = greatest_lower_bound(multiply(X_111,inverse(X_112)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_112,inverse(X_112)),identity) )],[refute_0_1069,refute_0_1070]) ).
cnf(refute_0_1072,plain,
multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) = greatest_lower_bound(multiply(X_111,inverse(X_112)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)),greatest_lower_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))) )],[refute_0_1068,refute_0_1071]) ).
cnf(refute_0_1073,plain,
greatest_lower_bound(multiply(X_111,inverse(X_112)),identity) = greatest_lower_bound(identity,multiply(X_111,inverse(X_112))),
inference(subst,[],[refute_0_164:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_111,inverse(X_112))))]]) ).
cnf(refute_0_1074,plain,
( multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) != greatest_lower_bound(multiply(X_111,inverse(X_112)),identity)
| greatest_lower_bound(multiply(X_111,inverse(X_112)),identity) != greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) = greatest_lower_bound(identity,multiply(X_111,inverse(X_112))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)),greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) ),[0],$fot(greatest_lower_bound(multiply(X_111,inverse(X_112)),identity))]]) ).
cnf(refute_0_1075,plain,
( multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) != greatest_lower_bound(multiply(X_111,inverse(X_112)),identity)
| multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) = greatest_lower_bound(identity,multiply(X_111,inverse(X_112))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,inverse(X_112)),identity),greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) = greatest_lower_bound(identity,multiply(X_111,inverse(X_112))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)),greatest_lower_bound(multiply(X_111,inverse(X_112)),identity)) )],[refute_0_1072,refute_0_1075]) ).
cnf(refute_0_1077,plain,
( multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)) != greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))
| multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)))),greatest_lower_bound(X_111,X_112)) != inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)))),greatest_lower_bound(X_111,X_112)),inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))) ),[0,0,0,1],$fot(greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))]]) ).
cnf(refute_0_1078,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)))),greatest_lower_bound(X_111,X_112)) != inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)),greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) )],[refute_0_1076,refute_0_1077]) ).
cnf(refute_0_1079,plain,
multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_111,X_112),inverse(X_112)))),greatest_lower_bound(X_111,X_112)),inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))) )],[refute_0_1067,refute_0_1078]) ).
cnf(refute_0_1080,plain,
multiply(inverse(multiply(greatest_lower_bound(X_123,X_124),inverse(X_124))),greatest_lower_bound(X_123,X_124)) = inverse(inverse(X_124)),
inference(subst,[],[refute_0_387:[bind(X_38,$fot(inverse(X_124))),bind(X_52,$fot(greatest_lower_bound(X_123,X_124)))]]) ).
cnf(refute_0_1081,plain,
multiply(greatest_lower_bound(X_123,X_124),inverse(X_124)) = greatest_lower_bound(identity,multiply(X_123,inverse(X_124))),
inference(subst,[],[refute_0_1076:[bind(X_111,$fot(X_123)),bind(X_112,$fot(X_124))]]) ).
cnf(refute_0_1082,plain,
( multiply(greatest_lower_bound(X_123,X_124),inverse(X_124)) != greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))
| multiply(inverse(multiply(greatest_lower_bound(X_123,X_124),inverse(X_124))),greatest_lower_bound(X_123,X_124)) != inverse(inverse(X_124))
| multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) = inverse(inverse(X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_123,X_124),inverse(X_124))),greatest_lower_bound(X_123,X_124)),inverse(inverse(X_124))) ),[0,0,0],$fot(greatest_lower_bound(identity,multiply(X_123,inverse(X_124))))]]) ).
cnf(refute_0_1083,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_123,X_124),inverse(X_124))),greatest_lower_bound(X_123,X_124)) != inverse(inverse(X_124))
| multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) = inverse(inverse(X_124)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_123,X_124),inverse(X_124)),greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) = inverse(inverse(X_124)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_123,X_124),inverse(X_124))),greatest_lower_bound(X_123,X_124)),inverse(inverse(X_124))) )],[refute_0_1080,refute_0_1083]) ).
cnf(refute_0_1085,plain,
inverse(inverse(X_124)) = X_124,
inference(subst,[],[refute_0_335:[bind(X_44,$fot(X_124))]]) ).
cnf(refute_0_1086,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) != inverse(inverse(X_124))
| inverse(inverse(X_124)) != X_124
| multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) = X_124 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)),X_124) ),[0],$fot(inverse(inverse(X_124)))]]) ).
cnf(refute_0_1087,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) != inverse(inverse(X_124))
| multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) = X_124 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_124)),X_124) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)) = X_124,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(X_123,inverse(X_124)))),greatest_lower_bound(X_123,X_124)),inverse(inverse(X_124))) )],[refute_0_1084,refute_0_1087]) ).
cnf(refute_0_1089,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)) = X_112,
inference(subst,[],[refute_0_1088:[bind(X_123,$fot(X_111)),bind(X_124,$fot(X_112))]]) ).
cnf(refute_0_1090,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) = greatest_lower_bound(identity,multiply(X_111,inverse(X_112))),
inference(subst,[],[refute_0_551:[bind(X_16,$fot(multiply(X_111,inverse(X_112)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1091,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))))]]) ).
cnf(refute_0_1092,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) != greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) = inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))]]) ).
cnf(refute_0_1093,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) != greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) = inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))))) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) = inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))) )],[refute_0_1090,refute_0_1093]) ).
cnf(refute_0_1095,plain,
multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)))]]) ).
cnf(refute_0_1096,plain,
( multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) != multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) != inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)),multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))))]]) ).
cnf(refute_0_1097,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) != inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)),multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112))) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))) )],[refute_0_1094,refute_0_1097]) ).
cnf(refute_0_1099,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)) != X_112
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112))
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = X_112 ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)))),bind(Z0,$fot(X_112))]]) ).
cnf(refute_0_1100,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)) != X_112
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = X_112 ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)),multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112))) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) = X_112,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(X_111,inverse(X_112)))),greatest_lower_bound(X_111,X_112)),X_112) )],[refute_0_1089,refute_0_1100]) ).
cnf(refute_0_1102,plain,
( multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) != X_112
| multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) != inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))
| X_112 = inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)),inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))) ),[0],$fot(X_112)]]) ).
cnf(refute_0_1103,plain,
( multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)) != inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))
| X_112 = inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)),X_112) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
X_112 = inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_111,inverse(X_112))))),greatest_lower_bound(X_111,X_112)),inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))) )],[refute_0_1079,refute_0_1103]) ).
cnf(refute_0_1105,plain,
( X_112 != inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))
| inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))) = X_112 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_112)),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))))]]) ).
cnf(refute_0_1106,plain,
inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112)))) = X_112,
inference(resolve,[$cnf( $equal(X_112,inverse(greatest_lower_bound(inverse(X_112),inverse(greatest_lower_bound(X_111,X_112))))) )],[refute_0_1104,refute_0_1105]) ).
cnf(refute_0_1107,plain,
inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))) = X_92,
inference(subst,[],[refute_0_1106:[bind(X_111,$fot(X_91)),bind(X_112,$fot(X_92))]]) ).
cnf(refute_0_1108,plain,
multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))]]) ).
cnf(refute_0_1109,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))
| inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))) != X_92
| multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) ),[1,0],$fot(X_92)]]) ).
cnf(refute_0_1110,plain,
( inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))) != X_92
| multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),X_92) )],[refute_0_1107,refute_0_1110]) ).
cnf(refute_0_1112,plain,
( multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != greatest_lower_bound(X_92,X_91)
| multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))
| multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(X_92,X_91) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))),bind(Y0,$fot(multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))))),bind(Z0,$fot(greatest_lower_bound(X_92,X_91)))]]) ).
cnf(refute_0_1113,plain,
( multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != greatest_lower_bound(X_92,X_91)
| multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(X_92,X_91) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) )],[refute_0_1111,refute_0_1112]) ).
cnf(refute_0_1114,plain,
multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) = greatest_lower_bound(X_92,X_91),
inference(resolve,[$cnf( $equal(multiply(X_92,greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),greatest_lower_bound(X_92,X_91)) )],[refute_0_1061,refute_0_1113]) ).
cnf(refute_0_1115,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))) != greatest_lower_bound(X_92,X_91)
| greatest_lower_bound(X_91,X_92) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))
| greatest_lower_bound(X_91,X_92) = greatest_lower_bound(X_92,X_91) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_91,X_92),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) ),[1],$fot(greatest_lower_bound(X_92,X_91))]]) ).
cnf(refute_0_1116,plain,
( greatest_lower_bound(X_91,X_92) != multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))
| greatest_lower_bound(X_91,X_92) = greatest_lower_bound(X_92,X_91) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91))),greatest_lower_bound(X_92,X_91)) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
greatest_lower_bound(X_91,X_92) = greatest_lower_bound(X_92,X_91),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_91,X_92),multiply(inverse(greatest_lower_bound(inverse(X_92),inverse(greatest_lower_bound(X_91,X_92)))),greatest_lower_bound(identity,multiply(inverse(X_92),X_91)))) )],[refute_0_1045,refute_0_1116]) ).
cnf(refute_0_1118,plain,
( greatest_lower_bound(X_91,X_92) != greatest_lower_bound(X_92,X_91)
| greatest_lower_bound(X_92,X_91) = greatest_lower_bound(X_91,X_92) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X_91,X_92))),bind(Y0,$fot(greatest_lower_bound(X_92,X_91)))]]) ).
cnf(refute_0_1119,plain,
greatest_lower_bound(X_92,X_91) = greatest_lower_bound(X_91,X_92),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_91,X_92),greatest_lower_bound(X_92,X_91)) )],[refute_0_1117,refute_0_1118]) ).
cnf(refute_0_1120,plain,
greatest_lower_bound(multiply(X_11,X_438),X_11) = greatest_lower_bound(X_11,multiply(X_11,X_438)),
inference(subst,[],[refute_0_1119:[bind(X_91,$fot(X_11)),bind(X_92,$fot(multiply(X_11,X_438)))]]) ).
cnf(refute_0_1121,plain,
( greatest_lower_bound(X_11,multiply(X_11,X_438)) != multiply(X_11,greatest_lower_bound(X_438,identity))
| greatest_lower_bound(multiply(X_11,X_438),X_11) != greatest_lower_bound(X_11,multiply(X_11,X_438))
| greatest_lower_bound(multiply(X_11,X_438),X_11) = multiply(X_11,greatest_lower_bound(X_438,identity)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(multiply(X_11,X_438),X_11))),bind(Y0,$fot(greatest_lower_bound(X_11,multiply(X_11,X_438)))),bind(Z0,$fot(multiply(X_11,greatest_lower_bound(X_438,identity))))]]) ).
cnf(refute_0_1122,plain,
( greatest_lower_bound(X_11,multiply(X_11,X_438)) != multiply(X_11,greatest_lower_bound(X_438,identity))
| greatest_lower_bound(multiply(X_11,X_438),X_11) = multiply(X_11,greatest_lower_bound(X_438,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_11,X_438),X_11),greatest_lower_bound(X_11,multiply(X_11,X_438))) )],[refute_0_1120,refute_0_1121]) ).
cnf(refute_0_1123,plain,
greatest_lower_bound(multiply(X_11,X_438),X_11) = multiply(X_11,greatest_lower_bound(X_438,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,multiply(X_11,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) )],[refute_0_795,refute_0_1122]) ).
cnf(refute_0_1124,plain,
( multiply(X_11,greatest_lower_bound(identity,X_438)) != greatest_lower_bound(multiply(X_11,X_438),X_11)
| greatest_lower_bound(multiply(X_11,X_438),X_11) != multiply(X_11,greatest_lower_bound(X_438,identity))
| multiply(X_11,greatest_lower_bound(identity,X_438)) = multiply(X_11,greatest_lower_bound(X_438,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) ),[0],$fot(greatest_lower_bound(multiply(X_11,X_438),X_11))]]) ).
cnf(refute_0_1125,plain,
( multiply(X_11,greatest_lower_bound(identity,X_438)) != greatest_lower_bound(multiply(X_11,X_438),X_11)
| multiply(X_11,greatest_lower_bound(identity,X_438)) = multiply(X_11,greatest_lower_bound(X_438,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) )],[refute_0_1123,refute_0_1124]) ).
cnf(refute_0_1126,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))) != greatest_lower_bound(multiply(X_11,X_438),X_11)
| multiply(X_11,greatest_lower_bound(identity,X_438)) = multiply(X_11,greatest_lower_bound(X_438,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_11,greatest_lower_bound(identity,X_438)),greatest_lower_bound(multiply(X_11,X_438),X_11)) )],[refute_0_974,refute_0_1125]) ).
cnf(refute_0_1127,plain,
multiply(X_11,greatest_lower_bound(identity,X_438)) = multiply(X_11,greatest_lower_bound(X_438,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_11,X_438),X_11),multiply(X_11,greatest_lower_bound(X_438,identity))),greatest_lower_bound(multiply(X_11,X_438),X_11)) )],[refute_0_798,refute_0_1126]) ).
cnf(refute_0_1128,plain,
( multiply(X_11,greatest_lower_bound(identity,X_438)) != multiply(X_11,greatest_lower_bound(X_438,identity))
| multiply(X_11,greatest_lower_bound(X_438,identity)) = multiply(X_11,greatest_lower_bound(identity,X_438)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X_11,greatest_lower_bound(identity,X_438)))),bind(Y0,$fot(multiply(X_11,greatest_lower_bound(X_438,identity))))]]) ).
cnf(refute_0_1129,plain,
multiply(X_11,greatest_lower_bound(X_438,identity)) = multiply(X_11,greatest_lower_bound(identity,X_438)),
inference(resolve,[$cnf( $equal(multiply(X_11,greatest_lower_bound(identity,X_438)),multiply(X_11,greatest_lower_bound(X_438,identity))) )],[refute_0_1127,refute_0_1128]) ).
cnf(refute_0_1130,plain,
multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) = multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),
inference(subst,[],[refute_0_1129:[bind(X_11,$fot(least_upper_bound(X_108,identity))),bind(X_438,$fot(inverse(X_108)))]]) ).
cnf(refute_0_1131,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) != multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) != greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)),greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))) ),[0],$fot(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))))]]) ).
cnf(refute_0_1132,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) != greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)),multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108)))) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
( multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) != greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))
| greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) = multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))))]]) ).
cnf(refute_0_1134,plain,
greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) = multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)),greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))) )],[refute_0_774,refute_0_1133]) ).
cnf(refute_0_1135,plain,
greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) = multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity)),
inference(subst,[],[refute_0_1134:[bind(X_70,$fot(X_108))]]) ).
cnf(refute_0_1136,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) != greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))
| greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))) != multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))))]]) ).
cnf(refute_0_1137,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) != greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108))),multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity))) )],[refute_0_1135,refute_0_1136]) ).
cnf(refute_0_1138,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)) != greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))
| multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))) )],[refute_0_1132,refute_0_1137]) ).
cnf(refute_0_1139,plain,
multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) = multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(inverse(X_108),identity)),greatest_lower_bound(least_upper_bound(X_108,identity),least_upper_bound(identity,inverse(X_108)))) )],[refute_0_791,refute_0_1138]) ).
cnf(refute_0_1140,plain,
( multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) != multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity))
| multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity)) = multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity))))]]) ).
cnf(refute_0_1141,plain,
multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity)) = multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,identity),greatest_lower_bound(identity,inverse(X_108))),multiply(greatest_lower_bound(identity,inverse(X_108)),least_upper_bound(X_108,identity))) )],[refute_0_1139,refute_0_1140]) ).
cnf(refute_0_1142,plain,
multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) = multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))),
inference(subst,[],[refute_0_1141:[bind(X_108,$fot(X_70))]]) ).
cnf(refute_0_1143,plain,
( multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) != multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70)))
| multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) != greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))
| multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)),greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))) ),[0],$fot(multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))))]]) ).
cnf(refute_0_1144,plain,
( multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)) != greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))
| multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)),multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70)))) )],[refute_0_1142,refute_0_1143]) ).
cnf(refute_0_1145,plain,
multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))) = greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_70)),least_upper_bound(X_70,identity)),greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))) )],[refute_0_774,refute_0_1144]) ).
cnf(refute_0_1146,plain,
( multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))) != greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))
| greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) = multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))))]]) ).
cnf(refute_0_1147,plain,
greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70))) = multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_70,identity),greatest_lower_bound(identity,inverse(X_70))),greatest_lower_bound(least_upper_bound(X_70,identity),least_upper_bound(identity,inverse(X_70)))) )],[refute_0_1145,refute_0_1146]) ).
cnf(refute_0_1148,plain,
greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) = multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))),
inference(subst,[],[refute_0_1147:[bind(X_70,$fot(X_139))]]) ).
cnf(refute_0_1149,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))]]) ).
cnf(refute_0_1150,plain,
( greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) != multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) != least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) = least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) ),[1,1],$fot(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))))]]) ).
cnf(refute_0_1151,plain,
( greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) != multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) = least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) )],[refute_0_1149,refute_0_1150]) ).
cnf(refute_0_1152,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) = least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))),multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) )],[refute_0_1148,refute_0_1151]) ).
cnf(refute_0_1153,plain,
( least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) != identity
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) != least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) = identity ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1154,plain,
( least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) != identity
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))),least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))))) )],[refute_0_1152,refute_0_1153]) ).
cnf(refute_0_1155,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))),identity) )],[refute_0_540,refute_0_1154]) ).
cnf(refute_0_1156,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))))]]) ).
cnf(refute_0_1157,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) != multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) != identity
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))),multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1158,plain,
( least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) != identity
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))),multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))) )],[refute_0_1156,refute_0_1157]) ).
cnf(refute_0_1159,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))),identity) )],[refute_0_1155,refute_0_1158]) ).
cnf(refute_0_1160,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) != inverse(least_upper_bound(identity,inverse(X_139)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) != multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity)
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) = inverse(least_upper_bound(identity,inverse(X_139))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_139)))))]]) ).
cnf(refute_0_1161,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity) != inverse(least_upper_bound(identity,inverse(X_139)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) = inverse(least_upper_bound(identity,inverse(X_139))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))),multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity)) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) = inverse(least_upper_bound(identity,inverse(X_139))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),identity),inverse(least_upper_bound(identity,inverse(X_139)))) )],[refute_0_487,refute_0_1161]) ).
cnf(refute_0_1163,plain,
multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) = least_upper_bound(inverse(X_98),multiply(inverse(X_98),greatest_lower_bound(X_97,X_98))),
inference(subst,[],[refute_0_68:[bind(X_66,$fot(inverse(X_98))),bind(X_67,$fot(greatest_lower_bound(X_97,X_98)))]]) ).
cnf(refute_0_1164,plain,
( multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)) != greatest_lower_bound(identity,multiply(inverse(X_98),X_97))
| multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) != least_upper_bound(inverse(X_98),multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)))
| multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) = least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)),least_upper_bound(inverse(X_98),multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))]]) ).
cnf(refute_0_1165,plain,
( multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) != least_upper_bound(inverse(X_98),multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)))
| multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) = least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) )],[refute_0_856,refute_0_1164]) ).
cnf(refute_0_1166,plain,
multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) = least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)),least_upper_bound(inverse(X_98),multiply(inverse(X_98),greatest_lower_bound(X_97,X_98)))) )],[refute_0_1163,refute_0_1165]) ).
cnf(refute_0_1167,plain,
multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) = multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))),
inference(subst,[],[refute_0_194:[bind(X_19,$fot(inverse(X_98))),bind(X_70,$fot(greatest_lower_bound(X_97,X_98)))]]) ).
cnf(refute_0_1168,plain,
( multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) != multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98)))
| multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) != least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))
| multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))) = least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)),least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))) ),[0],$fot(multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))))]]) ).
cnf(refute_0_1169,plain,
( multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)) != least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))
| multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))) = least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)),multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98)))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))) = least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(greatest_lower_bound(X_97,X_98),identity)),least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))) )],[refute_0_1166,refute_0_1169]) ).
cnf(refute_0_1171,plain,
( multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))) != least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))
| least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))))),bind(Y0,$fot(least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))))]]) ).
cnf(refute_0_1172,plain,
least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97))) = multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(identity,greatest_lower_bound(X_97,X_98))),least_upper_bound(inverse(X_98),greatest_lower_bound(identity,multiply(inverse(X_98),X_97)))) )],[refute_0_1170,refute_0_1171]) ).
cnf(refute_0_1173,plain,
least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))),
inference(subst,[],[refute_0_1172:[bind(X_97,$fot(least_upper_bound(X_139,identity))),bind(X_98,$fot(least_upper_bound(identity,inverse(X_139))))]]) ).
cnf(refute_0_1174,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity))))
| least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)))) != multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))))]]) ).
cnf(refute_0_1175,plain,
( least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)))) != multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity))))) )],[refute_0_374,refute_0_1174]) ).
cnf(refute_0_1176,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(X_139,identity)))),multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))) )],[refute_0_1173,refute_0_1175]) ).
cnf(refute_0_1177,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) != inverse(least_upper_bound(identity,inverse(X_139)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = inverse(least_upper_bound(identity,inverse(X_139))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_139)))))]]) ).
cnf(refute_0_1178,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))) != inverse(least_upper_bound(identity,inverse(X_139)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = inverse(least_upper_bound(identity,inverse(X_139))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))),multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))))) )],[refute_0_1176,refute_0_1177]) ).
cnf(refute_0_1179,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) = inverse(least_upper_bound(identity,inverse(X_139))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))),inverse(least_upper_bound(identity,inverse(X_139)))) )],[refute_0_1162,refute_0_1178]) ).
cnf(refute_0_1180,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != inverse(least_upper_bound(identity,inverse(X_139)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))
| inverse(least_upper_bound(identity,inverse(X_139))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))) ),[0],$fot(inverse(least_upper_bound(identity,inverse(X_139))))]]) ).
cnf(refute_0_1181,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))
| inverse(least_upper_bound(identity,inverse(X_139))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))),inverse(least_upper_bound(identity,inverse(X_139)))) )],[refute_0_1179,refute_0_1180]) ).
cnf(refute_0_1182,plain,
multiply(inverse(multiply(least_upper_bound(inverse(X_38),X_107),X_38)),least_upper_bound(inverse(X_38),X_107)) = inverse(X_38),
inference(subst,[],[refute_0_387:[bind(X_52,$fot(least_upper_bound(inverse(X_38),X_107)))]]) ).
cnf(refute_0_1183,plain,
multiply(least_upper_bound(inverse(X_101),X_103),X_101) = least_upper_bound(multiply(inverse(X_101),X_101),multiply(X_103,X_101)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_101)),bind(Y,$fot(inverse(X_101))),bind(Z,$fot(X_103))]]) ).
cnf(refute_0_1184,plain,
( multiply(inverse(X_101),X_101) != identity
| multiply(least_upper_bound(inverse(X_101),X_103),X_101) != least_upper_bound(multiply(inverse(X_101),X_101),multiply(X_103,X_101))
| multiply(least_upper_bound(inverse(X_101),X_103),X_101) = least_upper_bound(identity,multiply(X_103,X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_101),X_103),X_101),least_upper_bound(multiply(inverse(X_101),X_101),multiply(X_103,X_101))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1185,plain,
( multiply(least_upper_bound(inverse(X_101),X_103),X_101) != least_upper_bound(multiply(inverse(X_101),X_101),multiply(X_103,X_101))
| multiply(least_upper_bound(inverse(X_101),X_103),X_101) = least_upper_bound(identity,multiply(X_103,X_101)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),X_101),identity) )],[refute_0_343,refute_0_1184]) ).
cnf(refute_0_1186,plain,
multiply(least_upper_bound(inverse(X_101),X_103),X_101) = least_upper_bound(identity,multiply(X_103,X_101)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_101),X_103),X_101),least_upper_bound(multiply(inverse(X_101),X_101),multiply(X_103,X_101))) )],[refute_0_1183,refute_0_1185]) ).
cnf(refute_0_1187,plain,
multiply(least_upper_bound(inverse(X_38),X_107),X_38) = least_upper_bound(identity,multiply(X_107,X_38)),
inference(subst,[],[refute_0_1186:[bind(X_101,$fot(X_38)),bind(X_103,$fot(X_107))]]) ).
cnf(refute_0_1188,plain,
( multiply(inverse(multiply(least_upper_bound(inverse(X_38),X_107),X_38)),least_upper_bound(inverse(X_38),X_107)) != inverse(X_38)
| multiply(least_upper_bound(inverse(X_38),X_107),X_38) != least_upper_bound(identity,multiply(X_107,X_38))
| multiply(inverse(least_upper_bound(identity,multiply(X_107,X_38))),least_upper_bound(inverse(X_38),X_107)) = inverse(X_38) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(inverse(X_38),X_107),X_38)),least_upper_bound(inverse(X_38),X_107)),inverse(X_38)) ),[0,0,0],$fot(least_upper_bound(identity,multiply(X_107,X_38)))]]) ).
cnf(refute_0_1189,plain,
( multiply(inverse(multiply(least_upper_bound(inverse(X_38),X_107),X_38)),least_upper_bound(inverse(X_38),X_107)) != inverse(X_38)
| multiply(inverse(least_upper_bound(identity,multiply(X_107,X_38))),least_upper_bound(inverse(X_38),X_107)) = inverse(X_38) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_38),X_107),X_38),least_upper_bound(identity,multiply(X_107,X_38))) )],[refute_0_1187,refute_0_1188]) ).
cnf(refute_0_1190,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_107,X_38))),least_upper_bound(inverse(X_38),X_107)) = inverse(X_38),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(inverse(X_38),X_107),X_38)),least_upper_bound(inverse(X_38),X_107)),inverse(X_38)) )],[refute_0_1182,refute_0_1189]) ).
cnf(refute_0_1191,plain,
multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = inverse(inverse(least_upper_bound(inverse(X_426),X_427))),
inference(subst,[],[refute_0_1190:[bind(X_107,$fot(least_upper_bound(identity,multiply(X_426,X_427)))),bind(X_38,$fot(inverse(least_upper_bound(inverse(X_426),X_427))))]]) ).
cnf(refute_0_1192,plain,
inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(inverse(least_upper_bound(identity,multiply(X_179,X_180))))),bind(X_52,$fot(least_upper_bound(inverse(X_179),X_180)))]]) ).
cnf(refute_0_1193,plain,
multiply(least_upper_bound(inverse(X_38),X_74),inverse(multiply(X_38,least_upper_bound(inverse(X_38),X_74)))) = inverse(X_38),
inference(subst,[],[refute_0_54:[bind(X_51,$fot(least_upper_bound(inverse(X_38),X_74)))]]) ).
cnf(refute_0_1194,plain,
multiply(X_66,least_upper_bound(inverse(X_66),X_68)) = least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_66,X_68)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_66)),bind(Y,$fot(inverse(X_66))),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_1195,plain,
multiply(X_66,inverse(X_66)) = identity,
inference(subst,[],[refute_0_27:[bind(X_44,$fot(X_66))]]) ).
cnf(refute_0_1196,plain,
( multiply(X_66,inverse(X_66)) != identity
| multiply(X_66,least_upper_bound(inverse(X_66),X_68)) != least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_66,X_68))
| multiply(X_66,least_upper_bound(inverse(X_66),X_68)) = least_upper_bound(identity,multiply(X_66,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,least_upper_bound(inverse(X_66),X_68)),least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_66,X_68))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1197,plain,
( multiply(X_66,least_upper_bound(inverse(X_66),X_68)) != least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_66,X_68))
| multiply(X_66,least_upper_bound(inverse(X_66),X_68)) = least_upper_bound(identity,multiply(X_66,X_68)) ),
inference(resolve,[$cnf( $equal(multiply(X_66,inverse(X_66)),identity) )],[refute_0_1195,refute_0_1196]) ).
cnf(refute_0_1198,plain,
multiply(X_66,least_upper_bound(inverse(X_66),X_68)) = least_upper_bound(identity,multiply(X_66,X_68)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(inverse(X_66),X_68)),least_upper_bound(multiply(X_66,inverse(X_66)),multiply(X_66,X_68))) )],[refute_0_1194,refute_0_1197]) ).
cnf(refute_0_1199,plain,
multiply(X_38,least_upper_bound(inverse(X_38),X_74)) = least_upper_bound(identity,multiply(X_38,X_74)),
inference(subst,[],[refute_0_1198:[bind(X_66,$fot(X_38)),bind(X_68,$fot(X_74))]]) ).
cnf(refute_0_1200,plain,
( multiply(X_38,least_upper_bound(inverse(X_38),X_74)) != least_upper_bound(identity,multiply(X_38,X_74))
| multiply(least_upper_bound(inverse(X_38),X_74),inverse(multiply(X_38,least_upper_bound(inverse(X_38),X_74)))) != inverse(X_38)
| multiply(least_upper_bound(inverse(X_38),X_74),inverse(least_upper_bound(identity,multiply(X_38,X_74)))) = inverse(X_38) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_38),X_74),inverse(multiply(X_38,least_upper_bound(inverse(X_38),X_74)))),inverse(X_38)) ),[0,1,0],$fot(least_upper_bound(identity,multiply(X_38,X_74)))]]) ).
cnf(refute_0_1201,plain,
( multiply(least_upper_bound(inverse(X_38),X_74),inverse(multiply(X_38,least_upper_bound(inverse(X_38),X_74)))) != inverse(X_38)
| multiply(least_upper_bound(inverse(X_38),X_74),inverse(least_upper_bound(identity,multiply(X_38,X_74)))) = inverse(X_38) ),
inference(resolve,[$cnf( $equal(multiply(X_38,least_upper_bound(inverse(X_38),X_74)),least_upper_bound(identity,multiply(X_38,X_74))) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
multiply(least_upper_bound(inverse(X_38),X_74),inverse(least_upper_bound(identity,multiply(X_38,X_74)))) = inverse(X_38),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_38),X_74),inverse(multiply(X_38,least_upper_bound(inverse(X_38),X_74)))),inverse(X_38)) )],[refute_0_1193,refute_0_1201]) ).
cnf(refute_0_1203,plain,
multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180)))) = inverse(X_179),
inference(subst,[],[refute_0_1202:[bind(X_38,$fot(X_179)),bind(X_74,$fot(X_180))]]) ).
cnf(refute_0_1204,plain,
( multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180)))) != inverse(X_179)
| inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))
| inverse(inverse(X_179)) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))) ),[0,0],$fot(inverse(X_179))]]) ).
cnf(refute_0_1205,plain,
( inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))
| inverse(inverse(X_179)) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(X_179)) )],[refute_0_1203,refute_0_1204]) ).
cnf(refute_0_1206,plain,
inverse(inverse(X_179)) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))) )],[refute_0_1192,refute_0_1205]) ).
cnf(refute_0_1207,plain,
inverse(inverse(X_179)) = X_179,
inference(subst,[],[refute_0_335:[bind(X_44,$fot(X_179))]]) ).
cnf(refute_0_1208,plain,
( inverse(inverse(X_179)) != X_179
| inverse(inverse(X_179)) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))
| X_179 = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_179)),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))) ),[0],$fot(X_179)]]) ).
cnf(refute_0_1209,plain,
( inverse(inverse(X_179)) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))
| X_179 = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_179)),X_179) )],[refute_0_1207,refute_0_1208]) ).
cnf(refute_0_1210,plain,
inverse(multiply(X_52,inverse(X_44))) = multiply(X_44,multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44))))),
inference(subst,[],[refute_0_456:[bind(X_39,$fot(inverse(multiply(X_52,inverse(X_44)))))]]) ).
cnf(refute_0_1211,plain,
multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44)))) = inverse(X_52),
inference(subst,[],[refute_0_54:[bind(X_38,$fot(X_52)),bind(X_51,$fot(inverse(X_44)))]]) ).
cnf(refute_0_1212,plain,
( multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44)))) != inverse(X_52)
| inverse(multiply(X_52,inverse(X_44))) != multiply(X_44,multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44)))))
| inverse(multiply(X_52,inverse(X_44))) = multiply(X_44,inverse(X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_52,inverse(X_44))),multiply(X_44,multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44)))))) ),[1,1],$fot(inverse(X_52))]]) ).
cnf(refute_0_1213,plain,
( inverse(multiply(X_52,inverse(X_44))) != multiply(X_44,multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44)))))
| inverse(multiply(X_52,inverse(X_44))) = multiply(X_44,inverse(X_52)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44)))),inverse(X_52)) )],[refute_0_1211,refute_0_1212]) ).
cnf(refute_0_1214,plain,
inverse(multiply(X_52,inverse(X_44))) = multiply(X_44,inverse(X_52)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_52,inverse(X_44))),multiply(X_44,multiply(inverse(X_44),inverse(multiply(X_52,inverse(X_44)))))) )],[refute_0_1210,refute_0_1213]) ).
cnf(refute_0_1215,plain,
inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))) = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))),
inference(subst,[],[refute_0_1214:[bind(X_44,$fot(least_upper_bound(identity,multiply(X_179,X_180)))),bind(X_52,$fot(least_upper_bound(inverse(X_179),X_180)))]]) ).
cnf(refute_0_1216,plain,
multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) = inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(inverse(least_upper_bound(identity,multiply(X_179,X_180))))),bind(X_52,$fot(least_upper_bound(inverse(X_179),X_180)))]]) ).
cnf(refute_0_1217,plain,
( multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) != inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180)))))
| inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))) != multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180)))
| multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))))),bind(Z0,$fot(multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180)))))]]) ).
cnf(refute_0_1218,plain,
( inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))) != multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180)))
| multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))),inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180)))))) )],[refute_0_1216,refute_0_1217]) ).
cnf(refute_0_1219,plain,
multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(inverse(X_179),X_180),inverse(least_upper_bound(identity,multiply(X_179,X_180))))),multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180)))) )],[refute_0_1215,refute_0_1218]) ).
cnf(refute_0_1220,plain,
( X_179 != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))
| multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))) != multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180)))
| X_179 = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_179,multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180)))) ),[0],$fot(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))))]]) ).
cnf(refute_0_1221,plain,
( X_179 != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))
| X_179 = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180))),multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180)))) )],[refute_0_1219,refute_0_1220]) ).
cnf(refute_0_1222,plain,
( inverse(inverse(X_179)) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))
| X_179 = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))) ),
inference(resolve,[$cnf( $equal(X_179,multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))) )],[refute_0_1209,refute_0_1221]) ).
cnf(refute_0_1223,plain,
X_179 = multiply(least_upper_bound(identity,multiply(X_179,X_180)),inverse(least_upper_bound(inverse(X_179),X_180))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_179)),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_179,X_180)))),inverse(least_upper_bound(inverse(X_179),X_180)))) )],[refute_0_1206,refute_0_1222]) ).
cnf(refute_0_1224,plain,
X_426 = multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))),
inference(subst,[],[refute_0_1223:[bind(X_179,$fot(X_426)),bind(X_180,$fot(X_427))]]) ).
cnf(refute_0_1225,plain,
( X_426 != multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427)))
| multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))) = X_426 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X_426)),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427)))))]]) ).
cnf(refute_0_1226,plain,
multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))) = X_426,
inference(resolve,[$cnf( $equal(X_426,multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427)))) )],[refute_0_1224,refute_0_1225]) ).
cnf(refute_0_1227,plain,
( multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) != inverse(inverse(least_upper_bound(inverse(X_426),X_427)))
| multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))) != X_426
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = inverse(inverse(least_upper_bound(inverse(X_426),X_427))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) ),[0,0,0,1],$fot(X_426)]]) ).
cnf(refute_0_1228,plain,
( multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) != inverse(inverse(least_upper_bound(inverse(X_426),X_427)))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = inverse(inverse(least_upper_bound(inverse(X_426),X_427))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))),X_426) )],[refute_0_1226,refute_0_1227]) ).
cnf(refute_0_1229,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = inverse(inverse(least_upper_bound(inverse(X_426),X_427))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_426,X_427)),inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) )],[refute_0_1191,refute_0_1228]) ).
cnf(refute_0_1230,plain,
least_upper_bound(X_24,least_upper_bound(X_25,X_26)) = least_upper_bound(X_25,least_upper_bound(X_26,X_24)),
inference(subst,[],[refute_0_262:[bind(X,$fot(X_24)),bind(X_24,$fot(X_25)),bind(X_25,$fot(X_26))]]) ).
cnf(refute_0_1231,plain,
( least_upper_bound(X_24,least_upper_bound(X_25,X_26)) != least_upper_bound(X_25,least_upper_bound(X_26,X_24))
| least_upper_bound(X_24,least_upper_bound(X_26,X_25)) != least_upper_bound(X_24,least_upper_bound(X_25,X_26))
| least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(X_25,least_upper_bound(X_26,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_26,X_25)),least_upper_bound(X_24,least_upper_bound(X_25,X_26))) ),[1],$fot(least_upper_bound(X_25,least_upper_bound(X_26,X_24)))]]) ).
cnf(refute_0_1232,plain,
( least_upper_bound(X_24,least_upper_bound(X_26,X_25)) != least_upper_bound(X_24,least_upper_bound(X_25,X_26))
| least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(X_25,least_upper_bound(X_26,X_24)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_25,X_26)),least_upper_bound(X_25,least_upper_bound(X_26,X_24))) )],[refute_0_1230,refute_0_1231]) ).
cnf(refute_0_1233,plain,
least_upper_bound(X_24,least_upper_bound(X_26,X_25)) = least_upper_bound(X_25,least_upper_bound(X_26,X_24)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_26,X_25)),least_upper_bound(X_24,least_upper_bound(X_25,X_26))) )],[refute_0_627,refute_0_1232]) ).
cnf(refute_0_1234,plain,
( least_upper_bound(X_24,least_upper_bound(X_26,X_25)) != least_upper_bound(X_25,least_upper_bound(X_26,X_24))
| least_upper_bound(X_25,least_upper_bound(X_26,X_24)) = least_upper_bound(X_24,least_upper_bound(X_26,X_25)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_24,least_upper_bound(X_26,X_25)))),bind(Y0,$fot(least_upper_bound(X_25,least_upper_bound(X_26,X_24))))]]) ).
cnf(refute_0_1235,plain,
least_upper_bound(X_25,least_upper_bound(X_26,X_24)) = least_upper_bound(X_24,least_upper_bound(X_26,X_25)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(X_26,X_25)),least_upper_bound(X_25,least_upper_bound(X_26,X_24))) )],[refute_0_1233,refute_0_1234]) ).
cnf(refute_0_1236,plain,
least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)) = least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))),
inference(subst,[],[refute_0_1235:[bind(X_24,$fot(X_427)),bind(X_25,$fot(multiply(X_426,X_427))),bind(X_26,$fot(inverse(X_426)))]]) ).
cnf(refute_0_1237,plain,
inverse(inverse(least_upper_bound(inverse(X_426),X_427))) = least_upper_bound(inverse(X_426),X_427),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(least_upper_bound(inverse(X_426),X_427)))]]) ).
cnf(refute_0_1238,plain,
least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) = least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))]]) ).
cnf(refute_0_1239,plain,
( inverse(inverse(least_upper_bound(inverse(X_426),X_427))) != least_upper_bound(inverse(X_426),X_427)
| least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) != least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))
| least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) = least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))),least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) ),[1,1],$fot(least_upper_bound(inverse(X_426),X_427))]]) ).
cnf(refute_0_1240,plain,
( inverse(inverse(least_upper_bound(inverse(X_426),X_427))) != least_upper_bound(inverse(X_426),X_427)
| least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) = least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))),least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) )],[refute_0_1238,refute_0_1239]) ).
cnf(refute_0_1241,plain,
least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) = least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(inverse(X_426),X_427)) )],[refute_0_1237,refute_0_1240]) ).
cnf(refute_0_1242,plain,
( least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) != least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427))
| least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)) != least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))
| least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) = least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))),bind(Y0,$fot(least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)))),bind(Z0,$fot(least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))]]) ).
cnf(refute_0_1243,plain,
( least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)) != least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))
| least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) = least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))),least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427))) )],[refute_0_1241,refute_0_1242]) ).
cnf(refute_0_1244,plain,
least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) = least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_426,X_427),least_upper_bound(inverse(X_426),X_427)),least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))) )],[refute_0_1236,refute_0_1243]) ).
cnf(refute_0_1245,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) = least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))))]]) ).
cnf(refute_0_1246,plain,
( least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) != least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))
| least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) != least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))
| least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) = least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) ),[1,1],$fot(least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))]]) ).
cnf(refute_0_1247,plain,
( least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) != least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))
| least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) = least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) )],[refute_0_1245,refute_0_1246]) ).
cnf(refute_0_1248,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) = least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))),least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))) )],[refute_0_1244,refute_0_1247]) ).
cnf(refute_0_1249,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))))]]) ).
cnf(refute_0_1250,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) != multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))))
| least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) != least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))),multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))]]) ).
cnf(refute_0_1251,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))) != least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))),multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))))) )],[refute_0_1249,refute_0_1250]) ).
cnf(refute_0_1252,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) )],[refute_0_1248,refute_0_1251]) ).
cnf(refute_0_1253,plain,
multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))),
inference(subst,[],[monotony_lub1:[bind(Z,$fot(least_upper_bound(X_406,X_407)))]]) ).
cnf(refute_0_1254,plain,
least_upper_bound(Y,least_upper_bound(X_406,X_407)) = least_upper_bound(X_406,least_upper_bound(X_407,Y)),
inference(subst,[],[refute_0_262:[bind(X,$fot(Y)),bind(X_24,$fot(X_406)),bind(X_25,$fot(X_407))]]) ).
cnf(refute_0_1255,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407)))
| least_upper_bound(Y,least_upper_bound(X_406,X_407)) != least_upper_bound(X_406,least_upper_bound(X_407,Y))
| multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407)))) ),[0,1],$fot(least_upper_bound(X_406,least_upper_bound(X_407,Y)))]]) ).
cnf(refute_0_1256,plain,
( multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407)))
| multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_406,X_407)),least_upper_bound(X_406,least_upper_bound(X_407,Y))) )],[refute_0_1254,refute_0_1255]) ).
cnf(refute_0_1257,plain,
multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) = least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407)))) )],[refute_0_1253,refute_0_1256]) ).
cnf(refute_0_1258,plain,
least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))),
inference(subst,[],[refute_0_154:[bind(Z,$fot(least_upper_bound(X_406,X_407)))]]) ).
cnf(refute_0_1259,plain,
( multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407)))
| least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))) != multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407)))
| multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))),multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407)))) ),[0],$fot(least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))))]]) ).
cnf(refute_0_1260,plain,
( multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) != least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407)))
| multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407))),multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407)))) )],[refute_0_1258,refute_0_1259]) ).
cnf(refute_0_1261,plain,
multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) = multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))),least_upper_bound(multiply(X,Y),multiply(X,least_upper_bound(X_406,X_407)))) )],[refute_0_1257,refute_0_1260]) ).
cnf(refute_0_1262,plain,
( multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) != multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407)))
| multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))) = multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))))),bind(Y0,$fot(multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407)))))]]) ).
cnf(refute_0_1263,plain,
multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407))) = multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_406,least_upper_bound(X_407,Y))),multiply(X,least_upper_bound(Y,least_upper_bound(X_406,X_407)))) )],[refute_0_1261,refute_0_1262]) ).
cnf(refute_0_1264,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))),
inference(subst,[],[refute_0_1263:[bind(X,$fot(inverse(least_upper_bound(identity,X_426)))),bind(Y,$fot(inverse(inverse(least_upper_bound(inverse(X_426),X_427))))),bind(X_406,$fot(identity)),bind(X_407,$fot(multiply(X_426,X_427)))]]) ).
cnf(refute_0_1265,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) != multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) != multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))))]]) ).
cnf(refute_0_1266,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))) != multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))),multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427))))))) )],[refute_0_1264,refute_0_1265]) ).
cnf(refute_0_1267,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(multiply(X_426,X_427),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))))),multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))) )],[refute_0_1252,refute_0_1266]) ).
cnf(refute_0_1268,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) != multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) != inverse(inverse(least_upper_bound(inverse(X_426),X_427)))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = inverse(inverse(least_upper_bound(inverse(X_426),X_427))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) ),[0],$fot(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))))]]) ).
cnf(refute_0_1269,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) != inverse(inverse(least_upper_bound(inverse(X_426),X_427)))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = inverse(inverse(least_upper_bound(inverse(X_426),X_427))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))),multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))) )],[refute_0_1267,refute_0_1268]) ).
cnf(refute_0_1270,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) != inverse(inverse(least_upper_bound(inverse(X_426),X_427)))
| inverse(inverse(least_upper_bound(inverse(X_426),X_427))) != least_upper_bound(inverse(X_426),X_427)
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = least_upper_bound(inverse(X_426),X_427) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),least_upper_bound(inverse(X_426),X_427)) ),[0],$fot(inverse(inverse(least_upper_bound(inverse(X_426),X_427))))]]) ).
cnf(refute_0_1271,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) != inverse(inverse(least_upper_bound(inverse(X_426),X_427)))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = least_upper_bound(inverse(X_426),X_427) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(inverse(X_426),X_427)) )],[refute_0_1237,refute_0_1270]) ).
cnf(refute_0_1272,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))) != inverse(inverse(least_upper_bound(inverse(X_426),X_427)))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = least_upper_bound(inverse(X_426),X_427) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) )],[refute_0_1269,refute_0_1271]) ).
cnf(refute_0_1273,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = least_upper_bound(inverse(X_426),X_427),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(inverse(inverse(least_upper_bound(inverse(X_426),X_427))),least_upper_bound(identity,multiply(X_426,X_427)))),inverse(inverse(least_upper_bound(inverse(X_426),X_427)))) )],[refute_0_1229,refute_0_1272]) ).
cnf(refute_0_1274,plain,
multiply(multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)),Z) = multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(least_upper_bound(X_148,X_147)))),bind(Y,$fot(least_upper_bound(X_147,X_148)))]]) ).
cnf(refute_0_1275,plain,
multiply(inverse(least_upper_bound(X_18,Y)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))),
inference(subst,[],[refute_0_826:[bind(X_91,$fot(least_upper_bound(X_18,Y))),bind(X_92,$fot(least_upper_bound(Y,X_18)))]]) ).
cnf(refute_0_1276,plain,
( multiply(inverse(least_upper_bound(X_18,Y)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_18,Y)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))) ),[0,1],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_1277,plain,
( multiply(inverse(least_upper_bound(X_18,Y)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))
| multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_132,refute_0_1276]) ).
cnf(refute_0_1278,plain,
multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_18,Y)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))) )],[refute_0_1275,refute_0_1277]) ).
cnf(refute_0_1279,plain,
multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_18,Y)))]]) ).
cnf(refute_0_1280,plain,
( multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))
| multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) != identity
| identity = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1281,plain,
( multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))
| identity = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)),identity) )],[refute_0_1279,refute_0_1280]) ).
cnf(refute_0_1282,plain,
multiply(inverse(least_upper_bound(Y,X_18)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y))),
inference(subst,[],[refute_0_855:[bind(X_91,$fot(least_upper_bound(X_18,Y))),bind(X_92,$fot(least_upper_bound(Y,X_18)))]]) ).
cnf(refute_0_1283,plain,
( multiply(inverse(least_upper_bound(Y,X_18)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_18)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))) ),[0,1],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_1284,plain,
( multiply(inverse(least_upper_bound(Y,X_18)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))
| multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_132,refute_0_1283]) ).
cnf(refute_0_1285,plain,
multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_18)),greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))) )],[refute_0_1282,refute_0_1284]) ).
cnf(refute_0_1286,plain,
( multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y))) = multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))))]]) ).
cnf(refute_0_1287,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y))) = multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)))) )],[refute_0_1285,refute_0_1286]) ).
cnf(refute_0_1288,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))) = multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)),
inference(subst,[],[refute_0_1287:[bind(Y,$fot(X_18)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_1289,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))) != multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))
| identity != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))
| identity = multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))]]) ).
cnf(refute_0_1290,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))
| identity = multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))),multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18))) )],[refute_0_1288,refute_0_1289]) ).
cnf(refute_0_1291,plain,
( multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))
| identity = multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) ),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))) )],[refute_0_1281,refute_0_1290]) ).
cnf(refute_0_1292,plain,
identity = multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(X_18,Y)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)))) )],[refute_0_1278,refute_0_1291]) ).
cnf(refute_0_1293,plain,
identity = multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)),
inference(subst,[],[refute_0_1292:[bind(Y,$fot(X_147)),bind(X_18,$fot(X_148))]]) ).
cnf(refute_0_1294,plain,
( identity != multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148))
| multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)) = identity ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148))))]]) ).
cnf(refute_0_1295,plain,
multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148))) )],[refute_0_1293,refute_0_1294]) ).
cnf(refute_0_1296,plain,
( multiply(multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)),Z) != multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))
| multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)) != identity
| multiply(identity,Z) = multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)),Z),multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_1297,plain,
( multiply(multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)),Z) != multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))
| multiply(identity,Z) = multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)),identity) )],[refute_0_1295,refute_0_1296]) ).
cnf(refute_0_1298,plain,
multiply(identity,Z) = multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_148,X_147)),least_upper_bound(X_147,X_148)),Z),multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))) )],[refute_0_1274,refute_0_1297]) ).
cnf(refute_0_1299,plain,
multiply(identity,Z) = Z,
inference(subst,[],[left_identity:[bind(X,$fot(Z))]]) ).
cnf(refute_0_1300,plain,
( multiply(identity,Z) != Z
| multiply(identity,Z) != multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))
| Z = multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,Z),multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))) ),[0],$fot(Z)]]) ).
cnf(refute_0_1301,plain,
( multiply(identity,Z) != multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))
| Z = multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)) ),
inference(resolve,[$cnf( $equal(multiply(identity,Z),Z) )],[refute_0_1299,refute_0_1300]) ).
cnf(refute_0_1302,plain,
Z = multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)),
inference(resolve,[$cnf( $equal(multiply(identity,Z),multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))) )],[refute_0_1298,refute_0_1301]) ).
cnf(refute_0_1303,plain,
( Z != multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))
| multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)) = Z ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(Z)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))))]]) ).
cnf(refute_0_1304,plain,
multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z)) = Z,
inference(resolve,[$cnf( $equal(Z,multiply(inverse(least_upper_bound(X_148,X_147)),multiply(least_upper_bound(X_147,X_148),Z))) )],[refute_0_1302,refute_0_1303]) ).
cnf(refute_0_1305,plain,
multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))) = least_upper_bound(X_427,inverse(X_426)),
inference(subst,[],[refute_0_1304:[bind(Z,$fot(least_upper_bound(X_427,inverse(X_426)))),bind(X_147,$fot(X_426)),bind(X_148,$fot(identity))]]) ).
cnf(refute_0_1306,plain,
multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) = least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),multiply(inverse(X_75),least_upper_bound(identity,X_75))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(least_upper_bound(identity,X_75))),bind(Y,$fot(X_102)),bind(Z,$fot(inverse(X_75)))]]) ).
cnf(refute_0_1307,plain,
( multiply(inverse(X_75),least_upper_bound(identity,X_75)) != least_upper_bound(identity,inverse(X_75))
| multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) != least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),multiply(inverse(X_75),least_upper_bound(identity,X_75)))
| multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) = least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)),least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),multiply(inverse(X_75),least_upper_bound(identity,X_75)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_1308,plain,
( multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) != least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),multiply(inverse(X_75),least_upper_bound(identity,X_75)))
| multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) = least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) )],[refute_0_320,refute_0_1307]) ).
cnf(refute_0_1309,plain,
multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) = least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)),least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),multiply(inverse(X_75),least_upper_bound(identity,X_75)))) )],[refute_0_1306,refute_0_1308]) ).
cnf(refute_0_1310,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75))) = least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75)))),
inference(subst,[],[refute_0_629:[bind(X_24,$fot(identity)),bind(X_25,$fot(multiply(X_102,least_upper_bound(identity,X_75)))),bind(X_26,$fot(inverse(X_75)))]]) ).
cnf(refute_0_1311,plain,
least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75))),
inference(subst,[],[refute_0_312:[bind(Y,$fot(multiply(X_102,least_upper_bound(identity,X_75)))),bind(X_18,$fot(identity)),bind(X_34,$fot(inverse(X_75)))]]) ).
cnf(refute_0_1312,plain,
( least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) != least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75)))
| least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75))) != least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75))))
| least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75)))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75))))))]]) ).
cnf(refute_0_1313,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75))) != least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75))))
| least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75)))) )],[refute_0_1311,refute_0_1312]) ).
cnf(refute_0_1314,plain,
least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) = least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),inverse(X_75))),least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75))))) )],[refute_0_1310,refute_0_1313]) ).
cnf(refute_0_1315,plain,
( multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) != least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75)))
| least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))) != least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75))))
| multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) = least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)),least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75))))) ),[0],$fot(least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))))]]) ).
cnf(refute_0_1316,plain,
( multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) != least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75)))
| multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) = least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75))),least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75))))) )],[refute_0_1314,refute_0_1315]) ).
cnf(refute_0_1317,plain,
multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)) = least_upper_bound(identity,least_upper_bound(inverse(X_75),multiply(X_102,least_upper_bound(identity,X_75)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(X_75)),least_upper_bound(identity,X_75)),least_upper_bound(multiply(X_102,least_upper_bound(identity,X_75)),least_upper_bound(identity,inverse(X_75)))) )],[refute_0_1309,refute_0_1316]) ).
cnf(refute_0_1318,plain,
multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))))),
inference(subst,[],[refute_0_1317:[bind(X_75,$fot(inverse(multiply(X_432,X_102))))]]) ).
cnf(refute_0_1319,plain,
multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(multiply(X_102,identity),inverse(X_432)),
inference(subst,[],[refute_0_819:[bind(X_38,$fot(X_432)),bind(X_66,$fot(X_102)),bind(X_67,$fot(identity))]]) ).
cnf(refute_0_1320,plain,
( multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(multiply(X_102,identity),inverse(X_432))
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))))
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))))) ),[1,1,1],$fot(least_upper_bound(multiply(X_102,identity),inverse(X_432)))]]) ).
cnf(refute_0_1321,plain,
( multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))))
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) ),
inference(resolve,[$cnf( $equal(multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))),least_upper_bound(multiply(X_102,identity),inverse(X_432))) )],[refute_0_1319,refute_0_1320]) ).
cnf(refute_0_1322,plain,
multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))))) )],[refute_0_1318,refute_0_1321]) ).
cnf(refute_0_1323,plain,
multiply(X_102,identity) = X_102,
inference(subst,[],[refute_0_50:[bind(X_41,$fot(X_102))]]) ).
cnf(refute_0_1324,plain,
least_upper_bound(multiply(X_102,identity),inverse(X_432)) = least_upper_bound(multiply(X_102,identity),inverse(X_432)),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_102,identity),inverse(X_432)))]]) ).
cnf(refute_0_1325,plain,
( multiply(X_102,identity) != X_102
| least_upper_bound(multiply(X_102,identity),inverse(X_432)) != least_upper_bound(multiply(X_102,identity),inverse(X_432))
| least_upper_bound(multiply(X_102,identity),inverse(X_432)) = least_upper_bound(X_102,inverse(X_432)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_102,identity),inverse(X_432)),least_upper_bound(multiply(X_102,identity),inverse(X_432))) ),[1,0],$fot(X_102)]]) ).
cnf(refute_0_1326,plain,
( multiply(X_102,identity) != X_102
| least_upper_bound(multiply(X_102,identity),inverse(X_432)) = least_upper_bound(X_102,inverse(X_432)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,identity),inverse(X_432)),least_upper_bound(multiply(X_102,identity),inverse(X_432))) )],[refute_0_1324,refute_0_1325]) ).
cnf(refute_0_1327,plain,
least_upper_bound(multiply(X_102,identity),inverse(X_432)) = least_upper_bound(X_102,inverse(X_432)),
inference(resolve,[$cnf( $equal(multiply(X_102,identity),X_102) )],[refute_0_1323,refute_0_1326]) ).
cnf(refute_0_1328,plain,
( multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(multiply(X_102,identity),inverse(X_432))
| least_upper_bound(multiply(X_102,identity),inverse(X_432)) != least_upper_bound(X_102,inverse(X_432))
| multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(X_102,inverse(X_432)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))))),bind(Y0,$fot(least_upper_bound(multiply(X_102,identity),inverse(X_432)))),bind(Z0,$fot(least_upper_bound(X_102,inverse(X_432))))]]) ).
cnf(refute_0_1329,plain,
( least_upper_bound(multiply(X_102,identity),inverse(X_432)) != least_upper_bound(X_102,inverse(X_432))
| multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(X_102,inverse(X_432)) ),
inference(resolve,[$cnf( $equal(multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))),least_upper_bound(multiply(X_102,identity),inverse(X_432))) )],[refute_0_1319,refute_0_1328]) ).
cnf(refute_0_1330,plain,
multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = least_upper_bound(X_102,inverse(X_432)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,identity),inverse(X_432)),least_upper_bound(X_102,inverse(X_432))) )],[refute_0_1327,refute_0_1329]) ).
cnf(refute_0_1331,plain,
multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))) = multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))))]]) ).
cnf(refute_0_1332,plain,
( multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(X_102,inverse(X_432))
| multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))) != multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))))
| multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))),multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))))) ),[1,1],$fot(least_upper_bound(X_102,inverse(X_432)))]]) ).
cnf(refute_0_1333,plain,
( multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(X_102,inverse(X_432))
| multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))),multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))))) )],[refute_0_1331,refute_0_1332]) ).
cnf(refute_0_1334,plain,
multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))),
inference(resolve,[$cnf( $equal(multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))),least_upper_bound(X_102,inverse(X_432))) )],[refute_0_1330,refute_0_1333]) ).
cnf(refute_0_1335,plain,
multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_432,identity))),bind(Y,$fot(X_102)),bind(Z,$fot(least_upper_bound(identity,inverse(multiply(X_432,X_102)))))]]) ).
cnf(refute_0_1336,plain,
( multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))))
| multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))) != multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))
| multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))))),bind(Y0,$fot(multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))))),bind(Z0,$fot(multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))))]]) ).
cnf(refute_0_1337,plain,
( multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))) != multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))
| multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102)))))) )],[refute_0_1335,refute_0_1336]) ).
cnf(refute_0_1338,plain,
multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_432,identity),multiply(X_102,least_upper_bound(identity,inverse(multiply(X_432,X_102))))),multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))) )],[refute_0_1334,refute_0_1337]) ).
cnf(refute_0_1339,plain,
( multiply(least_upper_bound(X_102,identity),X_101) != least_upper_bound(X_101,multiply(X_102,X_101))
| least_upper_bound(X_101,multiply(X_102,X_101)) = multiply(least_upper_bound(X_102,identity),X_101) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(X_102,identity),X_101))),bind(Y0,$fot(least_upper_bound(X_101,multiply(X_102,X_101))))]]) ).
cnf(refute_0_1340,plain,
least_upper_bound(X_101,multiply(X_102,X_101)) = multiply(least_upper_bound(X_102,identity),X_101),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,identity),X_101),least_upper_bound(X_101,multiply(X_102,X_101))) )],[refute_0_530,refute_0_1339]) ).
cnf(refute_0_1341,plain,
least_upper_bound(X_102,multiply(X_432,X_102)) = multiply(least_upper_bound(X_432,identity),X_102),
inference(subst,[],[refute_0_1340:[bind(X_101,$fot(X_102)),bind(X_102,$fot(X_432))]]) ).
cnf(refute_0_1342,plain,
inverse(inverse(multiply(X_432,X_102))) = multiply(X_432,X_102),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(multiply(X_432,X_102)))]]) ).
cnf(refute_0_1343,plain,
least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))))]]) ).
cnf(refute_0_1344,plain,
( inverse(inverse(multiply(X_432,X_102))) != multiply(X_432,X_102)
| least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) != least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102))))
| least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(X_102,multiply(X_432,X_102)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102))))) ),[1,1],$fot(multiply(X_432,X_102))]]) ).
cnf(refute_0_1345,plain,
( inverse(inverse(multiply(X_432,X_102))) != multiply(X_432,X_102)
| least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(X_102,multiply(X_432,X_102)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102))))) )],[refute_0_1343,refute_0_1344]) ).
cnf(refute_0_1346,plain,
least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(X_102,multiply(X_432,X_102)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_432,X_102))),multiply(X_432,X_102)) )],[refute_0_1342,refute_0_1345]) ).
cnf(refute_0_1347,plain,
( least_upper_bound(X_102,multiply(X_432,X_102)) != multiply(least_upper_bound(X_432,identity),X_102)
| least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) != least_upper_bound(X_102,multiply(X_432,X_102))
| least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),X_102) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))))),bind(Y0,$fot(least_upper_bound(X_102,multiply(X_432,X_102)))),bind(Z0,$fot(multiply(least_upper_bound(X_432,identity),X_102)))]]) ).
cnf(refute_0_1348,plain,
( least_upper_bound(X_102,multiply(X_432,X_102)) != multiply(least_upper_bound(X_432,identity),X_102)
| least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),X_102) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(X_102,multiply(X_432,X_102))) )],[refute_0_1346,refute_0_1347]) ).
cnf(refute_0_1349,plain,
least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),X_102),
inference(resolve,[$cnf( $equal(least_upper_bound(X_102,multiply(X_432,X_102)),multiply(least_upper_bound(X_432,identity),X_102)) )],[refute_0_1341,refute_0_1348]) ).
cnf(refute_0_1350,plain,
multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))))]]) ).
cnf(refute_0_1351,plain,
( multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102))))
| least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) != multiply(least_upper_bound(X_432,identity),X_102)
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102))))) ),[1,0],$fot(multiply(least_upper_bound(X_432,identity),X_102))]]) ).
cnf(refute_0_1352,plain,
( least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))) != multiply(least_upper_bound(X_432,identity),X_102)
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102))))) )],[refute_0_1350,refute_0_1351]) ).
cnf(refute_0_1353,plain,
multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),multiply(least_upper_bound(X_432,identity),X_102)) )],[refute_0_1349,refute_0_1352]) ).
cnf(refute_0_1354,plain,
( multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102))))
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))))),bind(Y0,$fot(multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))))),bind(Z0,$fot(multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))))]]) ).
cnf(refute_0_1355,plain,
( multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102))))) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_432,identity),X_102),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))) )],[refute_0_1338,refute_0_1355]) ).
cnf(refute_0_1357,plain,
( multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))
| multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))
| multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))) ),[0],$fot(multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))))]]) ).
cnf(refute_0_1358,plain,
( multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))
| multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) = least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432)))) )],[refute_0_1356,refute_0_1357]) ).
cnf(refute_0_1359,plain,
least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))]]) ).
cnf(refute_0_1360,plain,
( inverse(inverse(multiply(X_432,X_102))) != multiply(X_432,X_102)
| least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))) != least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))
| least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(inverse(X_432),multiply(X_432,X_102)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) ),[1,1],$fot(multiply(X_432,X_102))]]) ).
cnf(refute_0_1361,plain,
( inverse(inverse(multiply(X_432,X_102))) != multiply(X_432,X_102)
| least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(inverse(X_432),multiply(X_432,X_102)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) )],[refute_0_1359,refute_0_1360]) ).
cnf(refute_0_1362,plain,
least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))) = least_upper_bound(inverse(X_432),multiply(X_432,X_102)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_432,X_102))),multiply(X_432,X_102)) )],[refute_0_1342,refute_0_1361]) ).
cnf(refute_0_1363,plain,
least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))]]) ).
cnf(refute_0_1364,plain,
( least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) != least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))
| least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))) != least_upper_bound(inverse(X_432),multiply(X_432,X_102))
| least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) ),[1,1],$fot(least_upper_bound(inverse(X_432),multiply(X_432,X_102)))]]) ).
cnf(refute_0_1365,plain,
( least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))) != least_upper_bound(inverse(X_432),multiply(X_432,X_102))
| least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) )],[refute_0_1363,refute_0_1364]) ).
cnf(refute_0_1366,plain,
least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(inverse(X_432),multiply(X_432,X_102))) )],[refute_0_1362,refute_0_1365]) ).
cnf(refute_0_1367,plain,
least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))]]) ).
cnf(refute_0_1368,plain,
( multiply(X_102,identity) != X_102
| least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) != least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))
| least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) ),[1,0],$fot(X_102)]]) ).
cnf(refute_0_1369,plain,
( multiply(X_102,identity) != X_102
| least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) )],[refute_0_1367,refute_0_1368]) ).
cnf(refute_0_1370,plain,
least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),
inference(resolve,[$cnf( $equal(multiply(X_102,identity),X_102) )],[refute_0_1323,refute_0_1369]) ).
cnf(refute_0_1371,plain,
( least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) != least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))
| least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) != least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))
| least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))),bind(Y0,$fot(least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))),bind(Z0,$fot(least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))))]]) ).
cnf(refute_0_1372,plain,
( least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) != least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))
| least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) )],[refute_0_1370,refute_0_1371]) ).
cnf(refute_0_1373,plain,
least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) = least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_102,least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) )],[refute_0_1366,refute_0_1372]) ).
cnf(refute_0_1374,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) = least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))))]]) ).
cnf(refute_0_1375,plain,
( least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) != least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))
| least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) != least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))
| least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))),least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))) ),[1,1],$fot(least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))]]) ).
cnf(refute_0_1376,plain,
( least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))) != least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))
| least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))),least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))) )],[refute_0_1374,refute_0_1375]) ).
cnf(refute_0_1377,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))),least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) )],[refute_0_1373,refute_0_1376]) ).
cnf(refute_0_1378,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(Y,least_upper_bound(X_208,identity))) = least_upper_bound(least_upper_bound(X_208,identity),Y),
inference(subst,[],[refute_0_132:[bind(X_18,$fot(least_upper_bound(X_208,identity)))]]) ).
cnf(refute_0_1379,plain,
inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))) = multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(inverse(X_145))),bind(X_52,$fot(greatest_lower_bound(identity,X_145)))]]) ).
cnf(refute_0_1380,plain,
multiply(greatest_lower_bound(identity,X_124),inverse(X_124)) = greatest_lower_bound(identity,multiply(identity,inverse(X_124))),
inference(subst,[],[refute_0_1076:[bind(X_111,$fot(identity)),bind(X_112,$fot(X_124))]]) ).
cnf(refute_0_1381,plain,
multiply(identity,inverse(X_124)) = inverse(X_124),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_124)))]]) ).
cnf(refute_0_1382,plain,
( multiply(greatest_lower_bound(identity,X_124),inverse(X_124)) != greatest_lower_bound(identity,multiply(identity,inverse(X_124)))
| multiply(identity,inverse(X_124)) != inverse(X_124)
| multiply(greatest_lower_bound(identity,X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_124),inverse(X_124)),greatest_lower_bound(identity,multiply(identity,inverse(X_124)))) ),[1,1],$fot(inverse(X_124))]]) ).
cnf(refute_0_1383,plain,
( multiply(greatest_lower_bound(identity,X_124),inverse(X_124)) != greatest_lower_bound(identity,multiply(identity,inverse(X_124)))
| multiply(greatest_lower_bound(identity,X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(X_124)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_124)),inverse(X_124)) )],[refute_0_1381,refute_0_1382]) ).
cnf(refute_0_1384,plain,
multiply(greatest_lower_bound(identity,X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(X_124)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_124),inverse(X_124)),greatest_lower_bound(identity,multiply(identity,inverse(X_124)))) )],[refute_0_1380,refute_0_1383]) ).
cnf(refute_0_1385,plain,
multiply(greatest_lower_bound(identity,X_145),inverse(X_145)) = greatest_lower_bound(identity,inverse(X_145)),
inference(subst,[],[refute_0_1384:[bind(X_124,$fot(X_145))]]) ).
cnf(refute_0_1386,plain,
( multiply(greatest_lower_bound(identity,X_145),inverse(X_145)) != greatest_lower_bound(identity,inverse(X_145))
| inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))) != multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))
| inverse(greatest_lower_bound(identity,inverse(X_145))) = multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))),multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_145)))]]) ).
cnf(refute_0_1387,plain,
( inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))) != multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))
| inverse(greatest_lower_bound(identity,inverse(X_145))) = multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_145),inverse(X_145)),greatest_lower_bound(identity,inverse(X_145))) )],[refute_0_1385,refute_0_1386]) ).
cnf(refute_0_1388,plain,
inverse(greatest_lower_bound(identity,inverse(X_145))) = multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))),multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))) )],[refute_0_1379,refute_0_1387]) ).
cnf(refute_0_1389,plain,
inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))) = multiply(X_145,inverse(greatest_lower_bound(identity,X_145))),
inference(subst,[],[refute_0_1214:[bind(X_44,$fot(X_145)),bind(X_52,$fot(greatest_lower_bound(identity,X_145)))]]) ).
cnf(refute_0_1390,plain,
multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) = inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(inverse(X_145))),bind(X_52,$fot(greatest_lower_bound(identity,X_145)))]]) ).
cnf(refute_0_1391,plain,
( multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) != inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145)))
| inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))) != multiply(X_145,inverse(greatest_lower_bound(identity,X_145)))
| multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) = multiply(X_145,inverse(greatest_lower_bound(identity,X_145))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))))),bind(Z0,$fot(multiply(X_145,inverse(greatest_lower_bound(identity,X_145)))))]]) ).
cnf(refute_0_1392,plain,
( inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))) != multiply(X_145,inverse(greatest_lower_bound(identity,X_145)))
| multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) = multiply(X_145,inverse(greatest_lower_bound(identity,X_145))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))),inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145)))) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) = multiply(X_145,inverse(greatest_lower_bound(identity,X_145))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_145),inverse(X_145))),multiply(X_145,inverse(greatest_lower_bound(identity,X_145)))) )],[refute_0_1389,refute_0_1392]) ).
cnf(refute_0_1394,plain,
( multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))) != multiply(X_145,inverse(greatest_lower_bound(identity,X_145)))
| inverse(greatest_lower_bound(identity,inverse(X_145))) != multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))
| inverse(greatest_lower_bound(identity,inverse(X_145))) = multiply(X_145,inverse(greatest_lower_bound(identity,X_145))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_145))),multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))) ),[1],$fot(multiply(X_145,inverse(greatest_lower_bound(identity,X_145))))]]) ).
cnf(refute_0_1395,plain,
( inverse(greatest_lower_bound(identity,inverse(X_145))) != multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))
| inverse(greatest_lower_bound(identity,inverse(X_145))) = multiply(X_145,inverse(greatest_lower_bound(identity,X_145))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145))),multiply(X_145,inverse(greatest_lower_bound(identity,X_145)))) )],[refute_0_1393,refute_0_1394]) ).
cnf(refute_0_1396,plain,
inverse(greatest_lower_bound(identity,inverse(X_145))) = multiply(X_145,inverse(greatest_lower_bound(identity,X_145))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_145))),multiply(inverse(inverse(X_145)),inverse(greatest_lower_bound(identity,X_145)))) )],[refute_0_1388,refute_0_1395]) ).
cnf(refute_0_1397,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity))))),
inference(subst,[],[refute_0_1396:[bind(X_145,$fot(least_upper_bound(X_205,least_upper_bound(X_206,identity))))]]) ).
cnf(refute_0_1398,plain,
greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_24,X_25),X)) = X,
inference(subst,[],[refute_0_127:[bind(Y,$fot(least_upper_bound(X_24,X_25)))]]) ).
cnf(refute_0_1399,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_24,X_25),X)) != X
| least_upper_bound(least_upper_bound(X_24,X_25),X) != least_upper_bound(X_24,least_upper_bound(X_25,X))
| greatest_lower_bound(X,least_upper_bound(X_24,least_upper_bound(X_25,X))) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_24,X_25),X)),X) ),[0,1],$fot(least_upper_bound(X_24,least_upper_bound(X_25,X)))]]) ).
cnf(refute_0_1400,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_24,X_25),X)) != X
| greatest_lower_bound(X,least_upper_bound(X_24,least_upper_bound(X_25,X))) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_24,X_25),X),least_upper_bound(X_24,least_upper_bound(X_25,X))) )],[refute_0_259,refute_0_1399]) ).
cnf(refute_0_1401,plain,
greatest_lower_bound(X,least_upper_bound(X_24,least_upper_bound(X_25,X))) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_24,X_25),X)),X) )],[refute_0_1398,refute_0_1400]) ).
cnf(refute_0_1402,plain,
greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity))) = identity,
inference(subst,[],[refute_0_1401:[bind(X,$fot(identity)),bind(X_24,$fot(X_205)),bind(X_25,$fot(X_206))]]) ).
cnf(refute_0_1403,plain,
( greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity))) != identity
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity)))))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity)))))) ),[1,1,0],$fot(identity)]]) ).
cnf(refute_0_1404,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity)))))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity))),identity) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(greatest_lower_bound(identity,least_upper_bound(X_205,least_upper_bound(X_206,identity)))))) )],[refute_0_1397,refute_0_1404]) ).
cnf(refute_0_1406,plain,
inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))) = least_upper_bound(identity,least_upper_bound(X_205,X_206)),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(least_upper_bound(identity,least_upper_bound(X_205,X_206))))]]) ).
cnf(refute_0_1407,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124))),
inference(subst,[],[refute_0_1076:[bind(X_111,$fot(inverse(least_upper_bound(inverse(X_124),identity)))),bind(X_112,$fot(X_124))]]) ).
cnf(refute_0_1408,plain,
inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))) = multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(least_upper_bound(X_75,identity))),bind(X_52,$fot(inverse(X_75)))]]) ).
cnf(refute_0_1409,plain,
( multiply(inverse(X_75),least_upper_bound(X_75,identity)) != least_upper_bound(identity,inverse(X_75))
| inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))) != multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))
| inverse(least_upper_bound(identity,inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))),multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_75)))]]) ).
cnf(refute_0_1410,plain,
( inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))) != multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))
| inverse(least_upper_bound(identity,inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_75),least_upper_bound(X_75,identity)),least_upper_bound(identity,inverse(X_75))) )],[refute_0_79,refute_0_1409]) ).
cnf(refute_0_1411,plain,
inverse(least_upper_bound(identity,inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))),multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))) )],[refute_0_1408,refute_0_1410]) ).
cnf(refute_0_1412,plain,
inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))) = multiply(inverse(least_upper_bound(X_75,identity)),X_75),
inference(subst,[],[refute_0_464:[bind(X_39,$fot(least_upper_bound(X_75,identity))),bind(X_55,$fot(X_75))]]) ).
cnf(refute_0_1413,plain,
multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) = inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(least_upper_bound(X_75,identity))),bind(X_52,$fot(inverse(X_75)))]]) ).
cnf(refute_0_1414,plain,
( multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) != inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity)))
| inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))) != multiply(inverse(least_upper_bound(X_75,identity)),X_75)
| multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),X_75) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))))),bind(Y0,$fot(inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_75,identity)),X_75)))]]) ).
cnf(refute_0_1415,plain,
( inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))) != multiply(inverse(least_upper_bound(X_75,identity)),X_75)
| multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),X_75) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))),inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity)))) )],[refute_0_1413,refute_0_1414]) ).
cnf(refute_0_1416,plain,
multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),X_75),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_75),least_upper_bound(X_75,identity))),multiply(inverse(least_upper_bound(X_75,identity)),X_75)) )],[refute_0_1412,refute_0_1415]) ).
cnf(refute_0_1417,plain,
( multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))) != multiply(inverse(least_upper_bound(X_75,identity)),X_75)
| inverse(least_upper_bound(identity,inverse(X_75))) != multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))
| inverse(least_upper_bound(identity,inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_75))),multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_75,identity)),X_75))]]) ).
cnf(refute_0_1418,plain,
( inverse(least_upper_bound(identity,inverse(X_75))) != multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))
| inverse(least_upper_bound(identity,inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),X_75) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75))),multiply(inverse(least_upper_bound(X_75,identity)),X_75)) )],[refute_0_1416,refute_0_1417]) ).
cnf(refute_0_1419,plain,
inverse(least_upper_bound(identity,inverse(X_75))) = multiply(inverse(least_upper_bound(X_75,identity)),X_75),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_75))),multiply(inverse(least_upper_bound(X_75,identity)),inverse(inverse(X_75)))) )],[refute_0_1411,refute_0_1418]) ).
cnf(refute_0_1420,plain,
inverse(least_upper_bound(identity,inverse(inverse(X_124)))) = multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)),
inference(subst,[],[refute_0_1419:[bind(X_75,$fot(inverse(X_124)))]]) ).
cnf(refute_0_1421,plain,
( inverse(least_upper_bound(identity,inverse(inverse(X_124)))) != multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124))
| multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)) = inverse(least_upper_bound(identity,inverse(inverse(X_124)))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(inverse(X_124)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124))))]]) ).
cnf(refute_0_1422,plain,
multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)) = inverse(least_upper_bound(identity,inverse(inverse(X_124)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(inverse(X_124)))),multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124))) )],[refute_0_1420,refute_0_1421]) ).
cnf(refute_0_1423,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)))
| multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)) != inverse(least_upper_bound(identity,inverse(inverse(X_124))))
| multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(inverse(X_124)))))]]) ).
cnf(refute_0_1424,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)))
| multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)),inverse(least_upper_bound(identity,inverse(inverse(X_124))))) )],[refute_0_1422,refute_0_1423]) ).
cnf(refute_0_1425,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_124),identity)),inverse(X_124)))) )],[refute_0_1407,refute_0_1424]) ).
cnf(refute_0_1426,plain,
multiply(least_upper_bound(X_124,identity),identity) = least_upper_bound(X_124,identity),
inference(subst,[],[refute_0_50:[bind(X_41,$fot(least_upper_bound(X_124,identity)))]]) ).
cnf(refute_0_1427,plain,
least_upper_bound(identity,multiply(X_124,identity)) = multiply(least_upper_bound(X_124,identity),identity),
inference(subst,[],[refute_0_1340:[bind(X_101,$fot(identity)),bind(X_102,$fot(X_124))]]) ).
cnf(refute_0_1428,plain,
( multiply(least_upper_bound(X_124,identity),identity) != least_upper_bound(X_124,identity)
| least_upper_bound(identity,multiply(X_124,identity)) != multiply(least_upper_bound(X_124,identity),identity)
| least_upper_bound(identity,multiply(X_124,identity)) = least_upper_bound(X_124,identity) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,multiply(X_124,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_124,identity),identity))),bind(Z0,$fot(least_upper_bound(X_124,identity)))]]) ).
cnf(refute_0_1429,plain,
( multiply(least_upper_bound(X_124,identity),identity) != least_upper_bound(X_124,identity)
| least_upper_bound(identity,multiply(X_124,identity)) = least_upper_bound(X_124,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_124,identity)),multiply(least_upper_bound(X_124,identity),identity)) )],[refute_0_1427,refute_0_1428]) ).
cnf(refute_0_1430,plain,
least_upper_bound(identity,multiply(X_124,identity)) = least_upper_bound(X_124,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_124,identity),identity),least_upper_bound(X_124,identity)) )],[refute_0_1426,refute_0_1429]) ).
cnf(refute_0_1431,plain,
multiply(X_66,least_upper_bound(X_67,inverse(X_66))) = least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(X_66))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_66)),bind(Y,$fot(X_67)),bind(Z,$fot(inverse(X_66)))]]) ).
cnf(refute_0_1432,plain,
( multiply(X_66,inverse(X_66)) != identity
| multiply(X_66,least_upper_bound(X_67,inverse(X_66))) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(X_66)))
| multiply(X_66,least_upper_bound(X_67,inverse(X_66))) = least_upper_bound(multiply(X_66,X_67),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,inverse(X_66))),least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(X_66)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1433,plain,
( multiply(X_66,least_upper_bound(X_67,inverse(X_66))) != least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(X_66)))
| multiply(X_66,least_upper_bound(X_67,inverse(X_66))) = least_upper_bound(multiply(X_66,X_67),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_66,inverse(X_66)),identity) )],[refute_0_1195,refute_0_1432]) ).
cnf(refute_0_1434,plain,
multiply(X_66,least_upper_bound(X_67,inverse(X_66))) = least_upper_bound(multiply(X_66,X_67),identity),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,inverse(X_66))),least_upper_bound(multiply(X_66,X_67),multiply(X_66,inverse(X_66)))) )],[refute_0_1431,refute_0_1433]) ).
cnf(refute_0_1435,plain,
least_upper_bound(multiply(X_66,X_67),identity) = least_upper_bound(identity,multiply(X_66,X_67)),
inference(subst,[],[refute_0_64:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_66,X_67)))]]) ).
cnf(refute_0_1436,plain,
( multiply(X_66,least_upper_bound(X_67,inverse(X_66))) != least_upper_bound(multiply(X_66,X_67),identity)
| least_upper_bound(multiply(X_66,X_67),identity) != least_upper_bound(identity,multiply(X_66,X_67))
| multiply(X_66,least_upper_bound(X_67,inverse(X_66))) = least_upper_bound(identity,multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_66,least_upper_bound(X_67,inverse(X_66))),least_upper_bound(identity,multiply(X_66,X_67))) ),[0],$fot(least_upper_bound(multiply(X_66,X_67),identity))]]) ).
cnf(refute_0_1437,plain,
( multiply(X_66,least_upper_bound(X_67,inverse(X_66))) != least_upper_bound(multiply(X_66,X_67),identity)
| multiply(X_66,least_upper_bound(X_67,inverse(X_66))) = least_upper_bound(identity,multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_66,X_67),identity),least_upper_bound(identity,multiply(X_66,X_67))) )],[refute_0_1435,refute_0_1436]) ).
cnf(refute_0_1438,plain,
multiply(X_66,least_upper_bound(X_67,inverse(X_66))) = least_upper_bound(identity,multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(X_66,least_upper_bound(X_67,inverse(X_66))),least_upper_bound(multiply(X_66,X_67),identity)) )],[refute_0_1434,refute_0_1437]) ).
cnf(refute_0_1439,plain,
multiply(X_124,least_upper_bound(identity,inverse(X_124))) = least_upper_bound(identity,multiply(X_124,identity)),
inference(subst,[],[refute_0_1438:[bind(X_66,$fot(X_124)),bind(X_67,$fot(identity))]]) ).
cnf(refute_0_1440,plain,
( multiply(X_124,least_upper_bound(identity,inverse(X_124))) != least_upper_bound(identity,multiply(X_124,identity))
| least_upper_bound(identity,multiply(X_124,identity)) != least_upper_bound(X_124,identity)
| multiply(X_124,least_upper_bound(identity,inverse(X_124))) = least_upper_bound(X_124,identity) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(X_124,least_upper_bound(identity,inverse(X_124))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_124,identity)))),bind(Z0,$fot(least_upper_bound(X_124,identity)))]]) ).
cnf(refute_0_1441,plain,
( least_upper_bound(identity,multiply(X_124,identity)) != least_upper_bound(X_124,identity)
| multiply(X_124,least_upper_bound(identity,inverse(X_124))) = least_upper_bound(X_124,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_124,least_upper_bound(identity,inverse(X_124))),least_upper_bound(identity,multiply(X_124,identity))) )],[refute_0_1439,refute_0_1440]) ).
cnf(refute_0_1442,plain,
multiply(X_124,least_upper_bound(identity,inverse(X_124))) = least_upper_bound(X_124,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_124,identity)),least_upper_bound(X_124,identity)) )],[refute_0_1430,refute_0_1441]) ).
cnf(refute_0_1443,plain,
inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))) = inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))))]]) ).
cnf(refute_0_1444,plain,
( multiply(X_124,least_upper_bound(identity,inverse(X_124))) != least_upper_bound(X_124,identity)
| inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))) != inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124))))
| inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))) = inverse(least_upper_bound(X_124,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))),inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124))))) ),[1,0],$fot(least_upper_bound(X_124,identity))]]) ).
cnf(refute_0_1445,plain,
( multiply(X_124,least_upper_bound(identity,inverse(X_124))) != least_upper_bound(X_124,identity)
| inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))) = inverse(least_upper_bound(X_124,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))),inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124))))) )],[refute_0_1443,refute_0_1444]) ).
cnf(refute_0_1446,plain,
inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))) = inverse(least_upper_bound(X_124,identity)),
inference(resolve,[$cnf( $equal(multiply(X_124,least_upper_bound(identity,inverse(X_124))),least_upper_bound(X_124,identity)) )],[refute_0_1442,refute_0_1445]) ).
cnf(refute_0_1447,plain,
inverse(multiply(X_52,least_upper_bound(identity,X_122))) = multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52)),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(least_upper_bound(identity,X_122)))]]) ).
cnf(refute_0_1448,plain,
multiply(X_52,least_upper_bound(identity,X_122)) = multiply(X_52,least_upper_bound(X_122,identity)),
inference(subst,[],[refute_0_192:[bind(X_19,$fot(X_52)),bind(X_70,$fot(X_122))]]) ).
cnf(refute_0_1449,plain,
( multiply(X_52,least_upper_bound(identity,X_122)) != multiply(X_52,least_upper_bound(X_122,identity))
| inverse(multiply(X_52,least_upper_bound(identity,X_122))) != multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))
| inverse(multiply(X_52,least_upper_bound(X_122,identity))) = multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_52,least_upper_bound(identity,X_122))),multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))) ),[0,0],$fot(multiply(X_52,least_upper_bound(X_122,identity)))]]) ).
cnf(refute_0_1450,plain,
( inverse(multiply(X_52,least_upper_bound(identity,X_122))) != multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))
| inverse(multiply(X_52,least_upper_bound(X_122,identity))) = multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52)) ),
inference(resolve,[$cnf( $equal(multiply(X_52,least_upper_bound(identity,X_122)),multiply(X_52,least_upper_bound(X_122,identity))) )],[refute_0_1448,refute_0_1449]) ).
cnf(refute_0_1451,plain,
inverse(multiply(X_52,least_upper_bound(X_122,identity))) = multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_52,least_upper_bound(identity,X_122))),multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))) )],[refute_0_1447,refute_0_1450]) ).
cnf(refute_0_1452,plain,
multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52)) = inverse(multiply(X_52,least_upper_bound(identity,X_122))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(least_upper_bound(identity,X_122)))]]) ).
cnf(refute_0_1453,plain,
( multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52)) != inverse(multiply(X_52,least_upper_bound(identity,X_122)))
| inverse(multiply(X_52,least_upper_bound(X_122,identity))) != multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))
| inverse(multiply(X_52,least_upper_bound(X_122,identity))) = inverse(multiply(X_52,least_upper_bound(identity,X_122))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_52,least_upper_bound(X_122,identity))),multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))) ),[1],$fot(inverse(multiply(X_52,least_upper_bound(identity,X_122))))]]) ).
cnf(refute_0_1454,plain,
( inverse(multiply(X_52,least_upper_bound(X_122,identity))) != multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))
| inverse(multiply(X_52,least_upper_bound(X_122,identity))) = inverse(multiply(X_52,least_upper_bound(identity,X_122))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52)),inverse(multiply(X_52,least_upper_bound(identity,X_122)))) )],[refute_0_1452,refute_0_1453]) ).
cnf(refute_0_1455,plain,
inverse(multiply(X_52,least_upper_bound(X_122,identity))) = inverse(multiply(X_52,least_upper_bound(identity,X_122))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_52,least_upper_bound(X_122,identity))),multiply(inverse(least_upper_bound(identity,X_122)),inverse(X_52))) )],[refute_0_1451,refute_0_1454]) ).
cnf(refute_0_1456,plain,
inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))) = inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))),
inference(subst,[],[refute_0_1455:[bind(X_122,$fot(inverse(X_124))),bind(X_52,$fot(X_124))]]) ).
cnf(refute_0_1457,plain,
( inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))) != inverse(least_upper_bound(X_124,identity))
| inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))) != inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124))))
| inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))) = inverse(least_upper_bound(X_124,identity)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))))),bind(Y0,$fot(inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))))),bind(Z0,$fot(inverse(least_upper_bound(X_124,identity))))]]) ).
cnf(refute_0_1458,plain,
( inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))) != inverse(least_upper_bound(X_124,identity))
| inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))) = inverse(least_upper_bound(X_124,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))),inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124))))) )],[refute_0_1456,refute_0_1457]) ).
cnf(refute_0_1459,plain,
inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))) = inverse(least_upper_bound(X_124,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_124,least_upper_bound(identity,inverse(X_124)))),inverse(least_upper_bound(X_124,identity))) )],[refute_0_1446,refute_0_1458]) ).
cnf(refute_0_1460,plain,
greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))) = greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))))]]) ).
cnf(refute_0_1461,plain,
( greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))) != greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))))
| inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))) != inverse(least_upper_bound(X_124,identity))
| greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))),greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))))) ),[1,1],$fot(inverse(least_upper_bound(X_124,identity)))]]) ).
cnf(refute_0_1462,plain,
( inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))) != inverse(least_upper_bound(X_124,identity))
| greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))),greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))))) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))),inverse(least_upper_bound(X_124,identity))) )],[refute_0_1459,refute_0_1462]) ).
cnf(refute_0_1464,plain,
multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) = greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124))),
inference(subst,[],[refute_0_826:[bind(X_92,$fot(inverse(X_124)))]]) ).
cnf(refute_0_1465,plain,
multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) = greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124))),
inference(subst,[],[refute_0_1076:[bind(X_111,$fot(inverse(X_91))),bind(X_112,$fot(X_124))]]) ).
cnf(refute_0_1466,plain,
( multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) != greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124)))
| greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124)))))]]) ).
cnf(refute_0_1467,plain,
greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)),greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124)))) )],[refute_0_1465,refute_0_1466]) ).
cnf(refute_0_1468,plain,
( multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) != greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124)))
| greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124))) != multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))
| multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))),multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124))))]]) ).
cnf(refute_0_1469,plain,
( multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) != greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124)))
| multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124))),multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))) )],[refute_0_1467,refute_0_1468]) ).
cnf(refute_0_1470,plain,
multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))),greatest_lower_bound(identity,multiply(inverse(X_91),inverse(X_124)))) )],[refute_0_1464,refute_0_1469]) ).
cnf(refute_0_1471,plain,
multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))) = greatest_lower_bound(identity,multiply(inverse(X_99),inverse(X_52))),
inference(subst,[],[refute_0_826:[bind(X_91,$fot(X_99)),bind(X_92,$fot(inverse(X_52)))]]) ).
cnf(refute_0_1472,plain,
inverse(multiply(X_52,X_99)) = multiply(inverse(X_99),inverse(X_52)),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(X_99))]]) ).
cnf(refute_0_1473,plain,
( inverse(multiply(X_52,X_99)) != multiply(inverse(X_99),inverse(X_52))
| multiply(inverse(X_99),inverse(X_52)) = inverse(multiply(X_52,X_99)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(multiply(X_52,X_99)))),bind(Y0,$fot(multiply(inverse(X_99),inverse(X_52))))]]) ).
cnf(refute_0_1474,plain,
multiply(inverse(X_99),inverse(X_52)) = inverse(multiply(X_52,X_99)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_52,X_99)),multiply(inverse(X_99),inverse(X_52))) )],[refute_0_1472,refute_0_1473]) ).
cnf(refute_0_1475,plain,
( multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))) != greatest_lower_bound(identity,multiply(inverse(X_99),inverse(X_52)))
| multiply(inverse(X_99),inverse(X_52)) != inverse(multiply(X_52,X_99))
| multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))) = greatest_lower_bound(identity,inverse(multiply(X_52,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))),greatest_lower_bound(identity,multiply(inverse(X_99),inverse(X_52)))) ),[1,1],$fot(inverse(multiply(X_52,X_99)))]]) ).
cnf(refute_0_1476,plain,
( multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))) != greatest_lower_bound(identity,multiply(inverse(X_99),inverse(X_52)))
| multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))) = greatest_lower_bound(identity,inverse(multiply(X_52,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),inverse(X_52)),inverse(multiply(X_52,X_99))) )],[refute_0_1474,refute_0_1475]) ).
cnf(refute_0_1477,plain,
multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))) = greatest_lower_bound(identity,inverse(multiply(X_52,X_99))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),greatest_lower_bound(X_99,inverse(X_52))),greatest_lower_bound(identity,multiply(inverse(X_99),inverse(X_52)))) )],[refute_0_1471,refute_0_1476]) ).
cnf(refute_0_1478,plain,
multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) = greatest_lower_bound(identity,inverse(multiply(X_124,X_91))),
inference(subst,[],[refute_0_1477:[bind(X_52,$fot(X_124)),bind(X_99,$fot(X_91))]]) ).
cnf(refute_0_1479,plain,
( multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) != multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))
| multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) != greatest_lower_bound(identity,inverse(multiply(X_124,X_91)))
| greatest_lower_bound(identity,inverse(multiply(X_124,X_91))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))),multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))) ),[0],$fot(greatest_lower_bound(identity,inverse(multiply(X_124,X_91))))]]) ).
cnf(refute_0_1480,plain,
( multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))) != multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))
| greatest_lower_bound(identity,inverse(multiply(X_124,X_91))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))),greatest_lower_bound(identity,inverse(multiply(X_124,X_91)))) )],[refute_0_1478,refute_0_1479]) ).
cnf(refute_0_1481,plain,
greatest_lower_bound(identity,inverse(multiply(X_124,X_91))) = multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),greatest_lower_bound(X_91,inverse(X_124))),multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))) )],[refute_0_1470,refute_0_1480]) ).
cnf(refute_0_1482,plain,
( greatest_lower_bound(identity,inverse(multiply(X_124,X_91))) != multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))
| multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(multiply(X_124,X_91))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(identity,inverse(multiply(X_124,X_91))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))))]]) ).
cnf(refute_0_1483,plain,
multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(multiply(X_124,X_91))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_124,X_91))),multiply(greatest_lower_bound(inverse(X_91),X_124),inverse(X_124))) )],[refute_0_1481,refute_0_1482]) ).
cnf(refute_0_1484,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))),
inference(subst,[],[refute_0_1483:[bind(X_91,$fot(least_upper_bound(inverse(X_124),identity)))]]) ).
cnf(refute_0_1485,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) != greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))))
| greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity)))
| multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity)))))]]) ).
cnf(refute_0_1486,plain,
( greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity)))
| multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)),greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity))))) )],[refute_0_1484,refute_0_1485]) ).
cnf(refute_0_1487,plain,
multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_124,least_upper_bound(inverse(X_124),identity)))),greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity)))) )],[refute_0_1463,refute_0_1486]) ).
cnf(refute_0_1488,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) != greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity)))
| multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))))]]) ).
cnf(refute_0_1489,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)),greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity)))) )],[refute_0_1487,refute_0_1488]) ).
cnf(refute_0_1490,plain,
least_upper_bound(identity,inverse(inverse(X_124))) = least_upper_bound(identity,inverse(inverse(X_124))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(inverse(X_124))))]]) ).
cnf(refute_0_1491,plain,
( inverse(inverse(X_124)) != X_124
| least_upper_bound(identity,inverse(inverse(X_124))) != least_upper_bound(identity,inverse(inverse(X_124)))
| least_upper_bound(identity,inverse(inverse(X_124))) = least_upper_bound(identity,X_124) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_124))),least_upper_bound(identity,inverse(inverse(X_124)))) ),[1,1],$fot(X_124)]]) ).
cnf(refute_0_1492,plain,
( inverse(inverse(X_124)) != X_124
| least_upper_bound(identity,inverse(inverse(X_124))) = least_upper_bound(identity,X_124) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_124))),least_upper_bound(identity,inverse(inverse(X_124)))) )],[refute_0_1490,refute_0_1491]) ).
cnf(refute_0_1493,plain,
least_upper_bound(identity,inverse(inverse(X_124))) = least_upper_bound(identity,X_124),
inference(resolve,[$cnf( $equal(inverse(inverse(X_124)),X_124) )],[refute_0_1085,refute_0_1492]) ).
cnf(refute_0_1494,plain,
inverse(least_upper_bound(identity,inverse(inverse(X_124)))) = inverse(least_upper_bound(identity,inverse(inverse(X_124)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(inverse(X_124)))))]]) ).
cnf(refute_0_1495,plain,
( inverse(least_upper_bound(identity,inverse(inverse(X_124)))) != inverse(least_upper_bound(identity,inverse(inverse(X_124))))
| least_upper_bound(identity,inverse(inverse(X_124))) != least_upper_bound(identity,X_124)
| inverse(least_upper_bound(identity,inverse(inverse(X_124)))) = inverse(least_upper_bound(identity,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(inverse(X_124)))),inverse(least_upper_bound(identity,inverse(inverse(X_124))))) ),[1,0],$fot(least_upper_bound(identity,X_124))]]) ).
cnf(refute_0_1496,plain,
( least_upper_bound(identity,inverse(inverse(X_124))) != least_upper_bound(identity,X_124)
| inverse(least_upper_bound(identity,inverse(inverse(X_124)))) = inverse(least_upper_bound(identity,X_124)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(inverse(X_124)))),inverse(least_upper_bound(identity,inverse(inverse(X_124))))) )],[refute_0_1494,refute_0_1495]) ).
cnf(refute_0_1497,plain,
inverse(least_upper_bound(identity,inverse(inverse(X_124)))) = inverse(least_upper_bound(identity,X_124)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_124))),least_upper_bound(identity,X_124)) )],[refute_0_1493,refute_0_1496]) ).
cnf(refute_0_1498,plain,
multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)),
inference(subst,[],[refute_0_855:[bind(X_91,$fot(X_97)),bind(X_92,$fot(least_upper_bound(X_97,identity)))]]) ).
cnf(refute_0_1499,plain,
inverse(least_upper_bound(identity,inverse(X_97))) = multiply(inverse(least_upper_bound(X_97,identity)),X_97),
inference(subst,[],[refute_0_1419:[bind(X_75,$fot(X_97))]]) ).
cnf(refute_0_1500,plain,
( inverse(least_upper_bound(identity,inverse(X_97))) != multiply(inverse(least_upper_bound(X_97,identity)),X_97)
| multiply(inverse(least_upper_bound(X_97,identity)),X_97) = inverse(least_upper_bound(identity,inverse(X_97))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_97))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_97,identity)),X_97)))]]) ).
cnf(refute_0_1501,plain,
multiply(inverse(least_upper_bound(X_97,identity)),X_97) = inverse(least_upper_bound(identity,inverse(X_97))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_97))),multiply(inverse(least_upper_bound(X_97,identity)),X_97)) )],[refute_0_1499,refute_0_1500]) ).
cnf(refute_0_1502,plain,
( multiply(inverse(least_upper_bound(X_97,identity)),X_97) != inverse(least_upper_bound(identity,inverse(X_97)))
| multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97))
| multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(X_97))))]]) ).
cnf(refute_0_1503,plain,
( multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97))
| multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),X_97),inverse(least_upper_bound(identity,inverse(X_97)))) )],[refute_0_1501,refute_0_1502]) ).
cnf(refute_0_1504,plain,
multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97))) )],[refute_0_1498,refute_0_1503]) ).
cnf(refute_0_1505,plain,
multiply(inverse(least_upper_bound(X_97,Y)),greatest_lower_bound(X_97,least_upper_bound(X_97,Y))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97)),
inference(subst,[],[refute_0_855:[bind(X_91,$fot(X_97)),bind(X_92,$fot(least_upper_bound(X_97,Y)))]]) ).
cnf(refute_0_1506,plain,
greatest_lower_bound(X_97,least_upper_bound(X_97,Y)) = X_97,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_1507,plain,
( multiply(inverse(least_upper_bound(X_97,Y)),greatest_lower_bound(X_97,least_upper_bound(X_97,Y))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97))
| greatest_lower_bound(X_97,least_upper_bound(X_97,Y)) != X_97
| multiply(inverse(least_upper_bound(X_97,Y)),X_97) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,Y)),greatest_lower_bound(X_97,least_upper_bound(X_97,Y))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97))) ),[0,1],$fot(X_97)]]) ).
cnf(refute_0_1508,plain,
( multiply(inverse(least_upper_bound(X_97,Y)),greatest_lower_bound(X_97,least_upper_bound(X_97,Y))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97))
| multiply(inverse(least_upper_bound(X_97,Y)),X_97) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_97,least_upper_bound(X_97,Y)),X_97) )],[refute_0_1506,refute_0_1507]) ).
cnf(refute_0_1509,plain,
multiply(inverse(least_upper_bound(X_97,Y)),X_97) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,Y)),greatest_lower_bound(X_97,least_upper_bound(X_97,Y))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97))) )],[refute_0_1505,refute_0_1508]) ).
cnf(refute_0_1510,plain,
( multiply(inverse(least_upper_bound(X_97,Y)),X_97) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97)) = multiply(inverse(least_upper_bound(X_97,Y)),X_97) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_97,Y)),X_97))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97))))]]) ).
cnf(refute_0_1511,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97)) = multiply(inverse(least_upper_bound(X_97,Y)),X_97),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,Y)),X_97),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,Y)),X_97))) )],[refute_0_1509,refute_0_1510]) ).
cnf(refute_0_1512,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)) = multiply(inverse(least_upper_bound(X_97,identity)),X_97),
inference(subst,[],[refute_0_1511:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_1513,plain,
( multiply(inverse(least_upper_bound(X_97,identity)),X_97) != inverse(least_upper_bound(identity,inverse(X_97)))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)) != multiply(inverse(least_upper_bound(X_97,identity)),X_97)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)) = inverse(least_upper_bound(identity,inverse(X_97))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_97,identity)),X_97))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_97)))))]]) ).
cnf(refute_0_1514,plain,
( multiply(inverse(least_upper_bound(X_97,identity)),X_97) != inverse(least_upper_bound(identity,inverse(X_97)))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)) = inverse(least_upper_bound(identity,inverse(X_97))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)),multiply(inverse(least_upper_bound(X_97,identity)),X_97)) )],[refute_0_1512,refute_0_1513]) ).
cnf(refute_0_1515,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)) = inverse(least_upper_bound(identity,inverse(X_97))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),X_97),inverse(least_upper_bound(identity,inverse(X_97)))) )],[refute_0_1501,refute_0_1514]) ).
cnf(refute_0_1516,plain,
( multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)) != inverse(least_upper_bound(identity,inverse(X_97)))
| multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) = inverse(least_upper_bound(identity,inverse(X_97))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_97)))))]]) ).
cnf(refute_0_1517,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)) != inverse(least_upper_bound(identity,inverse(X_97)))
| multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) = inverse(least_upper_bound(identity,inverse(X_97))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97))) )],[refute_0_1498,refute_0_1516]) ).
cnf(refute_0_1518,plain,
multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) = inverse(least_upper_bound(identity,inverse(X_97))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_97,identity)),X_97)),inverse(least_upper_bound(identity,inverse(X_97)))) )],[refute_0_1515,refute_0_1517]) ).
cnf(refute_0_1519,plain,
( multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97))))
| multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) != inverse(least_upper_bound(identity,inverse(X_97)))
| inverse(least_upper_bound(identity,inverse(X_97))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97))))) ),[0],$fot(inverse(least_upper_bound(identity,inverse(X_97))))]]) ).
cnf(refute_0_1520,plain,
( multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97))))
| inverse(least_upper_bound(identity,inverse(X_97))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))),inverse(least_upper_bound(identity,inverse(X_97)))) )],[refute_0_1518,refute_0_1519]) ).
cnf(refute_0_1521,plain,
inverse(least_upper_bound(identity,inverse(X_97))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_97,identity)),greatest_lower_bound(X_97,least_upper_bound(X_97,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97))))) )],[refute_0_1504,refute_0_1520]) ).
cnf(refute_0_1522,plain,
( inverse(least_upper_bound(identity,inverse(X_97))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97))))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))) = inverse(least_upper_bound(identity,inverse(X_97))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_97))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97))))))]]) ).
cnf(refute_0_1523,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97)))) = inverse(least_upper_bound(identity,inverse(X_97))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_97))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_97))))) )],[refute_0_1521,refute_0_1522]) ).
cnf(refute_0_1524,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) = inverse(least_upper_bound(identity,inverse(inverse(X_124)))),
inference(subst,[],[refute_0_1523:[bind(X_97,$fot(inverse(X_124)))]]) ).
cnf(refute_0_1525,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) != inverse(least_upper_bound(identity,inverse(inverse(X_124))))
| inverse(least_upper_bound(identity,inverse(inverse(X_124)))) != inverse(least_upper_bound(identity,X_124))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) = inverse(least_upper_bound(identity,X_124)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(inverse(X_124)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_124))))]]) ).
cnf(refute_0_1526,plain,
( inverse(least_upper_bound(identity,inverse(inverse(X_124)))) != inverse(least_upper_bound(identity,X_124))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) = inverse(least_upper_bound(identity,X_124)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))),inverse(least_upper_bound(identity,inverse(inverse(X_124))))) )],[refute_0_1524,refute_0_1525]) ).
cnf(refute_0_1527,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) = inverse(least_upper_bound(identity,X_124)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(inverse(X_124)))),inverse(least_upper_bound(identity,X_124))) )],[refute_0_1497,refute_0_1526]) ).
cnf(refute_0_1528,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))) != inverse(least_upper_bound(identity,X_124))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) = inverse(least_upper_bound(identity,X_124)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))),inverse(least_upper_bound(identity,X_124))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))))]]) ).
cnf(refute_0_1529,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) = inverse(least_upper_bound(identity,X_124)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124))))),inverse(least_upper_bound(identity,X_124))) )],[refute_0_1527,refute_0_1528]) ).
cnf(refute_0_1530,plain,
( multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) = inverse(least_upper_bound(identity,X_124)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))) )],[refute_0_1489,refute_0_1529]) ).
cnf(refute_0_1531,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_124,identity))) = inverse(least_upper_bound(identity,X_124)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(inverse(X_124),identity)),X_124),inverse(X_124)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(inverse(X_124)))))) )],[refute_0_1425,refute_0_1530]) ).
cnf(refute_0_1532,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(least_upper_bound(X,Y),identity))) = inverse(least_upper_bound(identity,least_upper_bound(X,Y))),
inference(subst,[],[refute_0_1531:[bind(X_124,$fot(least_upper_bound(X,Y)))]]) ).
cnf(refute_0_1533,plain,
least_upper_bound(X,least_upper_bound(Y,identity)) = least_upper_bound(least_upper_bound(X,Y),identity),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(identity))]]) ).
cnf(refute_0_1534,plain,
( least_upper_bound(X,least_upper_bound(Y,identity)) != least_upper_bound(least_upper_bound(X,Y),identity)
| least_upper_bound(least_upper_bound(X,Y),identity) = least_upper_bound(X,least_upper_bound(Y,identity)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,identity)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),identity)))]]) ).
cnf(refute_0_1535,plain,
least_upper_bound(least_upper_bound(X,Y),identity) = least_upper_bound(X,least_upper_bound(Y,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,identity)),least_upper_bound(least_upper_bound(X,Y),identity)) )],[refute_0_1533,refute_0_1534]) ).
cnf(refute_0_1536,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(least_upper_bound(X,Y),identity))) != inverse(least_upper_bound(identity,least_upper_bound(X,Y)))
| least_upper_bound(least_upper_bound(X,Y),identity) != least_upper_bound(X,least_upper_bound(Y,identity))
| greatest_lower_bound(identity,inverse(least_upper_bound(X,least_upper_bound(Y,identity)))) = inverse(least_upper_bound(identity,least_upper_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(least_upper_bound(X,Y),identity))),inverse(least_upper_bound(identity,least_upper_bound(X,Y)))) ),[0,1,0],$fot(least_upper_bound(X,least_upper_bound(Y,identity)))]]) ).
cnf(refute_0_1537,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(least_upper_bound(X,Y),identity))) != inverse(least_upper_bound(identity,least_upper_bound(X,Y)))
| greatest_lower_bound(identity,inverse(least_upper_bound(X,least_upper_bound(Y,identity)))) = inverse(least_upper_bound(identity,least_upper_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),identity),least_upper_bound(X,least_upper_bound(Y,identity))) )],[refute_0_1535,refute_0_1536]) ).
cnf(refute_0_1538,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X,least_upper_bound(Y,identity)))) = inverse(least_upper_bound(identity,least_upper_bound(X,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(least_upper_bound(X,Y),identity))),inverse(least_upper_bound(identity,least_upper_bound(X,Y)))) )],[refute_0_1532,refute_0_1537]) ).
cnf(refute_0_1539,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206))),
inference(subst,[],[refute_0_1538:[bind(X,$fot(X_205)),bind(Y,$fot(X_206))]]) ).
cnf(refute_0_1540,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))))]]) ).
cnf(refute_0_1541,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity)))) != inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity)))))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity)))))) ),[1,0],$fot(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206))))]]) ).
cnf(refute_0_1542,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity)))) != inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity)))))) )],[refute_0_1540,refute_0_1541]) ).
cnf(refute_0_1543,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity)))),inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))) )],[refute_0_1539,refute_0_1542]) ).
cnf(refute_0_1544,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206))))
| inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))) != least_upper_bound(identity,least_upper_bound(X_205,X_206))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = least_upper_bound(identity,least_upper_bound(X_205,X_206)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_205,X_206))))]]) ).
cnf(refute_0_1545,plain,
( inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))) != least_upper_bound(identity,least_upper_bound(X_205,X_206))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = least_upper_bound(identity,least_upper_bound(X_205,X_206)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206))))) )],[refute_0_1543,refute_0_1544]) ).
cnf(refute_0_1546,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) = least_upper_bound(identity,least_upper_bound(X_205,X_206)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,least_upper_bound(X_205,X_206)))),least_upper_bound(identity,least_upper_bound(X_205,X_206))) )],[refute_0_1406,refute_0_1545]) ).
cnf(refute_0_1547,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != least_upper_bound(identity,least_upper_bound(X_205,X_206))
| least_upper_bound(identity,least_upper_bound(X_205,X_206)) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_205,X_206)))]]) ).
cnf(refute_0_1548,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))
| least_upper_bound(identity,least_upper_bound(X_205,X_206)) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),least_upper_bound(identity,least_upper_bound(X_205,X_206))) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity) = least_upper_bound(X_205,least_upper_bound(X_206,identity)),
inference(subst,[],[refute_0_50:[bind(X_41,$fot(least_upper_bound(X_205,least_upper_bound(X_206,identity))))]]) ).
cnf(refute_0_1550,plain,
X_41 = multiply(inverse(identity),multiply(identity,X_41)),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(identity)),bind(X_39,$fot(X_41))]]) ).
cnf(refute_0_1551,plain,
multiply(identity,X_41) = X_41,
inference(subst,[],[left_identity:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_1552,plain,
( X_41 != multiply(inverse(identity),multiply(identity,X_41))
| multiply(identity,X_41) != X_41
| X_41 = multiply(inverse(identity),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(X_41,multiply(inverse(identity),multiply(identity,X_41))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_1553,plain,
( X_41 != multiply(inverse(identity),multiply(identity,X_41))
| X_41 = multiply(inverse(identity),X_41) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_41),X_41) )],[refute_0_1551,refute_0_1552]) ).
cnf(refute_0_1554,plain,
X_41 = multiply(inverse(identity),X_41),
inference(resolve,[$cnf( $equal(X_41,multiply(inverse(identity),multiply(identity,X_41))) )],[refute_0_1550,refute_0_1553]) ).
cnf(refute_0_1555,plain,
identity = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_1554:[bind(X_41,$fot(identity))]]) ).
cnf(refute_0_1556,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_48:[bind(X_41,$fot(inverse(identity)))]]) ).
cnf(refute_0_1557,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_1558,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_1556,refute_0_1557]) ).
cnf(refute_0_1559,plain,
( multiply(inverse(identity),identity) != inverse(identity)
| identity != multiply(inverse(identity),identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,multiply(inverse(identity),identity)) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_1560,plain,
( identity != multiply(inverse(identity),identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_1558,refute_0_1559]) ).
cnf(refute_0_1561,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,multiply(inverse(identity),identity)) )],[refute_0_1555,refute_0_1560]) ).
cnf(refute_0_1562,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(identity)),bind(Y0,$fot(inverse(identity)))]]) ).
cnf(refute_0_1563,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_1561,refute_0_1562]) ).
cnf(refute_0_1564,plain,
multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)))]]) ).
cnf(refute_0_1565,plain,
( multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))
| inverse(identity) != identity
| multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1566,plain,
( inverse(identity) != identity
| multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))) )],[refute_0_1564,refute_0_1565]) ).
cnf(refute_0_1567,plain,
multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) = multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1563,refute_0_1566]) ).
cnf(refute_0_1568,plain,
( multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity) != least_upper_bound(X_205,least_upper_bound(X_206,identity))
| multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity)
| multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity))),bind(Z0,$fot(least_upper_bound(X_205,least_upper_bound(X_206,identity))))]]) ).
cnf(refute_0_1569,plain,
( multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity) != least_upper_bound(X_205,least_upper_bound(X_206,identity))
| multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity)) )],[refute_0_1567,refute_0_1568]) ).
cnf(refute_0_1570,plain,
multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),identity),least_upper_bound(X_205,least_upper_bound(X_206,identity))) )],[refute_0_1549,refute_0_1569]) ).
cnf(refute_0_1571,plain,
( multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)) != least_upper_bound(X_205,least_upper_bound(X_206,identity))
| least_upper_bound(identity,least_upper_bound(X_205,X_206)) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))
| least_upper_bound(identity,least_upper_bound(X_205,X_206)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_205,X_206)),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))) ),[1],$fot(least_upper_bound(X_205,least_upper_bound(X_206,identity)))]]) ).
cnf(refute_0_1572,plain,
( least_upper_bound(identity,least_upper_bound(X_205,X_206)) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))
| least_upper_bound(identity,least_upper_bound(X_205,X_206)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity)),least_upper_bound(X_205,least_upper_bound(X_206,identity))) )],[refute_0_1570,refute_0_1571]) ).
cnf(refute_0_1573,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))) != multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))
| least_upper_bound(identity,least_upper_bound(X_205,X_206)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_205,X_206)),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))) )],[refute_0_1548,refute_0_1572]) ).
cnf(refute_0_1574,plain,
least_upper_bound(identity,least_upper_bound(X_205,X_206)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_205,least_upper_bound(X_206,identity))))),multiply(least_upper_bound(X_205,least_upper_bound(X_206,identity)),inverse(identity))) )],[refute_0_1405,refute_0_1573]) ).
cnf(refute_0_1575,plain,
least_upper_bound(identity,least_upper_bound(Y,X_208)) = least_upper_bound(Y,least_upper_bound(X_208,identity)),
inference(subst,[],[refute_0_1574:[bind(X_205,$fot(Y)),bind(X_206,$fot(X_208))]]) ).
cnf(refute_0_1576,plain,
( least_upper_bound(identity,least_upper_bound(Y,X_208)) != least_upper_bound(Y,least_upper_bound(X_208,identity))
| least_upper_bound(Y,least_upper_bound(X_208,identity)) = least_upper_bound(identity,least_upper_bound(Y,X_208)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(Y,X_208)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_208,identity))))]]) ).
cnf(refute_0_1577,plain,
least_upper_bound(Y,least_upper_bound(X_208,identity)) = least_upper_bound(identity,least_upper_bound(Y,X_208)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(Y,least_upper_bound(X_208,identity))) )],[refute_0_1575,refute_0_1576]) ).
cnf(refute_0_1578,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(Y,least_upper_bound(X_208,identity))) != least_upper_bound(least_upper_bound(X_208,identity),Y)
| least_upper_bound(Y,least_upper_bound(X_208,identity)) != least_upper_bound(identity,least_upper_bound(Y,X_208))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) = least_upper_bound(least_upper_bound(X_208,identity),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(Y,least_upper_bound(X_208,identity))),least_upper_bound(least_upper_bound(X_208,identity),Y)) ),[0,1],$fot(least_upper_bound(identity,least_upper_bound(Y,X_208)))]]) ).
cnf(refute_0_1579,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(Y,least_upper_bound(X_208,identity))) != least_upper_bound(least_upper_bound(X_208,identity),Y)
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) = least_upper_bound(least_upper_bound(X_208,identity),Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_208,identity)),least_upper_bound(identity,least_upper_bound(Y,X_208))) )],[refute_0_1577,refute_0_1578]) ).
cnf(refute_0_1580,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) = least_upper_bound(least_upper_bound(X_208,identity),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(Y,least_upper_bound(X_208,identity))),least_upper_bound(least_upper_bound(X_208,identity),Y)) )],[refute_0_1378,refute_0_1579]) ).
cnf(refute_0_1581,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X_29,least_upper_bound(X,Y))) = least_upper_bound(least_upper_bound(X,Y),X_29),
inference(subst,[],[refute_0_132:[bind(Y,$fot(X_29)),bind(X_18,$fot(least_upper_bound(X,Y)))]]) ).
cnf(refute_0_1582,plain,
least_upper_bound(X,least_upper_bound(Y,X_29)) = least_upper_bound(least_upper_bound(X,Y),X_29),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(X_29))]]) ).
cnf(refute_0_1583,plain,
( least_upper_bound(X,least_upper_bound(Y,X_29)) != least_upper_bound(least_upper_bound(X,Y),X_29)
| least_upper_bound(least_upper_bound(X,Y),X_29) = least_upper_bound(X,least_upper_bound(Y,X_29)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_29)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),X_29)))]]) ).
cnf(refute_0_1584,plain,
least_upper_bound(least_upper_bound(X,Y),X_29) = least_upper_bound(X,least_upper_bound(Y,X_29)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(least_upper_bound(X,Y),X_29)) )],[refute_0_1582,refute_0_1583]) ).
cnf(refute_0_1585,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X_29,least_upper_bound(X,Y))) != least_upper_bound(least_upper_bound(X,Y),X_29)
| least_upper_bound(least_upper_bound(X,Y),X_29) != least_upper_bound(X,least_upper_bound(Y,X_29))
| greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) = least_upper_bound(least_upper_bound(X,Y),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X_29,least_upper_bound(X,Y))),least_upper_bound(least_upper_bound(X,Y),X_29)) ),[0,0],$fot(least_upper_bound(X,least_upper_bound(Y,X_29)))]]) ).
cnf(refute_0_1586,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X_29,least_upper_bound(X,Y))) != least_upper_bound(least_upper_bound(X,Y),X_29)
| greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) = least_upper_bound(least_upper_bound(X,Y),X_29) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X,least_upper_bound(Y,X_29))) )],[refute_0_1584,refute_0_1585]) ).
cnf(refute_0_1587,plain,
greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) = least_upper_bound(least_upper_bound(X,Y),X_29),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X_29,least_upper_bound(X,Y))),least_upper_bound(least_upper_bound(X,Y),X_29)) )],[refute_0_1581,refute_0_1586]) ).
cnf(refute_0_1588,plain,
( greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) != least_upper_bound(least_upper_bound(X,Y),X_29)
| least_upper_bound(least_upper_bound(X,Y),X_29) != least_upper_bound(X,least_upper_bound(Y,X_29))
| greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) = least_upper_bound(X,least_upper_bound(Y,X_29)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(Y,X_29))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),X_29))]]) ).
cnf(refute_0_1589,plain,
( greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) != least_upper_bound(least_upper_bound(X,Y),X_29)
| greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) = least_upper_bound(X,least_upper_bound(Y,X_29)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X,least_upper_bound(Y,X_29))) )],[refute_0_1584,refute_0_1588]) ).
cnf(refute_0_1590,plain,
greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))) = least_upper_bound(X,least_upper_bound(Y,X_29)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(X_29,least_upper_bound(X,Y))),least_upper_bound(least_upper_bound(X,Y),X_29)) )],[refute_0_1587,refute_0_1589]) ).
cnf(refute_0_1591,plain,
greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(Y,X_208)),
inference(subst,[],[refute_0_1590:[bind(X,$fot(identity)),bind(X_29,$fot(X_208))]]) ).
cnf(refute_0_1592,plain,
least_upper_bound(least_upper_bound(X_208,identity),Y) = least_upper_bound(X_208,least_upper_bound(identity,Y)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_208)),bind(Y,$fot(identity)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1593,plain,
greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)))]]) ).
cnf(refute_0_1594,plain,
( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) != greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y))
| least_upper_bound(least_upper_bound(X_208,identity),Y) != least_upper_bound(X_208,least_upper_bound(identity,Y))
| greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y))) ),[1,1],$fot(least_upper_bound(X_208,least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_1595,plain,
( least_upper_bound(least_upper_bound(X_208,identity),Y) != least_upper_bound(X_208,least_upper_bound(identity,Y))
| greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y))) )],[refute_0_1593,refute_0_1594]) ).
cnf(refute_0_1596,plain,
greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(X_208,least_upper_bound(identity,Y))) )],[refute_0_1592,refute_0_1595]) ).
cnf(refute_0_1597,plain,
( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))) != least_upper_bound(identity,least_upper_bound(Y,X_208))
| greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) != greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y)))
| greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) = least_upper_bound(identity,least_upper_bound(Y,X_208)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(Y,X_208))))]]) ).
cnf(refute_0_1598,plain,
( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))) != least_upper_bound(identity,least_upper_bound(Y,X_208))
| greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) = least_upper_bound(identity,least_upper_bound(Y,X_208)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y)))) )],[refute_0_1596,refute_0_1597]) ).
cnf(refute_0_1599,plain,
greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) = least_upper_bound(identity,least_upper_bound(Y,X_208)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))),least_upper_bound(identity,least_upper_bound(Y,X_208))) )],[refute_0_1591,refute_0_1598]) ).
cnf(refute_0_1600,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)),
inference(subst,[],[refute_0_164:[bind(X,$fot(least_upper_bound(identity,least_upper_bound(Y,X_208)))),bind(Y,$fot(least_upper_bound(least_upper_bound(X_208,identity),Y)))]]) ).
cnf(refute_0_1601,plain,
( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) != least_upper_bound(identity,least_upper_bound(Y,X_208))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) != greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) = least_upper_bound(identity,least_upper_bound(Y,X_208)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(Y,X_208))))]]) ).
cnf(refute_0_1602,plain,
( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) != least_upper_bound(identity,least_upper_bound(Y,X_208))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) = least_upper_bound(identity,least_upper_bound(Y,X_208)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y))) )],[refute_0_1600,refute_0_1601]) ).
cnf(refute_0_1603,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) = least_upper_bound(identity,least_upper_bound(Y,X_208)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)),least_upper_bound(identity,least_upper_bound(Y,X_208))) )],[refute_0_1599,refute_0_1602]) ).
cnf(refute_0_1604,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) != least_upper_bound(identity,least_upper_bound(Y,X_208))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) != least_upper_bound(least_upper_bound(X_208,identity),Y)
| least_upper_bound(identity,least_upper_bound(Y,X_208)) = least_upper_bound(least_upper_bound(X_208,identity),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))),least_upper_bound(least_upper_bound(X_208,identity),Y)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(Y,X_208)))]]) ).
cnf(refute_0_1605,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) != least_upper_bound(least_upper_bound(X_208,identity),Y)
| least_upper_bound(identity,least_upper_bound(Y,X_208)) = least_upper_bound(least_upper_bound(X_208,identity),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))),least_upper_bound(identity,least_upper_bound(Y,X_208))) )],[refute_0_1603,refute_0_1604]) ).
cnf(refute_0_1606,plain,
( least_upper_bound(identity,least_upper_bound(Y,X_208)) != least_upper_bound(least_upper_bound(X_208,identity),Y)
| least_upper_bound(least_upper_bound(X_208,identity),Y) != least_upper_bound(X_208,least_upper_bound(identity,Y))
| least_upper_bound(identity,least_upper_bound(Y,X_208)) = least_upper_bound(X_208,least_upper_bound(identity,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(X_208,least_upper_bound(identity,Y))) ),[0],$fot(least_upper_bound(least_upper_bound(X_208,identity),Y))]]) ).
cnf(refute_0_1607,plain,
( least_upper_bound(identity,least_upper_bound(Y,X_208)) != least_upper_bound(least_upper_bound(X_208,identity),Y)
| least_upper_bound(identity,least_upper_bound(Y,X_208)) = least_upper_bound(X_208,least_upper_bound(identity,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(X_208,least_upper_bound(identity,Y))) )],[refute_0_1592,refute_0_1606]) ).
cnf(refute_0_1608,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))) != least_upper_bound(least_upper_bound(X_208,identity),Y)
| least_upper_bound(identity,least_upper_bound(Y,X_208)) = least_upper_bound(X_208,least_upper_bound(identity,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,X_208)),least_upper_bound(least_upper_bound(X_208,identity),Y)) )],[refute_0_1605,refute_0_1607]) ).
cnf(refute_0_1609,plain,
least_upper_bound(identity,least_upper_bound(Y,X_208)) = least_upper_bound(X_208,least_upper_bound(identity,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_208,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_208))),least_upper_bound(least_upper_bound(X_208,identity),Y)) )],[refute_0_1580,refute_0_1608]) ).
cnf(refute_0_1610,plain,
least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))) = least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)),
inference(subst,[],[refute_0_1609:[bind(Y,$fot(X_357)),bind(X_208,$fot(least_upper_bound(X_25,X_26)))]]) ).
cnf(refute_0_1611,plain,
least_upper_bound(X_357,least_upper_bound(X_26,X_25)) = least_upper_bound(X_357,least_upper_bound(X_25,X_26)),
inference(subst,[],[refute_0_627:[bind(X_24,$fot(X_357))]]) ).
cnf(refute_0_1612,plain,
( least_upper_bound(X_357,least_upper_bound(X_26,X_25)) != least_upper_bound(X_357,least_upper_bound(X_25,X_26))
| least_upper_bound(X_357,least_upper_bound(X_25,X_26)) = least_upper_bound(X_357,least_upper_bound(X_26,X_25)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_357,least_upper_bound(X_26,X_25)))),bind(Y0,$fot(least_upper_bound(X_357,least_upper_bound(X_25,X_26))))]]) ).
cnf(refute_0_1613,plain,
least_upper_bound(X_357,least_upper_bound(X_25,X_26)) = least_upper_bound(X_357,least_upper_bound(X_26,X_25)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_357,least_upper_bound(X_26,X_25)),least_upper_bound(X_357,least_upper_bound(X_25,X_26))) )],[refute_0_1611,refute_0_1612]) ).
cnf(refute_0_1614,plain,
( least_upper_bound(X_357,least_upper_bound(X_25,X_26)) != least_upper_bound(X_357,least_upper_bound(X_26,X_25))
| least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))) != least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357))
| least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) = least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))),least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357))) ),[0,1],$fot(least_upper_bound(X_357,least_upper_bound(X_26,X_25)))]]) ).
cnf(refute_0_1615,plain,
( least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))) != least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357))
| least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) = least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_357,least_upper_bound(X_25,X_26)),least_upper_bound(X_357,least_upper_bound(X_26,X_25))) )],[refute_0_1613,refute_0_1614]) ).
cnf(refute_0_1616,plain,
least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) = least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))),least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357))) )],[refute_0_1610,refute_0_1615]) ).
cnf(refute_0_1617,plain,
least_upper_bound(identity,least_upper_bound(X_24,X_26)) = least_upper_bound(X_24,least_upper_bound(identity,X_26)),
inference(subst,[],[refute_0_289:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_1618,plain,
multiply(inverse(X_68),least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(inverse(X_68),X_67),multiply(inverse(X_68),X_68)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_68))),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_1619,plain,
multiply(inverse(X_68),X_68) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_68))]]) ).
cnf(refute_0_1620,plain,
( multiply(inverse(X_68),X_68) != identity
| multiply(inverse(X_68),least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(inverse(X_68),X_67),multiply(inverse(X_68),X_68))
| multiply(inverse(X_68),least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(inverse(X_68),X_67),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_68),least_upper_bound(X_67,X_68)),least_upper_bound(multiply(inverse(X_68),X_67),multiply(inverse(X_68),X_68))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1621,plain,
( multiply(inverse(X_68),least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(inverse(X_68),X_67),multiply(inverse(X_68),X_68))
| multiply(inverse(X_68),least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(inverse(X_68),X_67),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_68),X_68),identity) )],[refute_0_1619,refute_0_1620]) ).
cnf(refute_0_1622,plain,
multiply(inverse(X_68),least_upper_bound(X_67,X_68)) = least_upper_bound(multiply(inverse(X_68),X_67),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_68),least_upper_bound(X_67,X_68)),least_upper_bound(multiply(inverse(X_68),X_67),multiply(inverse(X_68),X_68))) )],[refute_0_1618,refute_0_1621]) ).
cnf(refute_0_1623,plain,
least_upper_bound(multiply(inverse(X_68),X_67),identity) = least_upper_bound(identity,multiply(inverse(X_68),X_67)),
inference(subst,[],[refute_0_64:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_68),X_67)))]]) ).
cnf(refute_0_1624,plain,
( multiply(inverse(X_68),least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(inverse(X_68),X_67),identity)
| least_upper_bound(multiply(inverse(X_68),X_67),identity) != least_upper_bound(identity,multiply(inverse(X_68),X_67))
| multiply(inverse(X_68),least_upper_bound(X_67,X_68)) = least_upper_bound(identity,multiply(inverse(X_68),X_67)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_68),least_upper_bound(X_67,X_68)),least_upper_bound(identity,multiply(inverse(X_68),X_67))) ),[0],$fot(least_upper_bound(multiply(inverse(X_68),X_67),identity))]]) ).
cnf(refute_0_1625,plain,
( multiply(inverse(X_68),least_upper_bound(X_67,X_68)) != least_upper_bound(multiply(inverse(X_68),X_67),identity)
| multiply(inverse(X_68),least_upper_bound(X_67,X_68)) = least_upper_bound(identity,multiply(inverse(X_68),X_67)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_68),X_67),identity),least_upper_bound(identity,multiply(inverse(X_68),X_67))) )],[refute_0_1623,refute_0_1624]) ).
cnf(refute_0_1626,plain,
multiply(inverse(X_68),least_upper_bound(X_67,X_68)) = least_upper_bound(identity,multiply(inverse(X_68),X_67)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_68),least_upper_bound(X_67,X_68)),least_upper_bound(multiply(inverse(X_68),X_67),identity)) )],[refute_0_1622,refute_0_1625]) ).
cnf(refute_0_1627,plain,
multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68))),
inference(subst,[],[refute_0_1626:[bind(X_67,$fot(least_upper_bound(inverse(inverse(X_77)),X_68))),bind(X_68,$fot(X_77))]]) ).
cnf(refute_0_1628,plain,
multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68)) = least_upper_bound(identity,multiply(inverse(X_77),X_68)),
inference(subst,[],[refute_0_1198:[bind(X_66,$fot(inverse(X_77)))]]) ).
cnf(refute_0_1629,plain,
( multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68)) != least_upper_bound(identity,multiply(inverse(X_77),X_68))
| multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) != least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68)))
| multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)),least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_77),X_68)))]]) ).
cnf(refute_0_1630,plain,
( multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) != least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68)))
| multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68)),least_upper_bound(identity,multiply(inverse(X_77),X_68))) )],[refute_0_1628,refute_0_1629]) ).
cnf(refute_0_1631,plain,
multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)),least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(inverse(inverse(X_77)),X_68)))) )],[refute_0_1627,refute_0_1630]) ).
cnf(refute_0_1632,plain,
multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = least_upper_bound(multiply(X,least_upper_bound(X_72,inverse(X))),multiply(X,Z)),
inference(subst,[],[monotony_lub1:[bind(Y,$fot(least_upper_bound(X_72,inverse(X))))]]) ).
cnf(refute_0_1633,plain,
multiply(X,least_upper_bound(X_72,inverse(X))) = least_upper_bound(identity,multiply(X,X_72)),
inference(subst,[],[refute_0_1438:[bind(X_66,$fot(X)),bind(X_67,$fot(X_72))]]) ).
cnf(refute_0_1634,plain,
( multiply(X,least_upper_bound(X_72,inverse(X))) != least_upper_bound(identity,multiply(X,X_72))
| multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_72,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_72,inverse(X))),multiply(X,Z))) ),[1,0],$fot(least_upper_bound(identity,multiply(X,X_72)))]]) ).
cnf(refute_0_1635,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_72,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_72,inverse(X))),least_upper_bound(identity,multiply(X,X_72))) )],[refute_0_1633,refute_0_1634]) ).
cnf(refute_0_1636,plain,
multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_72,inverse(X))),multiply(X,Z))) )],[refute_0_1632,refute_0_1635]) ).
cnf(refute_0_1637,plain,
least_upper_bound(least_upper_bound(X_72,inverse(X)),Z) = least_upper_bound(X_72,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_72)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_1638,plain,
multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)))]]) ).
cnf(refute_0_1639,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) != multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z))
| least_upper_bound(least_upper_bound(X_72,inverse(X)),Z) != least_upper_bound(X_72,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z))) ),[1,1],$fot(least_upper_bound(X_72,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_1640,plain,
( least_upper_bound(least_upper_bound(X_72,inverse(X)),Z) != least_upper_bound(X_72,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z))) )],[refute_0_1638,refute_0_1639]) ).
cnf(refute_0_1641,plain,
multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) = multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_72,inverse(X)),Z),least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) )],[refute_0_1637,refute_0_1640]) ).
cnf(refute_0_1642,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) != multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z)))
| multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))
| multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))) ),[0],$fot(multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))))]]) ).
cnf(refute_0_1643,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))
| multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z)))) )],[refute_0_1641,refute_0_1642]) ).
cnf(refute_0_1644,plain,
least_upper_bound(multiply(X,X_72),multiply(X,Z)) = multiply(X,least_upper_bound(X_72,Z)),
inference(subst,[],[refute_0_154:[bind(Y,$fot(X_72))]]) ).
cnf(refute_0_1645,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))) = least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))))]]) ).
cnf(refute_0_1646,plain,
( least_upper_bound(multiply(X,X_72),multiply(X,Z)) != multiply(X,least_upper_bound(X_72,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))) != least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z)))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z)))) ),[1,1],$fot(multiply(X,least_upper_bound(X_72,Z)))]]) ).
cnf(refute_0_1647,plain,
( least_upper_bound(multiply(X,X_72),multiply(X,Z)) != multiply(X,least_upper_bound(X_72,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z)))) )],[refute_0_1645,refute_0_1646]) ).
cnf(refute_0_1648,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,X_72),multiply(X,Z)),multiply(X,least_upper_bound(X_72,Z))) )],[refute_0_1644,refute_0_1647]) ).
cnf(refute_0_1649,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) = least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))),
inference(subst,[],[refute_0_96:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X,X_72))),bind(Z,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_1650,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) != least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z)))))]]) ).
cnf(refute_0_1651,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)),least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z)))) )],[refute_0_1649,refute_0_1650]) ).
cnf(refute_0_1652,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_72),multiply(X,Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z)))) )],[refute_0_1648,refute_0_1651]) ).
cnf(refute_0_1653,plain,
( multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)) != least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z)))
| multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)))]]) ).
cnf(refute_0_1654,plain,
( multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))
| multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z)),least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z)))) )],[refute_0_1652,refute_0_1653]) ).
cnf(refute_0_1655,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))
| multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))),least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))) )],[refute_0_1643,refute_0_1654]) ).
cnf(refute_0_1656,plain,
multiply(X,least_upper_bound(X_72,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_72,Z))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_72,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_72)),multiply(X,Z))) )],[refute_0_1636,refute_0_1655]) ).
cnf(refute_0_1657,plain,
multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68))) = least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))),
inference(subst,[],[refute_0_1656:[bind(X,$fot(inverse(X_77))),bind(Z,$fot(X_68)),bind(X_72,$fot(X_77))]]) ).
cnf(refute_0_1658,plain,
multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68))),
inference(subst,[],[refute_0_176:[bind(X_66,$fot(inverse(X_77))),bind(X_67,$fot(X_77)),bind(X_68,$fot(least_upper_bound(inverse(inverse(X_77)),X_68)))]]) ).
cnf(refute_0_1659,plain,
( multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68))) != least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68)))
| multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) != multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68)))
| multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)))),bind(Y0,$fot(multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68)))))]]) ).
cnf(refute_0_1660,plain,
( multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68))) != least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68)))
| multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)),multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68)))) )],[refute_0_1658,refute_0_1659]) ).
cnf(refute_0_1661,plain,
multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) = least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(X_77,least_upper_bound(inverse(inverse(X_77)),X_68))),least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68)))) )],[refute_0_1657,refute_0_1660]) ).
cnf(refute_0_1662,plain,
( multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) != least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68)))
| multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))
| least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))))]]) ).
cnf(refute_0_1663,plain,
( multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))
| least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)),least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68)))) )],[refute_0_1661,refute_0_1662]) ).
cnf(refute_0_1664,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))) = least_upper_bound(identity,multiply(inverse(X_77),X_68)),
inference(subst,[],[refute_0_112:[bind(X_18,$fot(multiply(inverse(X_77),X_68))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_1665,plain,
( least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))) != least_upper_bound(identity,multiply(inverse(X_77),X_68))
| least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) = least_upper_bound(identity,multiply(inverse(X_77),X_68)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))),least_upper_bound(identity,multiply(inverse(X_77),X_68))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))))]]) ).
cnf(refute_0_1666,plain,
( least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))
| least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) = least_upper_bound(identity,multiply(inverse(X_77),X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68))),least_upper_bound(identity,multiply(inverse(X_77),X_68))) )],[refute_0_1664,refute_0_1665]) ).
cnf(refute_0_1667,plain,
( multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))
| least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) = least_upper_bound(identity,multiply(inverse(X_77),X_68)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))) )],[refute_0_1663,refute_0_1666]) ).
cnf(refute_0_1668,plain,
least_upper_bound(identity,multiply(inverse(X_77),least_upper_bound(X_77,X_68))) = least_upper_bound(identity,multiply(inverse(X_77),X_68)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(least_upper_bound(inverse(inverse(X_77)),X_68),X_77)),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_77),X_68)))) )],[refute_0_1631,refute_0_1667]) ).
cnf(refute_0_1669,plain,
least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_206,X_205)))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))),
inference(subst,[],[refute_0_1668:[bind(X_68,$fot(least_upper_bound(X_206,X_205))),bind(X_77,$fot(identity))]]) ).
cnf(refute_0_1670,plain,
least_upper_bound(identity,least_upper_bound(X_205,X_206)) = least_upper_bound(identity,least_upper_bound(X_206,X_205)),
inference(subst,[],[refute_0_627:[bind(X_24,$fot(identity)),bind(X_25,$fot(X_206)),bind(X_26,$fot(X_205))]]) ).
cnf(refute_0_1671,plain,
( least_upper_bound(identity,least_upper_bound(X_205,X_206)) != least_upper_bound(X_205,least_upper_bound(X_206,identity))
| least_upper_bound(identity,least_upper_bound(X_205,X_206)) != least_upper_bound(identity,least_upper_bound(X_206,X_205))
| least_upper_bound(identity,least_upper_bound(X_206,X_205)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_205,X_206)),least_upper_bound(X_205,least_upper_bound(X_206,identity))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_206,X_205)))]]) ).
cnf(refute_0_1672,plain,
( least_upper_bound(identity,least_upper_bound(X_205,X_206)) != least_upper_bound(X_205,least_upper_bound(X_206,identity))
| least_upper_bound(identity,least_upper_bound(X_206,X_205)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_205,X_206)),least_upper_bound(identity,least_upper_bound(X_206,X_205))) )],[refute_0_1670,refute_0_1671]) ).
cnf(refute_0_1673,plain,
least_upper_bound(identity,least_upper_bound(X_206,X_205)) = least_upper_bound(X_205,least_upper_bound(X_206,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_205,X_206)),least_upper_bound(X_205,least_upper_bound(X_206,identity))) )],[refute_0_1574,refute_0_1672]) ).
cnf(refute_0_1674,plain,
( least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_206,X_205)))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))
| least_upper_bound(identity,least_upper_bound(X_206,X_205)) != least_upper_bound(X_205,least_upper_bound(X_206,identity))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_206,X_205)))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))) ),[0,1,1],$fot(least_upper_bound(X_205,least_upper_bound(X_206,identity)))]]) ).
cnf(refute_0_1675,plain,
( least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_206,X_205)))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_206,X_205)),least_upper_bound(X_205,least_upper_bound(X_206,identity))) )],[refute_0_1673,refute_0_1674]) ).
cnf(refute_0_1676,plain,
least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_206,X_205)))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))) )],[refute_0_1669,refute_0_1675]) ).
cnf(refute_0_1677,plain,
multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_205,least_upper_bound(identity,X_206))))]]) ).
cnf(refute_0_1678,plain,
least_upper_bound(identity,least_upper_bound(X_206,identity)) = least_upper_bound(identity,X_206),
inference(subst,[],[refute_0_100:[bind(Y,$fot(X_206)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1679,plain,
least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))) = least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))]]) ).
cnf(refute_0_1680,plain,
( least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))) != least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))
| least_upper_bound(identity,least_upper_bound(X_206,identity)) != least_upper_bound(identity,X_206)
| least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_206))]]) ).
cnf(refute_0_1681,plain,
( least_upper_bound(identity,least_upper_bound(X_206,identity)) != least_upper_bound(identity,X_206)
| least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) )],[refute_0_1679,refute_0_1680]) ).
cnf(refute_0_1682,plain,
least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_206,identity)),least_upper_bound(identity,X_206)) )],[refute_0_1678,refute_0_1681]) ).
cnf(refute_0_1683,plain,
multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),
introduced(tautology,[refl,[$fot(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))))]]) ).
cnf(refute_0_1684,plain,
( multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))
| least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))) != least_upper_bound(X_205,least_upper_bound(identity,X_206))
| multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))) ),[1,1],$fot(least_upper_bound(X_205,least_upper_bound(identity,X_206)))]]) ).
cnf(refute_0_1685,plain,
( least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))) != least_upper_bound(X_205,least_upper_bound(identity,X_206))
| multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))) )],[refute_0_1683,refute_0_1684]) ).
cnf(refute_0_1686,plain,
multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))),least_upper_bound(X_205,least_upper_bound(identity,X_206))) )],[refute_0_1682,refute_0_1685]) ).
cnf(refute_0_1687,plain,
multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))))]]) ).
cnf(refute_0_1688,plain,
( multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1689,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))) )],[refute_0_1687,refute_0_1688]) ).
cnf(refute_0_1690,plain,
multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1563,refute_0_1689]) ).
cnf(refute_0_1691,plain,
( multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206)))
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))))),bind(Z0,$fot(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206)))))]]) ).
cnf(refute_0_1692,plain,
( multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206)))
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))) )],[refute_0_1690,refute_0_1691]) ).
cnf(refute_0_1693,plain,
multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206)))) )],[refute_0_1686,refute_0_1692]) ).
cnf(refute_0_1694,plain,
( multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))) != least_upper_bound(X_205,least_upper_bound(identity,X_206))
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206)))
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))))),bind(Z0,$fot(least_upper_bound(X_205,least_upper_bound(identity,X_206))))]]) ).
cnf(refute_0_1695,plain,
( multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))) != least_upper_bound(X_205,least_upper_bound(identity,X_206))
| multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206)))) )],[refute_0_1693,refute_0_1694]) ).
cnf(refute_0_1696,plain,
multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_205,least_upper_bound(identity,X_206))),least_upper_bound(X_205,least_upper_bound(identity,X_206))) )],[refute_0_1677,refute_0_1695]) ).
cnf(refute_0_1697,plain,
multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)) = least_upper_bound(multiply(inverse(X_38),inverse(X_52)),multiply(inverse(X_38),X_68)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_38))),bind(Y,$fot(inverse(X_52))),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_1698,plain,
( multiply(inverse(X_38),inverse(X_52)) != inverse(multiply(X_52,X_38))
| multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)) != least_upper_bound(multiply(inverse(X_38),inverse(X_52)),multiply(inverse(X_38),X_68))
| multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)) = least_upper_bound(inverse(multiply(X_52,X_38)),multiply(inverse(X_38),X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)),least_upper_bound(multiply(inverse(X_38),inverse(X_52)),multiply(inverse(X_38),X_68))) ),[1,0],$fot(inverse(multiply(X_52,X_38)))]]) ).
cnf(refute_0_1699,plain,
( multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)) != least_upper_bound(multiply(inverse(X_38),inverse(X_52)),multiply(inverse(X_38),X_68))
| multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)) = least_upper_bound(inverse(multiply(X_52,X_38)),multiply(inverse(X_38),X_68)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),inverse(X_52)),inverse(multiply(X_52,X_38))) )],[refute_0_467,refute_0_1698]) ).
cnf(refute_0_1700,plain,
multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)) = least_upper_bound(inverse(multiply(X_52,X_38)),multiply(inverse(X_38),X_68)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),least_upper_bound(inverse(X_52),X_68)),least_upper_bound(multiply(inverse(X_38),inverse(X_52)),multiply(inverse(X_38),X_68))) )],[refute_0_1697,refute_0_1699]) ).
cnf(refute_0_1701,plain,
multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_76,X_303)),X_303)),multiply(inverse(X_303),X_305)),
inference(subst,[],[refute_0_1700:[bind(X_38,$fot(X_303)),bind(X_52,$fot(inverse(least_upper_bound(X_76,X_303)))),bind(X_68,$fot(X_305))]]) ).
cnf(refute_0_1702,plain,
inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))) = multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))),
inference(subst,[],[refute_0_438:[bind(X_38,$fot(least_upper_bound(X_76,X_77))),bind(X_52,$fot(inverse(X_77)))]]) ).
cnf(refute_0_1703,plain,
multiply(inverse(X_77),least_upper_bound(X_76,X_77)) = least_upper_bound(identity,multiply(inverse(X_77),X_76)),
inference(subst,[],[refute_0_1626:[bind(X_67,$fot(X_76)),bind(X_68,$fot(X_77))]]) ).
cnf(refute_0_1704,plain,
( multiply(inverse(X_77),least_upper_bound(X_76,X_77)) != least_upper_bound(identity,multiply(inverse(X_77),X_76))
| inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))) != multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))
| inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) = multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))),multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))) ),[0,0],$fot(least_upper_bound(identity,multiply(inverse(X_77),X_76)))]]) ).
cnf(refute_0_1705,plain,
( inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))) != multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))
| inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) = multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_77),least_upper_bound(X_76,X_77)),least_upper_bound(identity,multiply(inverse(X_77),X_76))) )],[refute_0_1703,refute_0_1704]) ).
cnf(refute_0_1706,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) = multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))),multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))) )],[refute_0_1702,refute_0_1705]) ).
cnf(refute_0_1707,plain,
inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))) = multiply(inverse(least_upper_bound(X_76,X_77)),X_77),
inference(subst,[],[refute_0_464:[bind(X_39,$fot(least_upper_bound(X_76,X_77))),bind(X_55,$fot(X_77))]]) ).
cnf(refute_0_1708,plain,
multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) = inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))),
inference(subst,[],[refute_0_467:[bind(X_38,$fot(least_upper_bound(X_76,X_77))),bind(X_52,$fot(inverse(X_77)))]]) ).
cnf(refute_0_1709,plain,
( multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) != inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77)))
| inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))) != multiply(inverse(least_upper_bound(X_76,X_77)),X_77)
| multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) = multiply(inverse(least_upper_bound(X_76,X_77)),X_77) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))))),bind(Y0,$fot(inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_76,X_77)),X_77)))]]) ).
cnf(refute_0_1710,plain,
( inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))) != multiply(inverse(least_upper_bound(X_76,X_77)),X_77)
| multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) = multiply(inverse(least_upper_bound(X_76,X_77)),X_77) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))),inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77)))) )],[refute_0_1708,refute_0_1709]) ).
cnf(refute_0_1711,plain,
multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) = multiply(inverse(least_upper_bound(X_76,X_77)),X_77),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_77),least_upper_bound(X_76,X_77))),multiply(inverse(least_upper_bound(X_76,X_77)),X_77)) )],[refute_0_1707,refute_0_1710]) ).
cnf(refute_0_1712,plain,
( multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))) != multiply(inverse(least_upper_bound(X_76,X_77)),X_77)
| inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) != multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))
| inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) = multiply(inverse(least_upper_bound(X_76,X_77)),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))),multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_76,X_77)),X_77))]]) ).
cnf(refute_0_1713,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) != multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))
| inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) = multiply(inverse(least_upper_bound(X_76,X_77)),X_77) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77))),multiply(inverse(least_upper_bound(X_76,X_77)),X_77)) )],[refute_0_1711,refute_0_1712]) ).
cnf(refute_0_1714,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))) = multiply(inverse(least_upper_bound(X_76,X_77)),X_77),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_77),X_76))),multiply(inverse(least_upper_bound(X_76,X_77)),inverse(inverse(X_77)))) )],[refute_0_1706,refute_0_1713]) ).
cnf(refute_0_1715,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76))) = multiply(inverse(least_upper_bound(X_76,X_303)),X_303),
inference(subst,[],[refute_0_1714:[bind(X_77,$fot(X_303))]]) ).
cnf(refute_0_1716,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76))) != multiply(inverse(least_upper_bound(X_76,X_303)),X_303)
| multiply(inverse(least_upper_bound(X_76,X_303)),X_303) = inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_76,X_303)),X_303)))]]) ).
cnf(refute_0_1717,plain,
multiply(inverse(least_upper_bound(X_76,X_303)),X_303) = inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76))),multiply(inverse(least_upper_bound(X_76,X_303)),X_303)) )],[refute_0_1715,refute_0_1716]) ).
cnf(refute_0_1718,plain,
( multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) != least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_76,X_303)),X_303)),multiply(inverse(X_303),X_305))
| multiply(inverse(least_upper_bound(X_76,X_303)),X_303) != inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))
| multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_76,X_303)),X_303)),multiply(inverse(X_303),X_305))) ),[1,0,0],$fot(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76))))]]) ).
cnf(refute_0_1719,plain,
( multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) != least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_76,X_303)),X_303)),multiply(inverse(X_303),X_305))
| multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_76,X_303)),X_303),inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))) )],[refute_0_1717,refute_0_1718]) ).
cnf(refute_0_1720,plain,
multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_76,X_303)),X_303)),multiply(inverse(X_303),X_305))) )],[refute_0_1701,refute_0_1719]) ).
cnf(refute_0_1721,plain,
least_upper_bound(least_upper_bound(X_76,X_303),X_305) = least_upper_bound(X_76,least_upper_bound(X_303,X_305)),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_76)),bind(Y,$fot(X_303)),bind(Z,$fot(X_305))]]) ).
cnf(refute_0_1722,plain,
inverse(inverse(least_upper_bound(X_76,X_303))) = least_upper_bound(X_76,X_303),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(least_upper_bound(X_76,X_303)))]]) ).
cnf(refute_0_1723,plain,
least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) = least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305))]]) ).
cnf(refute_0_1724,plain,
( inverse(inverse(least_upper_bound(X_76,X_303))) != least_upper_bound(X_76,X_303)
| least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) != least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)
| least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) = least_upper_bound(least_upper_bound(X_76,X_303),X_305) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) ),[1,0],$fot(least_upper_bound(X_76,X_303))]]) ).
cnf(refute_0_1725,plain,
( inverse(inverse(least_upper_bound(X_76,X_303))) != least_upper_bound(X_76,X_303)
| least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) = least_upper_bound(least_upper_bound(X_76,X_303),X_305) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) )],[refute_0_1723,refute_0_1724]) ).
cnf(refute_0_1726,plain,
least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) = least_upper_bound(least_upper_bound(X_76,X_303),X_305),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_76,X_303))),least_upper_bound(X_76,X_303)) )],[refute_0_1722,refute_0_1725]) ).
cnf(refute_0_1727,plain,
( least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) != least_upper_bound(least_upper_bound(X_76,X_303),X_305)
| least_upper_bound(least_upper_bound(X_76,X_303),X_305) != least_upper_bound(X_76,least_upper_bound(X_303,X_305))
| least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) = least_upper_bound(X_76,least_upper_bound(X_303,X_305)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_76,X_303),X_305))),bind(Z0,$fot(least_upper_bound(X_76,least_upper_bound(X_303,X_305))))]]) ).
cnf(refute_0_1728,plain,
( least_upper_bound(least_upper_bound(X_76,X_303),X_305) != least_upper_bound(X_76,least_upper_bound(X_303,X_305))
| least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) = least_upper_bound(X_76,least_upper_bound(X_303,X_305)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305),least_upper_bound(least_upper_bound(X_76,X_303),X_305)) )],[refute_0_1726,refute_0_1727]) ).
cnf(refute_0_1729,plain,
least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) = least_upper_bound(X_76,least_upper_bound(X_303,X_305)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_76,X_303),X_305),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) )],[refute_0_1721,refute_0_1728]) ).
cnf(refute_0_1730,plain,
multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),
introduced(tautology,[refl,[$fot(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)))]]) ).
cnf(refute_0_1731,plain,
( multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) != multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305))
| least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) != least_upper_bound(X_76,least_upper_bound(X_303,X_305))
| multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305))) ),[1,1],$fot(least_upper_bound(X_76,least_upper_bound(X_303,X_305)))]]) ).
cnf(refute_0_1732,plain,
( least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305) != least_upper_bound(X_76,least_upper_bound(X_303,X_305))
| multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305))) )],[refute_0_1730,refute_0_1731]) ).
cnf(refute_0_1733,plain,
multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) = multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) )],[refute_0_1729,refute_0_1732]) ).
cnf(refute_0_1734,plain,
( multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) != multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305)))
| multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) != least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))
| multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) = least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))) ),[0],$fot(multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))))]]) ).
cnf(refute_0_1735,plain,
( multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) != least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))
| multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) = least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305)))) )],[refute_0_1733,refute_0_1734]) ).
cnf(refute_0_1736,plain,
least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)) = multiply(inverse(X_303),least_upper_bound(X_76,X_305)),
inference(subst,[],[refute_0_154:[bind(X,$fot(inverse(X_303))),bind(Y,$fot(X_76)),bind(Z,$fot(X_305))]]) ).
cnf(refute_0_1737,plain,
least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))))]]) ).
cnf(refute_0_1738,plain,
( least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)) != multiply(inverse(X_303),least_upper_bound(X_76,X_305))
| least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))) != least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)))
| least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))),least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)))) ),[1,1],$fot(multiply(inverse(X_303),least_upper_bound(X_76,X_305)))]]) ).
cnf(refute_0_1739,plain,
( least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)) != multiply(inverse(X_303),least_upper_bound(X_76,X_305))
| least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))),least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)))) )],[refute_0_1737,refute_0_1738]) ).
cnf(refute_0_1740,plain,
least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)),multiply(inverse(X_303),least_upper_bound(X_76,X_305))) )],[refute_0_1736,refute_0_1739]) ).
cnf(refute_0_1741,plain,
least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) = least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))),
inference(subst,[],[refute_0_96:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_303),X_76))),bind(Z,$fot(multiply(inverse(X_303),X_305)))]]) ).
cnf(refute_0_1742,plain,
( least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))) != least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))
| least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) != least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)))
| least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))))]]) ).
cnf(refute_0_1743,plain,
( least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))) != least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))
| least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)),least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305)))) )],[refute_0_1741,refute_0_1742]) ).
cnf(refute_0_1744,plain,
least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_303),X_76),multiply(inverse(X_303),X_305))),least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))) )],[refute_0_1740,refute_0_1743]) ).
cnf(refute_0_1745,plain,
inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))) = least_upper_bound(identity,multiply(inverse(X_303),X_76)),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(least_upper_bound(identity,multiply(inverse(X_303),X_76))))]]) ).
cnf(refute_0_1746,plain,
least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) = least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)))]]) ).
cnf(refute_0_1747,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))) != least_upper_bound(identity,multiply(inverse(X_303),X_76))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) != least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) = least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)),least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))) ),[1,0],$fot(least_upper_bound(identity,multiply(inverse(X_303),X_76)))]]) ).
cnf(refute_0_1748,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))) != least_upper_bound(identity,multiply(inverse(X_303),X_76))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) = least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)),least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))) )],[refute_0_1746,refute_0_1747]) ).
cnf(refute_0_1749,plain,
least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) = least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),least_upper_bound(identity,multiply(inverse(X_303),X_76))) )],[refute_0_1745,refute_0_1748]) ).
cnf(refute_0_1750,plain,
( least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) != least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305))
| least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) != least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))))]]) ).
cnf(refute_0_1751,plain,
( least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)) != least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)),least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305))) )],[refute_0_1749,refute_0_1750]) ).
cnf(refute_0_1752,plain,
least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(inverse(X_303),X_76)),multiply(inverse(X_303),X_305)),least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))) )],[refute_0_1744,refute_0_1751]) ).
cnf(refute_0_1753,plain,
( multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) != least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))
| least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)) != least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))
| multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))),least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))) ),[0],$fot(least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)))]]) ).
cnf(refute_0_1754,plain,
( multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) != least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))
| multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305)),least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))) )],[refute_0_1752,refute_0_1753]) ).
cnf(refute_0_1755,plain,
( multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)) != least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))
| multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))),least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))) )],[refute_0_1735,refute_0_1754]) ).
cnf(refute_0_1756,plain,
multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) = least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(inverse(inverse(least_upper_bound(X_76,X_303))),X_305)),least_upper_bound(inverse(inverse(least_upper_bound(identity,multiply(inverse(X_303),X_76)))),multiply(inverse(X_303),X_305))) )],[refute_0_1720,refute_0_1755]) ).
cnf(refute_0_1757,plain,
( multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) != least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))
| least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) = multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))))]]) ).
cnf(refute_0_1758,plain,
least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305))) = multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_303),least_upper_bound(X_76,least_upper_bound(X_303,X_305))),least_upper_bound(identity,multiply(inverse(X_303),least_upper_bound(X_76,X_305)))) )],[refute_0_1756,refute_0_1757]) ).
cnf(refute_0_1759,plain,
least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),
inference(subst,[],[refute_0_1758:[bind(X_303,$fot(identity)),bind(X_305,$fot(least_upper_bound(X_206,identity))),bind(X_76,$fot(X_205))]]) ).
cnf(refute_0_1760,plain,
( multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != least_upper_bound(X_205,least_upper_bound(identity,X_206))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) != multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))))),bind(Z0,$fot(least_upper_bound(X_205,least_upper_bound(identity,X_206))))]]) ).
cnf(refute_0_1761,plain,
( multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))) != least_upper_bound(X_205,least_upper_bound(identity,X_206))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))),multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity))))) )],[refute_0_1759,refute_0_1760]) ).
cnf(refute_0_1762,plain,
least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) = least_upper_bound(X_205,least_upper_bound(identity,X_206)),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(identity,least_upper_bound(X_206,identity)))),least_upper_bound(X_205,least_upper_bound(identity,X_206))) )],[refute_0_1696,refute_0_1761]) ).
cnf(refute_0_1763,plain,
( least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) != least_upper_bound(X_205,least_upper_bound(identity,X_206))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))
| least_upper_bound(X_205,least_upper_bound(identity,X_206)) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))) ),[0],$fot(least_upper_bound(X_205,least_upper_bound(identity,X_206)))]]) ).
cnf(refute_0_1764,plain,
( least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))
| least_upper_bound(X_205,least_upper_bound(identity,X_206)) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))),least_upper_bound(X_205,least_upper_bound(identity,X_206))) )],[refute_0_1762,refute_0_1763]) ).
cnf(refute_0_1765,plain,
multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))) = least_upper_bound(X_206,least_upper_bound(identity,X_205)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_206,least_upper_bound(identity,X_205))))]]) ).
cnf(refute_0_1766,plain,
multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) = multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))))]]) ).
cnf(refute_0_1767,plain,
( multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) != multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205)))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) = multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))),multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1768,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) = multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))),multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205)))) )],[refute_0_1766,refute_0_1767]) ).
cnf(refute_0_1769,plain,
multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) = multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1563,refute_0_1768]) ).
cnf(refute_0_1770,plain,
( multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))) != least_upper_bound(X_206,least_upper_bound(identity,X_205))
| multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) != multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205)))
| multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) = least_upper_bound(X_206,least_upper_bound(identity,X_205)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))))),bind(Z0,$fot(least_upper_bound(X_206,least_upper_bound(identity,X_205))))]]) ).
cnf(refute_0_1771,plain,
( multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))) != least_upper_bound(X_206,least_upper_bound(identity,X_205))
| multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) = least_upper_bound(X_206,least_upper_bound(identity,X_205)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))),multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205)))) )],[refute_0_1769,refute_0_1770]) ).
cnf(refute_0_1772,plain,
multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) = least_upper_bound(X_206,least_upper_bound(identity,X_205)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_206,least_upper_bound(identity,X_205))),least_upper_bound(X_206,least_upper_bound(identity,X_205))) )],[refute_0_1765,refute_0_1771]) ).
cnf(refute_0_1773,plain,
least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) = multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))),
inference(subst,[],[refute_0_1758:[bind(X_303,$fot(identity)),bind(X_305,$fot(X_205)),bind(X_76,$fot(X_206))]]) ).
cnf(refute_0_1774,plain,
( multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) != least_upper_bound(X_206,least_upper_bound(identity,X_205))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) != multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205)))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) = least_upper_bound(X_206,least_upper_bound(identity,X_205)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))))),bind(Z0,$fot(least_upper_bound(X_206,least_upper_bound(identity,X_205))))]]) ).
cnf(refute_0_1775,plain,
( multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))) != least_upper_bound(X_206,least_upper_bound(identity,X_205))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) = least_upper_bound(X_206,least_upper_bound(identity,X_205)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))),multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205)))) )],[refute_0_1773,refute_0_1774]) ).
cnf(refute_0_1776,plain,
least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) = least_upper_bound(X_206,least_upper_bound(identity,X_205)),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_206,least_upper_bound(identity,X_205))),least_upper_bound(X_206,least_upper_bound(identity,X_205))) )],[refute_0_1772,refute_0_1775]) ).
cnf(refute_0_1777,plain,
( least_upper_bound(X_205,least_upper_bound(identity,X_206)) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))
| least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))) != least_upper_bound(X_206,least_upper_bound(identity,X_205))
| least_upper_bound(X_205,least_upper_bound(identity,X_206)) = least_upper_bound(X_206,least_upper_bound(identity,X_205)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_205,least_upper_bound(identity,X_206)),least_upper_bound(X_206,least_upper_bound(identity,X_205))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))))]]) ).
cnf(refute_0_1778,plain,
( least_upper_bound(X_205,least_upper_bound(identity,X_206)) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))
| least_upper_bound(X_205,least_upper_bound(identity,X_206)) = least_upper_bound(X_206,least_upper_bound(identity,X_205)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205))),least_upper_bound(X_206,least_upper_bound(identity,X_205))) )],[refute_0_1776,refute_0_1777]) ).
cnf(refute_0_1779,plain,
( least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))
| least_upper_bound(X_205,least_upper_bound(identity,X_206)) = least_upper_bound(X_206,least_upper_bound(identity,X_205)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_205,least_upper_bound(identity,X_206)),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))) )],[refute_0_1764,refute_0_1778]) ).
cnf(refute_0_1780,plain,
least_upper_bound(X_205,least_upper_bound(identity,X_206)) = least_upper_bound(X_206,least_upper_bound(identity,X_205)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_205,least_upper_bound(X_206,identity)))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_206,X_205)))) )],[refute_0_1676,refute_0_1779]) ).
cnf(refute_0_1781,plain,
least_upper_bound(X_24,least_upper_bound(identity,X_26)) = least_upper_bound(X_26,least_upper_bound(identity,X_24)),
inference(subst,[],[refute_0_1780:[bind(X_205,$fot(X_24)),bind(X_206,$fot(X_26))]]) ).
cnf(refute_0_1782,plain,
( least_upper_bound(X_24,least_upper_bound(identity,X_26)) != least_upper_bound(X_26,least_upper_bound(identity,X_24))
| least_upper_bound(identity,least_upper_bound(X_24,X_26)) != least_upper_bound(X_24,least_upper_bound(identity,X_26))
| least_upper_bound(identity,least_upper_bound(X_24,X_26)) = least_upper_bound(X_26,least_upper_bound(identity,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_24,X_26)),least_upper_bound(X_24,least_upper_bound(identity,X_26))) ),[1],$fot(least_upper_bound(X_26,least_upper_bound(identity,X_24)))]]) ).
cnf(refute_0_1783,plain,
( least_upper_bound(identity,least_upper_bound(X_24,X_26)) != least_upper_bound(X_24,least_upper_bound(identity,X_26))
| least_upper_bound(identity,least_upper_bound(X_24,X_26)) = least_upper_bound(X_26,least_upper_bound(identity,X_24)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_24,least_upper_bound(identity,X_26)),least_upper_bound(X_26,least_upper_bound(identity,X_24))) )],[refute_0_1781,refute_0_1782]) ).
cnf(refute_0_1784,plain,
least_upper_bound(identity,least_upper_bound(X_24,X_26)) = least_upper_bound(X_26,least_upper_bound(identity,X_24)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_24,X_26)),least_upper_bound(X_24,least_upper_bound(identity,X_26))) )],[refute_0_1617,refute_0_1783]) ).
cnf(refute_0_1785,plain,
( least_upper_bound(identity,least_upper_bound(X_24,X_26)) != least_upper_bound(X_26,least_upper_bound(identity,X_24))
| least_upper_bound(X_26,least_upper_bound(identity,X_24)) = least_upper_bound(identity,least_upper_bound(X_24,X_26)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_24,X_26)))),bind(Y0,$fot(least_upper_bound(X_26,least_upper_bound(identity,X_24))))]]) ).
cnf(refute_0_1786,plain,
least_upper_bound(X_26,least_upper_bound(identity,X_24)) = least_upper_bound(identity,least_upper_bound(X_24,X_26)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_24,X_26)),least_upper_bound(X_26,least_upper_bound(identity,X_24))) )],[refute_0_1784,refute_0_1785]) ).
cnf(refute_0_1787,plain,
least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)) = least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))),
inference(subst,[],[refute_0_1786:[bind(X_24,$fot(X_357)),bind(X_26,$fot(least_upper_bound(X_25,X_26)))]]) ).
cnf(refute_0_1788,plain,
( least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) != least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357))
| least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)) != least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26)))
| least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) = least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))),least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)))]]) ).
cnf(refute_0_1789,plain,
( least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) != least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357))
| least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) = least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357)),least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26)))) )],[refute_0_1787,refute_0_1788]) ).
cnf(refute_0_1790,plain,
least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) = least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))),least_upper_bound(least_upper_bound(X_25,X_26),least_upper_bound(identity,X_357))) )],[refute_0_1616,refute_0_1789]) ).
cnf(refute_0_1791,plain,
( least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) != least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26)))
| least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))) = least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26)))))]]) ).
cnf(refute_0_1792,plain,
least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26))) = least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_26,X_25))),least_upper_bound(identity,least_upper_bound(X_357,least_upper_bound(X_25,X_26)))) )],[refute_0_1790,refute_0_1791]) ).
cnf(refute_0_1793,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))),
inference(subst,[],[refute_0_1792:[bind(X_25,$fot(inverse(inverse(multiply(X_432,X_102))))),bind(X_26,$fot(inverse(X_432))),bind(X_357,$fot(multiply(X_102,identity)))]]) ).
cnf(refute_0_1794,plain,
greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(least_upper_bound(X,Y),X_30)) = least_upper_bound(X_30,least_upper_bound(X,Y)),
inference(subst,[],[refute_0_132:[bind(Y,$fot(least_upper_bound(X,Y))),bind(X_18,$fot(X_30))]]) ).
cnf(refute_0_1795,plain,
least_upper_bound(X,least_upper_bound(Y,X_30)) = least_upper_bound(least_upper_bound(X,Y),X_30),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(X_30))]]) ).
cnf(refute_0_1796,plain,
( least_upper_bound(X,least_upper_bound(Y,X_30)) != least_upper_bound(least_upper_bound(X,Y),X_30)
| least_upper_bound(least_upper_bound(X,Y),X_30) = least_upper_bound(X,least_upper_bound(Y,X_30)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_30)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),X_30)))]]) ).
cnf(refute_0_1797,plain,
least_upper_bound(least_upper_bound(X,Y),X_30) = least_upper_bound(X,least_upper_bound(Y,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_30)),least_upper_bound(least_upper_bound(X,Y),X_30)) )],[refute_0_1795,refute_0_1796]) ).
cnf(refute_0_1798,plain,
( greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(least_upper_bound(X,Y),X_30)) != least_upper_bound(X_30,least_upper_bound(X,Y))
| least_upper_bound(least_upper_bound(X,Y),X_30) != least_upper_bound(X,least_upper_bound(Y,X_30))
| greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,X_30))) = least_upper_bound(X_30,least_upper_bound(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(least_upper_bound(X,Y),X_30)),least_upper_bound(X_30,least_upper_bound(X,Y))) ),[0,1],$fot(least_upper_bound(X,least_upper_bound(Y,X_30)))]]) ).
cnf(refute_0_1799,plain,
( greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(least_upper_bound(X,Y),X_30)) != least_upper_bound(X_30,least_upper_bound(X,Y))
| greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,X_30))) = least_upper_bound(X_30,least_upper_bound(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_30),least_upper_bound(X,least_upper_bound(Y,X_30))) )],[refute_0_1797,refute_0_1798]) ).
cnf(refute_0_1800,plain,
greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,X_30))) = least_upper_bound(X_30,least_upper_bound(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_30,least_upper_bound(X,Y)),least_upper_bound(least_upper_bound(X,Y),X_30)),least_upper_bound(X_30,least_upper_bound(X,Y))) )],[refute_0_1794,refute_0_1799]) ).
cnf(refute_0_1801,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_407,X_405)))) = least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),
inference(subst,[],[refute_0_1800:[bind(X_30,$fot(least_upper_bound(X_407,X_405)))]]) ).
cnf(refute_0_1802,plain,
least_upper_bound(X_405,least_upper_bound(Y,X_407)) = least_upper_bound(Y,least_upper_bound(X_407,X_405)),
inference(subst,[],[refute_0_262:[bind(X,$fot(X_405)),bind(X_24,$fot(Y)),bind(X_25,$fot(X_407))]]) ).
cnf(refute_0_1803,plain,
( least_upper_bound(X_405,least_upper_bound(Y,X_407)) != least_upper_bound(Y,least_upper_bound(X_407,X_405))
| least_upper_bound(Y,least_upper_bound(X_407,X_405)) = least_upper_bound(X_405,least_upper_bound(Y,X_407)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_405,least_upper_bound(Y,X_407)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_407,X_405))))]]) ).
cnf(refute_0_1804,plain,
least_upper_bound(Y,least_upper_bound(X_407,X_405)) = least_upper_bound(X_405,least_upper_bound(Y,X_407)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_405,least_upper_bound(Y,X_407)),least_upper_bound(Y,least_upper_bound(X_407,X_405))) )],[refute_0_1802,refute_0_1803]) ).
cnf(refute_0_1805,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_407,X_405)))) != least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))
| least_upper_bound(Y,least_upper_bound(X_407,X_405)) != least_upper_bound(X_405,least_upper_bound(Y,X_407))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_407,X_405)))),least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))) ),[0,1,1],$fot(least_upper_bound(X_405,least_upper_bound(Y,X_407)))]]) ).
cnf(refute_0_1806,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_407,X_405)))) != least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_407,X_405)),least_upper_bound(X_405,least_upper_bound(Y,X_407))) )],[refute_0_1804,refute_0_1805]) ).
cnf(refute_0_1807,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_407,X_405)))),least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))) )],[refute_0_1801,refute_0_1806]) ).
cnf(refute_0_1808,plain,
greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),
inference(subst,[],[refute_0_1800:[bind(X,$fot(X_325)),bind(Y,$fot(least_upper_bound(Y,X_26))),bind(X_30,$fot(X_327))]]) ).
cnf(refute_0_1809,plain,
least_upper_bound(Y,least_upper_bound(X_325,X_26)) = least_upper_bound(X_325,least_upper_bound(Y,X_26)),
inference(subst,[],[refute_0_289:[bind(X_24,$fot(X_325))]]) ).
cnf(refute_0_1810,plain,
( least_upper_bound(Y,least_upper_bound(X_325,X_26)) != least_upper_bound(X_325,least_upper_bound(Y,X_26))
| least_upper_bound(X_325,least_upper_bound(Y,X_26)) = least_upper_bound(Y,least_upper_bound(X_325,X_26)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_325,X_26)))),bind(Y0,$fot(least_upper_bound(X_325,least_upper_bound(Y,X_26))))]]) ).
cnf(refute_0_1811,plain,
least_upper_bound(X_325,least_upper_bound(Y,X_26)) = least_upper_bound(Y,least_upper_bound(X_325,X_26)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_325,X_26)),least_upper_bound(X_325,least_upper_bound(Y,X_26))) )],[refute_0_1809,refute_0_1810]) ).
cnf(refute_0_1812,plain,
( greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) != least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))
| least_upper_bound(X_325,least_upper_bound(Y,X_26)) != least_upper_bound(Y,least_upper_bound(X_325,X_26))
| greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))) ),[0,0,1],$fot(least_upper_bound(Y,least_upper_bound(X_325,X_26)))]]) ).
cnf(refute_0_1813,plain,
( greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) != least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))
| greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_325,least_upper_bound(Y,X_26)),least_upper_bound(Y,least_upper_bound(X_325,X_26))) )],[refute_0_1811,refute_0_1812]) ).
cnf(refute_0_1814,plain,
greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))) )],[refute_0_1808,refute_0_1813]) ).
cnf(refute_0_1815,plain,
least_upper_bound(least_upper_bound(Y,X_26),X_327) = least_upper_bound(Y,least_upper_bound(X_26,X_327)),
inference(subst,[],[refute_0_96:[bind(X,$fot(Y)),bind(Y,$fot(X_26)),bind(Z,$fot(X_327))]]) ).
cnf(refute_0_1816,plain,
least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)) = least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)))]]) ).
cnf(refute_0_1817,plain,
( least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)) != least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))
| least_upper_bound(least_upper_bound(Y,X_26),X_327) != least_upper_bound(Y,least_upper_bound(X_26,X_327))
| least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)) = least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_26,X_327)))]]) ).
cnf(refute_0_1818,plain,
( least_upper_bound(least_upper_bound(Y,X_26),X_327) != least_upper_bound(Y,least_upper_bound(X_26,X_327))
| least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)) = least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) )],[refute_0_1816,refute_0_1817]) ).
cnf(refute_0_1819,plain,
least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)) = least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_26),X_327),least_upper_bound(Y,least_upper_bound(X_26,X_327))) )],[refute_0_1815,refute_0_1818]) ).
cnf(refute_0_1820,plain,
greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))))]]) ).
cnf(refute_0_1821,plain,
( greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) != greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)))
| least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)) != least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))
| greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)))) ),[1,1],$fot(least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327))))]]) ).
cnf(refute_0_1822,plain,
( least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)) != least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))
| greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)))) )],[refute_0_1820,refute_0_1821]) ).
cnf(refute_0_1823,plain,
greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) = greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327)),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))) )],[refute_0_1819,refute_0_1822]) ).
cnf(refute_0_1824,plain,
( greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) != greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327))))
| greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) != least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))
| greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))) = least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))))]]) ).
cnf(refute_0_1825,plain,
( greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))) != least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))
| greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))) = least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327))))) )],[refute_0_1823,refute_0_1824]) ).
cnf(refute_0_1826,plain,
greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(Y,least_upper_bound(X_26,X_327)))) = least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_327,least_upper_bound(Y,least_upper_bound(X_325,X_26))),least_upper_bound(X_325,least_upper_bound(least_upper_bound(Y,X_26),X_327))),least_upper_bound(X_327,least_upper_bound(X_325,least_upper_bound(Y,X_26)))) )],[refute_0_1814,refute_0_1825]) ).
cnf(refute_0_1827,plain,
greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))),
inference(subst,[],[refute_0_1826:[bind(Y,$fot(X_405)),bind(X_26,$fot(Y)),bind(X_325,$fot(X)),bind(X_327,$fot(X_407))]]) ).
cnf(refute_0_1828,plain,
least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) = least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_407)),bind(Y,$fot(X_405)),bind(Z,$fot(least_upper_bound(X,Y)))]]) ).
cnf(refute_0_1829,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))))]]) ).
cnf(refute_0_1830,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407))))
| least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) != least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407))))) ),[1,0],$fot(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))))]]) ).
cnf(refute_0_1831,plain,
( least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) != least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407))))) )],[refute_0_1829,refute_0_1830]) ).
cnf(refute_0_1832,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))) )],[refute_0_1828,refute_0_1831]) ).
cnf(refute_0_1833,plain,
( greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y)))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407))))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))))),bind(Z0,$fot(least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y)))))]]) ).
cnf(refute_0_1834,plain,
( greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y)))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407))))) )],[refute_0_1832,refute_0_1833]) ).
cnf(refute_0_1835,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) = least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y)))) )],[refute_0_1827,refute_0_1834]) ).
cnf(refute_0_1836,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y)))
| greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))
| least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) = least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))) ),[0],$fot(least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))))]]) ).
cnf(refute_0_1837,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))
| least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) = least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y)))) )],[refute_0_1835,refute_0_1836]) ).
cnf(refute_0_1838,plain,
( least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) != least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))
| least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)) != least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))
| least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) = least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))),least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)))]]) ).
cnf(refute_0_1839,plain,
( least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) != least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))
| least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) = least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))) )],[refute_0_1828,refute_0_1838]) ).
cnf(refute_0_1840,plain,
( greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))) != least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))
| least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) = least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))),least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))) )],[refute_0_1837,refute_0_1839]) ).
cnf(refute_0_1841,plain,
least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) = least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y)),least_upper_bound(X,least_upper_bound(X_405,least_upper_bound(Y,X_407)))),least_upper_bound(least_upper_bound(X_407,X_405),least_upper_bound(X,Y))) )],[refute_0_1807,refute_0_1840]) ).
cnf(refute_0_1842,plain,
( least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) != least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))
| least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))) = least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))))),bind(Y0,$fot(least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))))]]) ).
cnf(refute_0_1843,plain,
least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y))) = least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_407,least_upper_bound(X,least_upper_bound(X_405,Y))),least_upper_bound(X_407,least_upper_bound(X_405,least_upper_bound(X,Y)))) )],[refute_0_1841,refute_0_1842]) ).
cnf(refute_0_1844,plain,
least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432)))),
inference(subst,[],[refute_0_1843:[bind(X,$fot(multiply(X_102,identity))),bind(Y,$fot(inverse(X_432))),bind(X_405,$fot(inverse(inverse(multiply(X_432,X_102))))),bind(X_407,$fot(identity))]]) ).
cnf(refute_0_1845,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432)))) != least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) != least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432))))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))))]]) ).
cnf(refute_0_1846,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432)))) != least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))),least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432))))) )],[refute_0_1844,refute_0_1845]) ).
cnf(refute_0_1847,plain,
least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(inverse(multiply(X_432,X_102))),inverse(X_432)))),least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))) )],[refute_0_1793,refute_0_1846]) ).
cnf(refute_0_1848,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) != least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) != least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))))]]) ).
cnf(refute_0_1849,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))) != least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))),least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102))))))) )],[refute_0_1847,refute_0_1848]) ).
cnf(refute_0_1850,plain,
least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_102,identity),least_upper_bound(inverse(X_432),inverse(inverse(multiply(X_432,X_102)))))),least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))) )],[refute_0_1377,refute_0_1849]) ).
cnf(refute_0_1851,plain,
( multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))
| least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))) != least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))
| multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))),least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))))]]) ).
cnf(refute_0_1852,plain,
( multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))
| multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432)))),least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))) )],[refute_0_1850,refute_0_1851]) ).
cnf(refute_0_1853,plain,
( multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))) != least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))
| multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))),least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))) )],[refute_0_1358,refute_0_1852]) ).
cnf(refute_0_1854,plain,
multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) = least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_102,inverse(inverse(multiply(X_432,X_102)))),least_upper_bound(identity,inverse(multiply(X_432,X_102)))),least_upper_bound(identity,least_upper_bound(inverse(inverse(multiply(X_432,X_102))),least_upper_bound(multiply(X_102,identity),inverse(X_432))))) )],[refute_0_1322,refute_0_1853]) ).
cnf(refute_0_1855,plain,
( multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) != least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))
| least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))))]]) ).
cnf(refute_0_1856,plain,
least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102)))) = multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_432,identity),least_upper_bound(X_102,inverse(X_432))),least_upper_bound(identity,least_upper_bound(X_102,least_upper_bound(inverse(X_432),multiply(X_432,X_102))))) )],[refute_0_1854,refute_0_1855]) ).
cnf(refute_0_1857,plain,
least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))) = multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426))),
inference(subst,[],[refute_0_1856:[bind(X_102,$fot(X_427)),bind(X_432,$fot(X_426))]]) ).
cnf(refute_0_1858,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))))]]) ).
cnf(refute_0_1859,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) != multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))
| least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))) != multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))) ),[1,1],$fot(multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426))))]]) ).
cnf(refute_0_1860,plain,
( least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))) != multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))))) )],[refute_0_1858,refute_0_1859]) ).
cnf(refute_0_1861,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427)))),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))) )],[refute_0_1857,refute_0_1860]) ).
cnf(refute_0_1862,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))) != least_upper_bound(X_427,inverse(X_426))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) != multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426))))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = least_upper_bound(X_427,inverse(X_426)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))))),bind(Z0,$fot(least_upper_bound(X_427,inverse(X_426))))]]) ).
cnf(refute_0_1863,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))) != least_upper_bound(X_427,inverse(X_426))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = least_upper_bound(X_427,inverse(X_426)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426))))) )],[refute_0_1861,refute_0_1862]) ).
cnf(refute_0_1864,plain,
multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) = least_upper_bound(X_427,inverse(X_426)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),multiply(least_upper_bound(X_426,identity),least_upper_bound(X_427,inverse(X_426)))),least_upper_bound(X_427,inverse(X_426))) )],[refute_0_1305,refute_0_1863]) ).
cnf(refute_0_1865,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) != least_upper_bound(X_427,inverse(X_426))
| multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) != least_upper_bound(inverse(X_426),X_427)
| least_upper_bound(X_427,inverse(X_426)) = least_upper_bound(inverse(X_426),X_427) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),least_upper_bound(inverse(X_426),X_427)) ),[0],$fot(least_upper_bound(X_427,inverse(X_426)))]]) ).
cnf(refute_0_1866,plain,
( multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))) != least_upper_bound(inverse(X_426),X_427)
| least_upper_bound(X_427,inverse(X_426)) = least_upper_bound(inverse(X_426),X_427) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),least_upper_bound(X_427,inverse(X_426))) )],[refute_0_1864,refute_0_1865]) ).
cnf(refute_0_1867,plain,
least_upper_bound(X_427,inverse(X_426)) = least_upper_bound(inverse(X_426),X_427),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_426)),least_upper_bound(identity,least_upper_bound(X_427,least_upper_bound(inverse(X_426),multiply(X_426,X_427))))),least_upper_bound(inverse(X_426),X_427)) )],[refute_0_1273,refute_0_1866]) ).
cnf(refute_0_1868,plain,
( least_upper_bound(X_427,inverse(X_426)) != least_upper_bound(inverse(X_426),X_427)
| least_upper_bound(inverse(X_426),X_427) = least_upper_bound(X_427,inverse(X_426)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(least_upper_bound(X_427,inverse(X_426)))),bind(Y0,$fot(least_upper_bound(inverse(X_426),X_427)))]]) ).
cnf(refute_0_1869,plain,
least_upper_bound(inverse(X_426),X_427) = least_upper_bound(X_427,inverse(X_426)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_427,inverse(X_426)),least_upper_bound(inverse(X_426),X_427)) )],[refute_0_1867,refute_0_1868]) ).
cnf(refute_0_1870,plain,
least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)) = least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139)))),
inference(subst,[],[refute_0_1869:[bind(X_426,$fot(least_upper_bound(identity,inverse(X_139)))),bind(X_427,$fot(greatest_lower_bound(identity,X_139)))]]) ).
cnf(refute_0_1871,plain,
( inverse(least_upper_bound(identity,inverse(X_139))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))
| least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)) != least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139))))
| inverse(least_upper_bound(identity,inverse(X_139))) = least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139))))) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)))]]) ).
cnf(refute_0_1872,plain,
( inverse(least_upper_bound(identity,inverse(X_139))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))
| inverse(least_upper_bound(identity,inverse(X_139))) = least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139)),least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139))))) )],[refute_0_1870,refute_0_1871]) ).
cnf(refute_0_1873,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))
| inverse(least_upper_bound(identity,inverse(X_139))) = least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))) )],[refute_0_1181,refute_0_1872]) ).
cnf(refute_0_1874,plain,
inverse(least_upper_bound(identity,inverse(X_139))) = least_upper_bound(greatest_lower_bound(identity,X_139),inverse(least_upper_bound(identity,inverse(X_139)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(X_139,identity),inverse(inverse(least_upper_bound(identity,inverse(X_139))))))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_139))),greatest_lower_bound(identity,X_139))) )],[refute_0_421,refute_0_1873]) ).
cnf(refute_0_1875,plain,
inverse(least_upper_bound(identity,inverse(X_508))) = least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),
inference(subst,[],[refute_0_1874:[bind(X_139,$fot(X_508))]]) ).
cnf(refute_0_1876,plain,
( inverse(least_upper_bound(identity,inverse(X_508))) != least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))
| least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = inverse(least_upper_bound(identity,inverse(X_508))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_508))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))))]]) ).
cnf(refute_0_1877,plain,
least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = inverse(least_upper_bound(identity,inverse(X_508))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_508))),least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) )],[refute_0_1875,refute_0_1876]) ).
cnf(refute_0_1878,plain,
( multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) != inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))
| least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != inverse(least_upper_bound(identity,inverse(X_508)))
| multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) = inverse(inverse(least_upper_bound(identity,inverse(X_508)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))),inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))) ),[1,0],$fot(inverse(least_upper_bound(identity,inverse(X_508))))]]) ).
cnf(refute_0_1879,plain,
( multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) != inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))
| multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) = inverse(inverse(least_upper_bound(identity,inverse(X_508)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),inverse(least_upper_bound(identity,inverse(X_508)))) )],[refute_0_1877,refute_0_1878]) ).
cnf(refute_0_1880,plain,
multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) = inverse(inverse(least_upper_bound(identity,inverse(X_508)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))),inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))) )],[refute_0_355,refute_0_1879]) ).
cnf(refute_0_1881,plain,
greatest_lower_bound(greatest_lower_bound(identity,X_508),least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) = greatest_lower_bound(identity,X_508),
inference(subst,[],[glb_absorbtion:[bind(X,$fot(greatest_lower_bound(identity,X_508))),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_508)))))]]) ).
cnf(refute_0_1882,plain,
( greatest_lower_bound(greatest_lower_bound(identity,X_508),least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) != greatest_lower_bound(identity,X_508)
| least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != inverse(least_upper_bound(identity,inverse(X_508)))
| greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = greatest_lower_bound(identity,X_508) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_508),least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))),greatest_lower_bound(identity,X_508)) ),[0,1],$fot(inverse(least_upper_bound(identity,inverse(X_508))))]]) ).
cnf(refute_0_1883,plain,
( greatest_lower_bound(greatest_lower_bound(identity,X_508),least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) != greatest_lower_bound(identity,X_508)
| greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = greatest_lower_bound(identity,X_508) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),inverse(least_upper_bound(identity,inverse(X_508)))) )],[refute_0_1877,refute_0_1882]) ).
cnf(refute_0_1884,plain,
greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = greatest_lower_bound(identity,X_508),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_508),least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))),greatest_lower_bound(identity,X_508)) )],[refute_0_1881,refute_0_1883]) ).
cnf(refute_0_1885,plain,
greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y))))) = inverse(least_upper_bound(X_279,inverse(Y))),
inference(subst,[],[refute_0_127:[bind(X,$fot(inverse(least_upper_bound(X_279,inverse(Y)))))]]) ).
cnf(refute_0_1886,plain,
multiply(least_upper_bound(X_78,X_79),inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79)))) = inverse(inverse(X_78)),
inference(subst,[],[refute_0_54:[bind(X_38,$fot(inverse(X_78))),bind(X_51,$fot(least_upper_bound(X_78,X_79)))]]) ).
cnf(refute_0_1887,plain,
( multiply(inverse(X_78),least_upper_bound(X_78,X_79)) != least_upper_bound(identity,multiply(inverse(X_78),X_79))
| multiply(least_upper_bound(X_78,X_79),inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79)))) != inverse(inverse(X_78))
| multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) = inverse(inverse(X_78)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_78,X_79),inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79)))),inverse(inverse(X_78))) ),[0,1,0],$fot(least_upper_bound(identity,multiply(inverse(X_78),X_79)))]]) ).
cnf(refute_0_1888,plain,
( multiply(least_upper_bound(X_78,X_79),inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79)))) != inverse(inverse(X_78))
| multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) = inverse(inverse(X_78)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_78),least_upper_bound(X_78,X_79)),least_upper_bound(identity,multiply(inverse(X_78),X_79))) )],[refute_0_445,refute_0_1887]) ).
cnf(refute_0_1889,plain,
multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) = inverse(inverse(X_78)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,X_79),inverse(multiply(inverse(X_78),least_upper_bound(X_78,X_79)))),inverse(inverse(X_78))) )],[refute_0_1886,refute_0_1888]) ).
cnf(refute_0_1890,plain,
inverse(inverse(X_78)) = X_78,
inference(subst,[],[refute_0_335:[bind(X_44,$fot(X_78))]]) ).
cnf(refute_0_1891,plain,
( multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) != inverse(inverse(X_78))
| inverse(inverse(X_78)) != X_78
| multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) = X_78 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))),X_78) ),[0],$fot(inverse(inverse(X_78)))]]) ).
cnf(refute_0_1892,plain,
( multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) != inverse(inverse(X_78))
| multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) = X_78 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_78)),X_78) )],[refute_0_1890,refute_0_1891]) ).
cnf(refute_0_1893,plain,
multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))) = X_78,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,X_79),inverse(least_upper_bound(identity,multiply(inverse(X_78),X_79)))),inverse(inverse(X_78))) )],[refute_0_1889,refute_0_1892]) ).
cnf(refute_0_1894,plain,
multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))))) = X_78,
inference(subst,[],[refute_0_1893:[bind(X_79,$fot(inverse(least_upper_bound(X_202,inverse(X_78)))))]]) ).
cnf(refute_0_1895,plain,
multiply(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),inverse(X_108)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108))),
inference(subst,[],[refute_0_394:[bind(X_102,$fot(X_108)),bind(X_103,$fot(greatest_lower_bound(X_11,X_108)))]]) ).
cnf(refute_0_1896,plain,
least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)) = X_108,
inference(subst,[],[refute_0_89:[bind(X_10,$fot(X_108))]]) ).
cnf(refute_0_1897,plain,
( multiply(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),inverse(X_108)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))
| least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)) != X_108
| multiply(X_108,inverse(X_108)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),inverse(X_108)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))) ),[0,0],$fot(X_108)]]) ).
cnf(refute_0_1898,plain,
( multiply(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),inverse(X_108)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))
| multiply(X_108,inverse(X_108)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),X_108) )],[refute_0_1896,refute_0_1897]) ).
cnf(refute_0_1899,plain,
multiply(X_108,inverse(X_108)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),inverse(X_108)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))) )],[refute_0_1895,refute_0_1898]) ).
cnf(refute_0_1900,plain,
multiply(X_108,inverse(X_108)) = identity,
inference(subst,[],[refute_0_27:[bind(X_44,$fot(X_108))]]) ).
cnf(refute_0_1901,plain,
( multiply(X_108,inverse(X_108)) != identity
| multiply(X_108,inverse(X_108)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_108,inverse(X_108)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1902,plain,
( multiply(X_108,inverse(X_108)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108))) ),
inference(resolve,[$cnf( $equal(multiply(X_108,inverse(X_108)),identity) )],[refute_0_1900,refute_0_1901]) ).
cnf(refute_0_1903,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(X_108,inverse(X_108)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_108),inverse(X_108)))) )],[refute_0_1899,refute_0_1902]) ).
cnf(refute_0_1904,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_157,least_upper_bound(Y,X_157)),inverse(least_upper_bound(Y,X_157)))),
inference(subst,[],[refute_0_1903:[bind(X_108,$fot(least_upper_bound(Y,X_157))),bind(X_11,$fot(X_157))]]) ).
cnf(refute_0_1905,plain,
greatest_lower_bound(X_157,least_upper_bound(Y,X_157)) = X_157,
inference(subst,[],[refute_0_127:[bind(X,$fot(X_157))]]) ).
cnf(refute_0_1906,plain,
( greatest_lower_bound(X_157,least_upper_bound(Y,X_157)) != X_157
| identity != least_upper_bound(identity,multiply(greatest_lower_bound(X_157,least_upper_bound(Y,X_157)),inverse(least_upper_bound(Y,X_157))))
| identity = least_upper_bound(identity,multiply(X_157,inverse(least_upper_bound(Y,X_157)))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(X_157,least_upper_bound(Y,X_157)),inverse(least_upper_bound(Y,X_157))))) ),[1,1,0],$fot(X_157)]]) ).
cnf(refute_0_1907,plain,
( identity != least_upper_bound(identity,multiply(greatest_lower_bound(X_157,least_upper_bound(Y,X_157)),inverse(least_upper_bound(Y,X_157))))
| identity = least_upper_bound(identity,multiply(X_157,inverse(least_upper_bound(Y,X_157)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_157,least_upper_bound(Y,X_157)),X_157) )],[refute_0_1905,refute_0_1906]) ).
cnf(refute_0_1908,plain,
identity = least_upper_bound(identity,multiply(X_157,inverse(least_upper_bound(Y,X_157)))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(X_157,least_upper_bound(Y,X_157)),inverse(least_upper_bound(Y,X_157))))) )],[refute_0_1904,refute_0_1907]) ).
cnf(refute_0_1909,plain,
identity = least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))),
inference(subst,[],[refute_0_1908:[bind(Y,$fot(X_202)),bind(X_157,$fot(inverse(X_78)))]]) ).
cnf(refute_0_1910,plain,
( identity != least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78)))))
| least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))) = identity ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78)))))))]]) ).
cnf(refute_0_1911,plain,
least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78)))))) )],[refute_0_1909,refute_0_1910]) ).
cnf(refute_0_1912,plain,
( multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))))) != X_78
| least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))) != identity
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = X_78 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))))),X_78) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_1913,plain,
( multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))))) != X_78
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = X_78 ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))),identity) )],[refute_0_1911,refute_0_1912]) ).
cnf(refute_0_1914,plain,
multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = X_78,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(least_upper_bound(identity,multiply(inverse(X_78),inverse(least_upper_bound(X_202,inverse(X_78))))))),X_78) )],[refute_0_1894,refute_0_1913]) ).
cnf(refute_0_1915,plain,
multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity) = least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),
inference(subst,[],[refute_0_50:[bind(X_41,$fot(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78))))))]]) ).
cnf(refute_0_1916,plain,
multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)))]]) ).
cnf(refute_0_1917,plain,
( multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) != multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity))
| inverse(identity) != identity
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)),multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1918,plain,
( inverse(identity) != identity
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)),multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity))) )],[refute_0_1916,refute_0_1917]) ).
cnf(refute_0_1919,plain,
multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1563,refute_0_1918]) ).
cnf(refute_0_1920,plain,
( multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity) != least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78))))
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) != multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity)
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity))),bind(Z0,$fot(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78))))))]]) ).
cnf(refute_0_1921,plain,
( multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity) != least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78))))
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)),multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity)) )],[refute_0_1919,refute_0_1920]) ).
cnf(refute_0_1922,plain,
multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) = least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),identity),least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78))))) )],[refute_0_1915,refute_0_1921]) ).
cnf(refute_0_1923,plain,
( multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) != X_78
| multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) != least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78))))
| least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))) = X_78 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)),X_78) ),[0],$fot(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))))]]) ).
cnf(refute_0_1924,plain,
( multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)) != X_78
| least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))) = X_78 ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)),least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78))))) )],[refute_0_1922,refute_0_1923]) ).
cnf(refute_0_1925,plain,
least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))) = X_78,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_78,inverse(least_upper_bound(X_202,inverse(X_78)))),inverse(identity)),X_78) )],[refute_0_1914,refute_0_1924]) ).
cnf(refute_0_1926,plain,
least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))) = Y,
inference(subst,[],[refute_0_1925:[bind(X_202,$fot(X_279)),bind(X_78,$fot(Y))]]) ).
cnf(refute_0_1927,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y))))) != inverse(least_upper_bound(X_279,inverse(Y)))
| least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))) != Y
| greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y) = inverse(least_upper_bound(X_279,inverse(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y))))),inverse(least_upper_bound(X_279,inverse(Y)))) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_1928,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y))))) != inverse(least_upper_bound(X_279,inverse(Y)))
| greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y) = inverse(least_upper_bound(X_279,inverse(Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))),Y) )],[refute_0_1926,refute_0_1927]) ).
cnf(refute_0_1929,plain,
greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y) = inverse(least_upper_bound(X_279,inverse(Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),least_upper_bound(Y,inverse(least_upper_bound(X_279,inverse(Y))))),inverse(least_upper_bound(X_279,inverse(Y)))) )],[refute_0_1885,refute_0_1928]) ).
cnf(refute_0_1930,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))) = greatest_lower_bound(X_31,X_32),
inference(subst,[],[refute_0_127:[bind(X,$fot(greatest_lower_bound(X_31,X_32)))]]) ).
cnf(refute_0_1931,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))) = greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(least_upper_bound(Y,greatest_lower_bound(X_31,X_32))))]]) ).
cnf(refute_0_1932,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))) != greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))))]]) ).
cnf(refute_0_1933,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))) = greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))),greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))) )],[refute_0_1931,refute_0_1932]) ).
cnf(refute_0_1934,plain,
( greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))) != greatest_lower_bound(X_31,X_32)
| greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32))))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))) = greatest_lower_bound(X_31,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))),greatest_lower_bound(X_31,X_32)) ),[0],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))))]]) ).
cnf(refute_0_1935,plain,
( greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))) != greatest_lower_bound(X_31,X_32)
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))) = greatest_lower_bound(X_31,X_32) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))),greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32))))) )],[refute_0_1933,refute_0_1934]) ).
cnf(refute_0_1936,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,least_upper_bound(Y,greatest_lower_bound(X_31,X_32)))) = greatest_lower_bound(X_31,X_32),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X_32),least_upper_bound(Y,greatest_lower_bound(X_31,X_32))),greatest_lower_bound(X_31,X_32)) )],[refute_0_1930,refute_0_1935]) ).
cnf(refute_0_1937,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))),
inference(subst,[],[refute_0_1936:[bind(X_32,$fot(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))))]]) ).
cnf(refute_0_1938,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,X_254),
inference(subst,[],[refute_0_1936:[bind(Y,$fot(X_252)),bind(X_32,$fot(X_254))]]) ).
cnf(refute_0_1939,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,X_254)
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))))),greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) ),[0,1,1,1],$fot(greatest_lower_bound(X_31,X_254))]]) ).
cnf(refute_0_1940,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,X_254)) )],[refute_0_1938,refute_0_1939]) ).
cnf(refute_0_1941,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))))),greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) )],[refute_0_1937,refute_0_1940]) ).
cnf(refute_0_1942,plain,
greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))) = greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_254)),bind(Y,$fot(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))),bind(Z,$fot(least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))]]) ).
cnf(refute_0_1943,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))))]]) ).
cnf(refute_0_1944,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))) != greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) ),[1,1],$fot(greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))))]]) ).
cnf(refute_0_1945,plain,
( greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))) != greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) )],[refute_0_1943,refute_0_1944]) ).
cnf(refute_0_1946,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))),greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) )],[refute_0_1942,refute_0_1945]) ).
cnf(refute_0_1947,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) ),[0],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))))]]) ).
cnf(refute_0_1948,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))))) )],[refute_0_1946,refute_0_1947]) ).
cnf(refute_0_1949,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,X_254)
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_31,X_254) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(X_31,X_254)) ),[0],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))))]]) ).
cnf(refute_0_1950,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_31,X_254) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,X_254)) )],[refute_0_1938,refute_0_1949]) ).
cnf(refute_0_1951,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_31,X_254) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) )],[refute_0_1948,refute_0_1950]) ).
cnf(refute_0_1952,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_31,X_254),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) )],[refute_0_1941,refute_0_1951]) ).
cnf(refute_0_1953,plain,
greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)))) = greatest_lower_bound(X_11,X_16),
inference(subst,[],[refute_0_1401:[bind(X,$fot(greatest_lower_bound(X_11,X_16))),bind(X_24,$fot(X_205)),bind(X_25,$fot(greatest_lower_bound(X_16,X_11)))]]) ).
cnf(refute_0_1954,plain,
( greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)))) != greatest_lower_bound(X_11,X_16)
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) != greatest_lower_bound(X_16,X_11)
| greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))) = greatest_lower_bound(X_11,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)))),greatest_lower_bound(X_11,X_16)) ),[0,1,1],$fot(greatest_lower_bound(X_16,X_11))]]) ).
cnf(refute_0_1955,plain,
( greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)))) != greatest_lower_bound(X_11,X_16)
| greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))) = greatest_lower_bound(X_11,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)),greatest_lower_bound(X_16,X_11)) )],[refute_0_222,refute_0_1954]) ).
cnf(refute_0_1956,plain,
greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))) = greatest_lower_bound(X_11,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)))),greatest_lower_bound(X_11,X_16)) )],[refute_0_1953,refute_0_1955]) ).
cnf(refute_0_1957,plain,
greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))) = greatest_lower_bound(X_11,greatest_lower_bound(X_16,least_upper_bound(X_205,greatest_lower_bound(X_16,X_11)))),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_11)),bind(Y,$fot(X_16)),bind(Z,$fot(least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))))]]) ).
cnf(refute_0_1958,plain,
( greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))) != greatest_lower_bound(X_11,X_16)
| greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))) != greatest_lower_bound(X_11,greatest_lower_bound(X_16,least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))))
| greatest_lower_bound(X_11,greatest_lower_bound(X_16,least_upper_bound(X_205,greatest_lower_bound(X_16,X_11)))) = greatest_lower_bound(X_11,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_11,X_16)) ),[0],$fot(greatest_lower_bound(X_11,greatest_lower_bound(X_16,least_upper_bound(X_205,greatest_lower_bound(X_16,X_11)))))]]) ).
cnf(refute_0_1959,plain,
( greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))) != greatest_lower_bound(X_11,X_16)
| greatest_lower_bound(X_11,greatest_lower_bound(X_16,least_upper_bound(X_205,greatest_lower_bound(X_16,X_11)))) = greatest_lower_bound(X_11,X_16) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_11,greatest_lower_bound(X_16,least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))))) )],[refute_0_1957,refute_0_1958]) ).
cnf(refute_0_1960,plain,
greatest_lower_bound(X_11,greatest_lower_bound(X_16,least_upper_bound(X_205,greatest_lower_bound(X_16,X_11)))) = greatest_lower_bound(X_11,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(X_205,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_11,X_16)) )],[refute_0_1956,refute_0_1959]) ).
cnf(refute_0_1961,plain,
greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) = greatest_lower_bound(X_254,X_31),
inference(subst,[],[refute_0_1960:[bind(X_11,$fot(X_254)),bind(X_16,$fot(X_31)),bind(X_205,$fot(Y))]]) ).
cnf(refute_0_1962,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,X)),
inference(subst,[],[refute_0_751:[bind(Y,$fot(X_31)),bind(X_31,$fot(X_32)),bind(X_33,$fot(X))]]) ).
cnf(refute_0_1963,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))
| greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,X))
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,X))) ),[0],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)))]]) ).
cnf(refute_0_1964,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_32,X)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,X))) )],[refute_0_1962,refute_0_1963]) ).
cnf(refute_0_1965,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X_31,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_31,greatest_lower_bound(X_32,X))) )],[refute_0_724,refute_0_1964]) ).
cnf(refute_0_1966,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(X_32,greatest_lower_bound(X_31,X))
| greatest_lower_bound(X_32,greatest_lower_bound(X_31,X)) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)))),bind(Y0,$fot(greatest_lower_bound(X_32,greatest_lower_bound(X_31,X))))]]) ).
cnf(refute_0_1967,plain,
greatest_lower_bound(X_32,greatest_lower_bound(X_31,X)) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_32,greatest_lower_bound(X_31,X))) )],[refute_0_1965,refute_0_1966]) ).
cnf(refute_0_1968,plain,
greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),
inference(subst,[],[refute_0_1967:[bind(X,$fot(X_254)),bind(X_32,$fot(least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))]]) ).
cnf(refute_0_1969,plain,
( greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_254,X_31)
| greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)) != greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))
| greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_254,X_31) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)))),bind(Y0,$fot(greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))))),bind(Z0,$fot(greatest_lower_bound(X_254,X_31)))]]) ).
cnf(refute_0_1970,plain,
( greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_254,X_31)
| greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_254,X_31) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) )],[refute_0_1968,refute_0_1969]) ).
cnf(refute_0_1971,plain,
greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_254,X_31),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_254,greatest_lower_bound(X_31,least_upper_bound(Y,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_254,X_31)) )],[refute_0_1961,refute_0_1970]) ).
cnf(refute_0_1972,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)),
inference(subst,[],[refute_0_724:[bind(X_32,$fot(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))))]]) ).
cnf(refute_0_1973,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))) != greatest_lower_bound(X_31,X_254)
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))) ),[0,1],$fot(greatest_lower_bound(X_31,X_254))]]) ).
cnf(refute_0_1974,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))),greatest_lower_bound(X_31,X_254)) )],[refute_0_1938,refute_0_1973]) ).
cnf(refute_0_1975,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))) )],[refute_0_1972,refute_0_1974]) ).
cnf(refute_0_1976,plain,
greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X) = greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_254)),bind(Y,$fot(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_1977,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) = greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)))]]) ).
cnf(refute_0_1978,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) != greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))
| greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X) != greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))) ),[1,1],$fot(greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)))]]) ).
cnf(refute_0_1979,plain,
( greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X) != greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))) )],[refute_0_1977,refute_0_1978]) ).
cnf(refute_0_1980,plain,
greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X),greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))) )],[refute_0_1976,refute_0_1979]) ).
cnf(refute_0_1981,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) != greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))
| greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)))
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)))) ),[0],$fot(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)))]]) ).
cnf(refute_0_1982,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) != greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))
| greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X)),greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)))) )],[refute_0_1980,refute_0_1981]) ).
cnf(refute_0_1983,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) = greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,greatest_lower_bound(greatest_lower_bound(X_254,least_upper_bound(X_252,greatest_lower_bound(X_31,X_254))),X))) )],[refute_0_1975,refute_0_1982]) ).
cnf(refute_0_1984,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) != greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)))
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)))),bind(Y0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)))))]]) ).
cnf(refute_0_1985,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X))) = greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),X)))) )],[refute_0_1983,refute_0_1984]) ).
cnf(refute_0_1986,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)),
inference(subst,[],[refute_0_1985:[bind(X,$fot(least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))]]) ).
cnf(refute_0_1987,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254))
| greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)) != greatest_lower_bound(X_254,X_31)
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_254,X_31) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)))),bind(Z0,$fot(greatest_lower_bound(X_254,X_31)))]]) ).
cnf(refute_0_1988,plain,
( greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)) != greatest_lower_bound(X_254,X_31)
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_254,X_31) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254))) )],[refute_0_1986,refute_0_1987]) ).
cnf(refute_0_1989,plain,
greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) = greatest_lower_bound(X_254,X_31),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_31,X_254)),greatest_lower_bound(X_254,X_31)) )],[refute_0_1971,refute_0_1988]) ).
cnf(refute_0_1990,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(X_254,X_31)
| greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(X_31,X_254)
| greatest_lower_bound(X_254,X_31) = greatest_lower_bound(X_31,X_254) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(X_31,X_254)) ),[0],$fot(greatest_lower_bound(X_254,X_31))]]) ).
cnf(refute_0_1991,plain,
( greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))) != greatest_lower_bound(X_31,X_254)
| greatest_lower_bound(X_254,X_31) = greatest_lower_bound(X_31,X_254) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(X_254,X_31)) )],[refute_0_1989,refute_0_1990]) ).
cnf(refute_0_1992,plain,
greatest_lower_bound(X_254,X_31) = greatest_lower_bound(X_31,X_254),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,greatest_lower_bound(X_254,greatest_lower_bound(least_upper_bound(X_252,greatest_lower_bound(X_31,X_254)),least_upper_bound(Y,greatest_lower_bound(X_31,X_254))))),greatest_lower_bound(X_31,X_254)) )],[refute_0_1952,refute_0_1991]) ).
cnf(refute_0_1993,plain,
( greatest_lower_bound(X_254,X_31) != greatest_lower_bound(X_31,X_254)
| greatest_lower_bound(X_31,X_254) = greatest_lower_bound(X_254,X_31) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(greatest_lower_bound(X_254,X_31))),bind(Y0,$fot(greatest_lower_bound(X_31,X_254)))]]) ).
cnf(refute_0_1994,plain,
greatest_lower_bound(X_31,X_254) = greatest_lower_bound(X_254,X_31),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_254,X_31),greatest_lower_bound(X_31,X_254)) )],[refute_0_1992,refute_0_1993]) ).
cnf(refute_0_1995,plain,
greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y) = greatest_lower_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))),
inference(subst,[],[refute_0_1994:[bind(X_254,$fot(Y)),bind(X_31,$fot(inverse(least_upper_bound(X_279,inverse(Y)))))]]) ).
cnf(refute_0_1996,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y) != greatest_lower_bound(Y,inverse(least_upper_bound(X_279,inverse(Y))))
| greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y) != inverse(least_upper_bound(X_279,inverse(Y)))
| greatest_lower_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))) = inverse(least_upper_bound(X_279,inverse(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y),inverse(least_upper_bound(X_279,inverse(Y)))) ),[0],$fot(greatest_lower_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))))]]) ).
cnf(refute_0_1997,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y) != inverse(least_upper_bound(X_279,inverse(Y)))
| greatest_lower_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))) = inverse(least_upper_bound(X_279,inverse(Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y),greatest_lower_bound(Y,inverse(least_upper_bound(X_279,inverse(Y))))) )],[refute_0_1995,refute_0_1996]) ).
cnf(refute_0_1998,plain,
greatest_lower_bound(Y,inverse(least_upper_bound(X_279,inverse(Y)))) = inverse(least_upper_bound(X_279,inverse(Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_279,inverse(Y))),Y),inverse(least_upper_bound(X_279,inverse(Y)))) )],[refute_0_1929,refute_0_1997]) ).
cnf(refute_0_1999,plain,
greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))) = inverse(least_upper_bound(identity,inverse(X_508))),
inference(subst,[],[refute_0_1998:[bind(Y,$fot(X_508)),bind(X_279,$fot(identity))]]) ).
cnf(refute_0_2000,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))) = greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171)))),
inference(subst,[],[refute_0_751:[bind(Y,$fot(identity)),bind(X_33,$fot(inverse(least_upper_bound(identity,X_171))))]]) ).
cnf(refute_0_2001,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))),
inference(subst,[],[refute_0_551:[bind(X_16,$fot(inverse(least_upper_bound(X_125,identity)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2002,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))) = inverse(least_upper_bound(identity,X_125)),
inference(subst,[],[refute_0_1531:[bind(X_124,$fot(X_125))]]) ).
cnf(refute_0_2003,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))) != inverse(least_upper_bound(identity,X_125))
| greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) = inverse(least_upper_bound(identity,X_125)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))),inverse(least_upper_bound(identity,X_125))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))))]]) ).
cnf(refute_0_2004,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) = inverse(least_upper_bound(identity,X_125)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))),inverse(least_upper_bound(identity,X_125))) )],[refute_0_2002,refute_0_2003]) ).
cnf(refute_0_2005,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) = inverse(least_upper_bound(identity,X_125)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))),greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) )],[refute_0_2001,refute_0_2004]) ).
cnf(refute_0_2006,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))) = greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))),
inference(subst,[],[refute_0_751:[bind(Y,$fot(identity)),bind(X_33,$fot(inverse(least_upper_bound(X_125,identity))))]]) ).
cnf(refute_0_2007,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))) != greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))) != inverse(least_upper_bound(identity,X_125))
| greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))) = greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_125))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))),greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_125)))]]) ).
cnf(refute_0_2008,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))) != greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))))
| greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))) = greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_125))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))),inverse(least_upper_bound(identity,X_125))) )],[refute_0_2002,refute_0_2007]) ).
cnf(refute_0_2009,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))) = greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_125))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(X_125,identity)))),greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity))))) )],[refute_0_2006,refute_0_2008]) ).
cnf(refute_0_2010,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_125))),
inference(subst,[],[refute_0_2009:[bind(X_31,$fot(identity))]]) ).
cnf(refute_0_2011,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_125)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) != inverse(least_upper_bound(identity,X_125))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_125))) = inverse(least_upper_bound(identity,X_125)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))),inverse(least_upper_bound(identity,X_125))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_125))))]]) ).
cnf(refute_0_2012,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))) != inverse(least_upper_bound(identity,X_125))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_125))) = inverse(least_upper_bound(identity,X_125)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_125)))) )],[refute_0_2010,refute_0_2011]) ).
cnf(refute_0_2013,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_125))) = inverse(least_upper_bound(identity,X_125)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(least_upper_bound(X_125,identity)))),inverse(least_upper_bound(identity,X_125))) )],[refute_0_2005,refute_0_2012]) ).
cnf(refute_0_2014,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171))) = inverse(least_upper_bound(identity,X_171)),
inference(subst,[],[refute_0_2013:[bind(X_125,$fot(X_171))]]) ).
cnf(refute_0_2015,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))) != greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171))))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171))) != inverse(least_upper_bound(identity,X_171))
| greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))) = greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))),greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171))))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_171)))]]) ).
cnf(refute_0_2016,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))) != greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171))))
| greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))) = greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171))),inverse(least_upper_bound(identity,X_171))) )],[refute_0_2014,refute_0_2015]) ).
cnf(refute_0_2017,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))) = greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_31,inverse(least_upper_bound(identity,X_171)))),greatest_lower_bound(X_31,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_171))))) )],[refute_0_2000,refute_0_2016]) ).
cnf(refute_0_2018,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) = greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))),
inference(subst,[],[refute_0_2017:[bind(X_171,$fot(inverse(X_508))),bind(X_31,$fot(X_508))]]) ).
cnf(refute_0_2019,plain,
( greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))) != inverse(least_upper_bound(identity,inverse(X_508)))
| greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) != greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))
| greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) = inverse(least_upper_bound(identity,inverse(X_508))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))))),bind(Y0,$fot(greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_508)))))]]) ).
cnf(refute_0_2020,plain,
( greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))) != inverse(least_upper_bound(identity,inverse(X_508)))
| greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) = inverse(least_upper_bound(identity,inverse(X_508))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))),greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) )],[refute_0_2018,refute_0_2019]) ).
cnf(refute_0_2021,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) = inverse(least_upper_bound(identity,inverse(X_508))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))),inverse(least_upper_bound(identity,inverse(X_508)))) )],[refute_0_1999,refute_0_2020]) ).
cnf(refute_0_2022,plain,
greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))),
inference(subst,[],[refute_0_214:[bind(X,$fot(identity)),bind(Y,$fot(X_508)),bind(Z,$fot(inverse(least_upper_bound(identity,inverse(X_508)))))]]) ).
cnf(refute_0_2023,plain,
( greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))))
| greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) != inverse(least_upper_bound(identity,inverse(X_508)))
| greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = inverse(least_upper_bound(identity,inverse(X_508))) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_508)))))]]) ).
cnf(refute_0_2024,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))) != inverse(least_upper_bound(identity,inverse(X_508)))
| greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = inverse(least_upper_bound(identity,inverse(X_508))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508)))))) )],[refute_0_2022,refute_0_2023]) ).
cnf(refute_0_2025,plain,
greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = inverse(least_upper_bound(identity,inverse(X_508))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_508,inverse(least_upper_bound(identity,inverse(X_508))))),inverse(least_upper_bound(identity,inverse(X_508)))) )],[refute_0_2021,refute_0_2024]) ).
cnf(refute_0_2026,plain,
( greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != greatest_lower_bound(identity,X_508)
| greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != inverse(least_upper_bound(identity,inverse(X_508)))
| inverse(least_upper_bound(identity,inverse(X_508))) = greatest_lower_bound(identity,X_508) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),greatest_lower_bound(identity,X_508)) ),[0],$fot(inverse(least_upper_bound(identity,inverse(X_508))))]]) ).
cnf(refute_0_2027,plain,
( greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != greatest_lower_bound(identity,X_508)
| inverse(least_upper_bound(identity,inverse(X_508))) = greatest_lower_bound(identity,X_508) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),inverse(least_upper_bound(identity,inverse(X_508)))) )],[refute_0_2025,refute_0_2026]) ).
cnf(refute_0_2028,plain,
inverse(least_upper_bound(identity,inverse(X_508))) = greatest_lower_bound(identity,X_508),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),greatest_lower_bound(identity,X_508)) )],[refute_0_1884,refute_0_2027]) ).
cnf(refute_0_2029,plain,
( inverse(least_upper_bound(identity,inverse(X_508))) != greatest_lower_bound(identity,X_508)
| least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != inverse(least_upper_bound(identity,inverse(X_508)))
| least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = greatest_lower_bound(identity,X_508) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(X_508))))),bind(Z0,$fot(greatest_lower_bound(identity,X_508)))]]) ).
cnf(refute_0_2030,plain,
( inverse(least_upper_bound(identity,inverse(X_508))) != greatest_lower_bound(identity,X_508)
| least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = greatest_lower_bound(identity,X_508) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),inverse(least_upper_bound(identity,inverse(X_508)))) )],[refute_0_1877,refute_0_2029]) ).
cnf(refute_0_2031,plain,
least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) = greatest_lower_bound(identity,X_508),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_508))),greatest_lower_bound(identity,X_508)) )],[refute_0_2028,refute_0_2030]) ).
cnf(refute_0_2032,plain,
inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) = inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))))]]) ).
cnf(refute_0_2033,plain,
( inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) != inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))
| least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != greatest_lower_bound(identity,X_508)
| inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) = inverse(greatest_lower_bound(identity,X_508)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))),inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))) ),[1,0],$fot(greatest_lower_bound(identity,X_508))]]) ).
cnf(refute_0_2034,plain,
( least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))) != greatest_lower_bound(identity,X_508)
| inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) = inverse(greatest_lower_bound(identity,X_508)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))),inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))) )],[refute_0_2032,refute_0_2033]) ).
cnf(refute_0_2035,plain,
inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) = inverse(greatest_lower_bound(identity,X_508)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))),greatest_lower_bound(identity,X_508)) )],[refute_0_2031,refute_0_2034]) ).
cnf(refute_0_2036,plain,
( multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) != inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))
| inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) != inverse(greatest_lower_bound(identity,X_508))
| multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) = inverse(greatest_lower_bound(identity,X_508)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))))),bind(Y0,$fot(inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_508))))]]) ).
cnf(refute_0_2037,plain,
( inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))) != inverse(greatest_lower_bound(identity,X_508))
| multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) = inverse(greatest_lower_bound(identity,X_508)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))),inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508)))))) )],[refute_0_355,refute_0_2036]) ).
cnf(refute_0_2038,plain,
multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) = inverse(greatest_lower_bound(identity,X_508)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(identity,X_508),inverse(least_upper_bound(identity,inverse(X_508))))),inverse(greatest_lower_bound(identity,X_508))) )],[refute_0_2035,refute_0_2037]) ).
cnf(refute_0_2039,plain,
( multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) != inverse(greatest_lower_bound(identity,X_508))
| multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) != inverse(inverse(least_upper_bound(identity,inverse(X_508))))
| inverse(greatest_lower_bound(identity,X_508)) = inverse(inverse(least_upper_bound(identity,inverse(X_508)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))),inverse(inverse(least_upper_bound(identity,inverse(X_508))))) ),[0],$fot(inverse(greatest_lower_bound(identity,X_508)))]]) ).
cnf(refute_0_2040,plain,
( multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) != inverse(inverse(least_upper_bound(identity,inverse(X_508))))
| inverse(greatest_lower_bound(identity,X_508)) = inverse(inverse(least_upper_bound(identity,inverse(X_508)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))),inverse(greatest_lower_bound(identity,X_508))) )],[refute_0_2038,refute_0_2039]) ).
cnf(refute_0_2041,plain,
inverse(inverse(least_upper_bound(identity,inverse(X_508)))) = least_upper_bound(identity,inverse(X_508)),
inference(subst,[],[refute_0_335:[bind(X_44,$fot(least_upper_bound(identity,inverse(X_508))))]]) ).
cnf(refute_0_2042,plain,
( inverse(greatest_lower_bound(identity,X_508)) != inverse(inverse(least_upper_bound(identity,inverse(X_508))))
| inverse(inverse(least_upper_bound(identity,inverse(X_508)))) != least_upper_bound(identity,inverse(X_508))
| inverse(greatest_lower_bound(identity,X_508)) = least_upper_bound(identity,inverse(X_508)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,X_508)),least_upper_bound(identity,inverse(X_508))) ),[0],$fot(inverse(inverse(least_upper_bound(identity,inverse(X_508)))))]]) ).
cnf(refute_0_2043,plain,
( inverse(greatest_lower_bound(identity,X_508)) != inverse(inverse(least_upper_bound(identity,inverse(X_508))))
| inverse(greatest_lower_bound(identity,X_508)) = least_upper_bound(identity,inverse(X_508)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_508)))),least_upper_bound(identity,inverse(X_508))) )],[refute_0_2041,refute_0_2042]) ).
cnf(refute_0_2044,plain,
( multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))) != inverse(inverse(least_upper_bound(identity,inverse(X_508))))
| inverse(greatest_lower_bound(identity,X_508)) = least_upper_bound(identity,inverse(X_508)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_508)),inverse(inverse(least_upper_bound(identity,inverse(X_508))))) )],[refute_0_2040,refute_0_2043]) ).
cnf(refute_0_2045,plain,
inverse(greatest_lower_bound(identity,X_508)) = least_upper_bound(identity,inverse(X_508)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_508)),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_508),least_upper_bound(identity,inverse(X_508)))))),inverse(inverse(least_upper_bound(identity,inverse(X_508))))) )],[refute_0_1880,refute_0_2044]) ).
cnf(refute_0_2046,plain,
( inverse(greatest_lower_bound(identity,X_508)) != least_upper_bound(identity,inverse(X_508))
| least_upper_bound(identity,inverse(X_508)) = inverse(greatest_lower_bound(identity,X_508)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_508)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_508))))]]) ).
cnf(refute_0_2047,plain,
least_upper_bound(identity,inverse(X_508)) = inverse(greatest_lower_bound(identity,X_508)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_508)),least_upper_bound(identity,inverse(X_508))) )],[refute_0_2045,refute_0_2046]) ).
cnf(refute_0_2048,plain,
least_upper_bound(identity,inverse(X_86)) = inverse(greatest_lower_bound(identity,X_86)),
inference(subst,[],[refute_0_2047:[bind(X_508,$fot(X_86))]]) ).
cnf(refute_0_2049,plain,
inverse(least_upper_bound(identity,inverse(X_86))) = inverse(least_upper_bound(identity,inverse(X_86))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(X_86))))]]) ).
cnf(refute_0_2050,plain,
( inverse(least_upper_bound(identity,inverse(X_86))) != inverse(least_upper_bound(identity,inverse(X_86)))
| least_upper_bound(identity,inverse(X_86)) != inverse(greatest_lower_bound(identity,X_86))
| inverse(least_upper_bound(identity,inverse(X_86))) = inverse(inverse(greatest_lower_bound(identity,X_86))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_86))),inverse(least_upper_bound(identity,inverse(X_86)))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,X_86)))]]) ).
cnf(refute_0_2051,plain,
( least_upper_bound(identity,inverse(X_86)) != inverse(greatest_lower_bound(identity,X_86))
| inverse(least_upper_bound(identity,inverse(X_86))) = inverse(inverse(greatest_lower_bound(identity,X_86))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_86))),inverse(least_upper_bound(identity,inverse(X_86)))) )],[refute_0_2049,refute_0_2050]) ).
cnf(refute_0_2052,plain,
inverse(least_upper_bound(identity,inverse(X_86))) = inverse(inverse(greatest_lower_bound(identity,X_86))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_86)),inverse(greatest_lower_bound(identity,X_86))) )],[refute_0_2048,refute_0_2051]) ).
cnf(refute_0_2053,plain,
( inverse(inverse(greatest_lower_bound(identity,X_86))) != greatest_lower_bound(identity,X_86)
| inverse(least_upper_bound(identity,inverse(X_86))) != inverse(inverse(greatest_lower_bound(identity,X_86)))
| inverse(least_upper_bound(identity,inverse(X_86))) = greatest_lower_bound(identity,X_86) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_86))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(identity,X_86))))),bind(Z0,$fot(greatest_lower_bound(identity,X_86)))]]) ).
cnf(refute_0_2054,plain,
( inverse(inverse(greatest_lower_bound(identity,X_86))) != greatest_lower_bound(identity,X_86)
| inverse(least_upper_bound(identity,inverse(X_86))) = greatest_lower_bound(identity,X_86) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_86))),inverse(inverse(greatest_lower_bound(identity,X_86)))) )],[refute_0_2052,refute_0_2053]) ).
cnf(refute_0_2055,plain,
inverse(least_upper_bound(identity,inverse(X_86))) = greatest_lower_bound(identity,X_86),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,X_86))),greatest_lower_bound(identity,X_86)) )],[refute_0_340,refute_0_2054]) ).
cnf(refute_0_2056,plain,
multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))))]]) ).
cnf(refute_0_2057,plain,
( multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) != multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86))))
| inverse(least_upper_bound(identity,inverse(X_86))) != greatest_lower_bound(identity,X_86)
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86))))) ),[1,1],$fot(greatest_lower_bound(identity,X_86))]]) ).
cnf(refute_0_2058,plain,
( inverse(least_upper_bound(identity,inverse(X_86))) != greatest_lower_bound(identity,X_86)
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86))))) )],[refute_0_2056,refute_0_2057]) ).
cnf(refute_0_2059,plain,
multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_86))),greatest_lower_bound(identity,X_86)) )],[refute_0_2055,refute_0_2058]) ).
cnf(refute_0_2060,plain,
( multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) != X_86
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) != multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))
| multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) = X_86 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),X_86) ),[0],$fot(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))]]) ).
cnf(refute_0_2061,plain,
( multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) != X_86
| multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) = X_86 ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) )],[refute_0_2059,refute_0_2060]) ).
cnf(refute_0_2062,plain,
multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) = X_86,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),X_86) )],[refute_0_339,refute_0_2061]) ).
cnf(refute_0_2063,plain,
multiply(least_upper_bound(identity,multiply(identity,X_91)),greatest_lower_bound(identity,multiply(identity,X_91))) = multiply(identity,X_91),
inference(subst,[],[refute_0_2062:[bind(X_86,$fot(multiply(identity,X_91)))]]) ).
cnf(refute_0_2064,plain,
multiply(identity,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(identity,multiply(identity,X_91)),
inference(subst,[],[refute_0_785:[bind(X_90,$fot(identity))]]) ).
cnf(refute_0_2065,plain,
( multiply(identity,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(identity,multiply(identity,X_91))
| greatest_lower_bound(identity,multiply(identity,X_91)) = multiply(identity,greatest_lower_bound(X_91,identity)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(multiply(identity,greatest_lower_bound(X_91,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(identity,X_91))))]]) ).
cnf(refute_0_2066,plain,
greatest_lower_bound(identity,multiply(identity,X_91)) = multiply(identity,greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_91,identity)),greatest_lower_bound(identity,multiply(identity,X_91))) )],[refute_0_2064,refute_0_2065]) ).
cnf(refute_0_2067,plain,
( multiply(least_upper_bound(identity,multiply(identity,X_91)),greatest_lower_bound(identity,multiply(identity,X_91))) != multiply(identity,X_91)
| greatest_lower_bound(identity,multiply(identity,X_91)) != multiply(identity,greatest_lower_bound(X_91,identity))
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(identity,X_91) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),greatest_lower_bound(identity,multiply(identity,X_91))),multiply(identity,X_91)) ),[0,1],$fot(multiply(identity,greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_2068,plain,
( multiply(least_upper_bound(identity,multiply(identity,X_91)),greatest_lower_bound(identity,multiply(identity,X_91))) != multiply(identity,X_91)
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(identity,X_91) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) )],[refute_0_2066,refute_0_2067]) ).
cnf(refute_0_2069,plain,
multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(identity,X_91),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),greatest_lower_bound(identity,multiply(identity,X_91))),multiply(identity,X_91)) )],[refute_0_2063,refute_0_2068]) ).
cnf(refute_0_2070,plain,
multiply(identity,greatest_lower_bound(X_91,identity)) = greatest_lower_bound(X_91,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_2071,plain,
multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))))]]) ).
cnf(refute_0_2072,plain,
( multiply(identity,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(X_91,identity)
| multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity)))
| multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity)))) ),[1,1],$fot(greatest_lower_bound(X_91,identity))]]) ).
cnf(refute_0_2073,plain,
( multiply(identity,greatest_lower_bound(X_91,identity)) != greatest_lower_bound(X_91,identity)
| multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity)))) )],[refute_0_2071,refute_0_2072]) ).
cnf(refute_0_2074,plain,
multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_91,identity)),greatest_lower_bound(X_91,identity)) )],[refute_0_2070,refute_0_2073]) ).
cnf(refute_0_2075,plain,
multiply(identity,least_upper_bound(X_91,identity)) = least_upper_bound(X_91,identity),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_91,identity)))]]) ).
cnf(refute_0_2076,plain,
least_upper_bound(identity,multiply(identity,X_91)) = multiply(identity,least_upper_bound(X_91,identity)),
inference(subst,[],[refute_0_179:[bind(X_66,$fot(identity)),bind(X_67,$fot(X_91))]]) ).
cnf(refute_0_2077,plain,
( multiply(identity,least_upper_bound(X_91,identity)) != least_upper_bound(X_91,identity)
| least_upper_bound(identity,multiply(identity,X_91)) != multiply(identity,least_upper_bound(X_91,identity))
| least_upper_bound(identity,multiply(identity,X_91)) = least_upper_bound(X_91,identity) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,X_91)))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_91,identity)))),bind(Z0,$fot(least_upper_bound(X_91,identity)))]]) ).
cnf(refute_0_2078,plain,
( multiply(identity,least_upper_bound(X_91,identity)) != least_upper_bound(X_91,identity)
| least_upper_bound(identity,multiply(identity,X_91)) = least_upper_bound(X_91,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,least_upper_bound(X_91,identity))) )],[refute_0_2076,refute_0_2077]) ).
cnf(refute_0_2079,plain,
least_upper_bound(identity,multiply(identity,X_91)) = least_upper_bound(X_91,identity),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_91,identity)),least_upper_bound(X_91,identity)) )],[refute_0_2075,refute_0_2078]) ).
cnf(refute_0_2080,plain,
multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))))]]) ).
cnf(refute_0_2081,plain,
( multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity)))
| least_upper_bound(identity,multiply(identity,X_91)) != least_upper_bound(X_91,identity)
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity)))) ),[1,0],$fot(least_upper_bound(X_91,identity))]]) ).
cnf(refute_0_2082,plain,
( least_upper_bound(identity,multiply(identity,X_91)) != least_upper_bound(X_91,identity)
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity)))) )],[refute_0_2080,refute_0_2081]) ).
cnf(refute_0_2083,plain,
multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_91)),least_upper_bound(X_91,identity)) )],[refute_0_2079,refute_0_2082]) ).
cnf(refute_0_2084,plain,
( multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity))
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity)))
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) ),
inference(subst,[],[refute_0_149:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))))),bind(Z0,$fot(multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity))))]]) ).
cnf(refute_0_2085,plain,
( multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity))
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity)))) )],[refute_0_2083,refute_0_2084]) ).
cnf(refute_0_2086,plain,
multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) = multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity))) )],[refute_0_2074,refute_0_2085]) ).
cnf(refute_0_2087,plain,
( multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(identity,X_91)
| multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity))
| multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) = multiply(identity,X_91) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(identity,X_91)) ),[0],$fot(multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)))]]) ).
cnf(refute_0_2088,plain,
( multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(identity,X_91)
| multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) = multiply(identity,X_91) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity))) )],[refute_0_2086,refute_0_2087]) ).
cnf(refute_0_2089,plain,
multiply(identity,X_91) = X_91,
inference(subst,[],[left_identity:[bind(X,$fot(X_91))]]) ).
cnf(refute_0_2090,plain,
( multiply(identity,X_91) != X_91
| multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) != multiply(identity,X_91)
| multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) = X_91 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)),multiply(identity,X_91)) ),[1],$fot(X_91)]]) ).
cnf(refute_0_2091,plain,
( multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) != multiply(identity,X_91)
| multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) = X_91 ),
inference(resolve,[$cnf( $equal(multiply(identity,X_91),X_91) )],[refute_0_2089,refute_0_2090]) ).
cnf(refute_0_2092,plain,
( multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))) != multiply(identity,X_91)
| multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) = X_91 ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)),multiply(identity,X_91)) )],[refute_0_2088,refute_0_2091]) ).
cnf(refute_0_2093,plain,
multiply(least_upper_bound(X_91,identity),greatest_lower_bound(X_91,identity)) = X_91,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(identity,X_91)),multiply(identity,greatest_lower_bound(X_91,identity))),multiply(identity,X_91)) )],[refute_0_2069,refute_0_2092]) ).
cnf(refute_0_2094,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = a,
inference(subst,[],[refute_0_2093:[bind(X_91,$fot(a))]]) ).
cnf(refute_0_2095,plain,
( multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != a
| a != a
| a = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a,multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity))) ),[1],$fot(a)]]) ).
cnf(refute_0_2096,plain,
( a != a
| a = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),a) )],[refute_0_2094,refute_0_2095]) ).
cnf(refute_0_2097,plain,
a != a,
inference(resolve,[$cnf( $equal(a,multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity))) )],[refute_0_2096,prove_p19]) ).
cnf(refute_0_2098,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_2099,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_2098,refute_0_2097]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP167-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 13:09:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 57.53/57.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.53/57.77
% 57.53/57.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.85/58.02
%------------------------------------------------------------------------------