%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP181-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 10:37:28 EDT 2022
% Result : Unsatisfiable 115.78s 115.97s
% Output : CNFRefutation 116.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 173
% Number of leaves : 1221
% Syntax : Number of clauses : 5839 (2929 unt; 0 nHn;3476 RR)
% Number of literals : 10051 (10050 equ;4214 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 9512 ( 211 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p12_1,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ).
cnf(p12_2,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c) ).
cnf(prove_p12,negated_conjecture,
a != b ).
cnf(refute_0_0,plain,
multiply(multiply(inverse(X_45),X_45),X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_45),X_45) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(inverse(X_45),X_45),X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| multiply(inverse(X_45),X_45) != identity
| multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_45),X_45),X_46),multiply(inverse(X_45),multiply(X_45,X_46))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_45),X_45),X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),X_45),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_45),X_45),X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_46) = X_46,
inference(subst,[],[left_identity:[bind(X,$fot(X_46))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_46) != X_46
| multiply(identity,X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| X_46 = multiply(inverse(X_45),multiply(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_46),multiply(inverse(X_45),multiply(X_45,X_46))) ),[0],$fot(X_46)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
| X_46 = multiply(inverse(X_45),multiply(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_46),X_46) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_46 = multiply(inverse(X_45),multiply(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(identity,X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
b = multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))),bind(X_46,$fot(b))]]) ).
cnf(refute_0_10,plain,
multiply(X_55,inverse(multiply(X_45,X_55))) = multiply(inverse(X_45),multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55))))),
inference(subst,[],[refute_0_8:[bind(X_46,$fot(multiply(X_55,inverse(multiply(X_45,X_55)))))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(subst,[],[associativity:[bind(Z,$fot(inverse(multiply(X,Y))))]]) ).
cnf(refute_0_12,plain,
multiply(inverse(inverse(X_50)),inverse(X_50)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_50)))]]) ).
cnf(refute_0_13,plain,
multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48))),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(inverse(X_47))),bind(X_46,$fot(multiply(X_47,X_48)))]]) ).
cnf(refute_0_14,plain,
X_48 = multiply(inverse(X_47),multiply(X_47,X_48)),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(X_47)),bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_17,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( X_48 != multiply(inverse(X_47),multiply(X_47,X_48))
| multiply(inverse(X_47),multiply(X_47,X_48)) = X_48 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(inverse(X_47),multiply(X_47,X_48))))]]) ).
cnf(refute_0_19,plain,
multiply(inverse(X_47),multiply(X_47,X_48)) = X_48,
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(X_47),multiply(X_47,X_48))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))
| multiply(inverse(X_47),multiply(X_47,X_48)) != X_48
| multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))) ),[1,1],$fot(X_48)]]) ).
cnf(refute_0_21,plain,
( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))
| multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_47),multiply(X_47,X_48)),X_48) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48),
inference(resolve,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_50,inverse(X_50)) = multiply(inverse(inverse(X_50)),inverse(X_50)),
inference(subst,[],[refute_0_22:[bind(X_47,$fot(X_50)),bind(X_48,$fot(inverse(X_50)))]]) ).
cnf(refute_0_24,plain,
( multiply(X_50,inverse(X_50)) != multiply(inverse(inverse(X_50)),inverse(X_50))
| multiply(inverse(inverse(X_50)),inverse(X_50)) = multiply(X_50,inverse(X_50)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_50,inverse(X_50)))),bind(Y0,$fot(multiply(inverse(inverse(X_50)),inverse(X_50))))]]) ).
cnf(refute_0_25,plain,
multiply(inverse(inverse(X_50)),inverse(X_50)) = multiply(X_50,inverse(X_50)),
inference(resolve,[$cnf( $equal(multiply(X_50,inverse(X_50)),multiply(inverse(inverse(X_50)),inverse(X_50))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( multiply(inverse(inverse(X_50)),inverse(X_50)) != multiply(X_50,inverse(X_50))
| multiply(inverse(inverse(X_50)),inverse(X_50)) != identity
| multiply(X_50,inverse(X_50)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_50)),inverse(X_50)),identity) ),[0],$fot(multiply(X_50,inverse(X_50)))]]) ).
cnf(refute_0_27,plain,
( multiply(inverse(inverse(X_50)),inverse(X_50)) != identity
| multiply(X_50,inverse(X_50)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),inverse(X_50)),multiply(X_50,inverse(X_50))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_50,inverse(X_50)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),inverse(X_50)),identity) )],[refute_0_12,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_30,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_31,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( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),identity) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) )],[refute_0_11,refute_0_31]) ).
cnf(refute_0_33,plain,
identity = multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_45)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_34,plain,
( identity != multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55))))
| multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55))))))]]) ).
cnf(refute_0_35,plain,
multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55))))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))) != identity
| multiply(X_55,inverse(multiply(X_45,X_55))) != multiply(inverse(X_45),multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))))
| multiply(X_55,inverse(multiply(X_45,X_55))) = multiply(inverse(X_45),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,inverse(multiply(X_45,X_55))),multiply(inverse(X_45),multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_37,plain,
( multiply(X_55,inverse(multiply(X_45,X_55))) != multiply(inverse(X_45),multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))))
| multiply(X_55,inverse(multiply(X_45,X_55))) = multiply(inverse(X_45),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))),identity) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(X_55,inverse(multiply(X_45,X_55))) = multiply(inverse(X_45),identity),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(multiply(X_45,X_55))),multiply(inverse(X_45),multiply(X_45,multiply(X_55,inverse(multiply(X_45,X_55)))))) )],[refute_0_10,refute_0_37]) ).
cnf(refute_0_39,plain,
X_48 = multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48)),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(inverse(X_48))),bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_40,plain,
multiply(inverse(X_48),X_48) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_48))]]) ).
cnf(refute_0_41,plain,
( X_48 != multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))
| multiply(inverse(X_48),X_48) != identity
| X_48 = multiply(inverse(inverse(X_48)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_42,plain,
( X_48 != multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))
| X_48 = multiply(inverse(inverse(X_48)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_48),X_48),identity) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
X_48 = multiply(inverse(inverse(X_48)),identity),
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),X_48)
| multiply(inverse(inverse(X_47)),X_48) = multiply(X_47,X_48) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_47,X_48))),bind(Y0,$fot(multiply(inverse(inverse(X_47)),X_48)))]]) ).
cnf(refute_0_45,plain,
multiply(inverse(inverse(X_47)),X_48) = multiply(X_47,X_48),
inference(resolve,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),X_48)) )],[refute_0_22,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(inverse(inverse(X_48)),identity) = multiply(X_48,identity),
inference(subst,[],[refute_0_45:[bind(X_47,$fot(X_48)),bind(X_48,$fot(identity))]]) ).
cnf(refute_0_47,plain,
( X_48 != multiply(inverse(inverse(X_48)),identity)
| multiply(inverse(inverse(X_48)),identity) != multiply(X_48,identity)
| X_48 = multiply(X_48,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_48,multiply(X_48,identity)) ),[0],$fot(multiply(inverse(inverse(X_48)),identity))]]) ).
cnf(refute_0_48,plain,
( X_48 != multiply(inverse(inverse(X_48)),identity)
| X_48 = multiply(X_48,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_48)),identity),multiply(X_48,identity)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
X_48 = multiply(X_48,identity),
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),identity)) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
( X_48 != multiply(X_48,identity)
| multiply(X_48,identity) = X_48 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(X_48,identity)))]]) ).
cnf(refute_0_51,plain,
multiply(X_48,identity) = X_48,
inference(resolve,[$cnf( $equal(X_48,multiply(X_48,identity)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(inverse(X_45),identity) = inverse(X_45),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(X_45)))]]) ).
cnf(refute_0_53,plain,
( multiply(X_55,inverse(multiply(X_45,X_55))) != multiply(inverse(X_45),identity)
| multiply(inverse(X_45),identity) != inverse(X_45)
| multiply(X_55,inverse(multiply(X_45,X_55))) = inverse(X_45) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_55,inverse(multiply(X_45,X_55))),inverse(X_45)) ),[0],$fot(multiply(inverse(X_45),identity))]]) ).
cnf(refute_0_54,plain,
( multiply(X_55,inverse(multiply(X_45,X_55))) != multiply(inverse(X_45),identity)
| multiply(X_55,inverse(multiply(X_45,X_55))) = inverse(X_45) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),identity),inverse(X_45)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(X_55,inverse(multiply(X_45,X_55))) = inverse(X_45),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(multiply(X_45,X_55))),multiply(inverse(X_45),identity)) )],[refute_0_38,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))) = inverse(inverse(X_86)),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(inverse(X_86))),bind(X_55,$fot(least_upper_bound(identity,X_86)))]]) ).
cnf(refute_0_57,plain,
multiply(inverse(X_84),least_upper_bound(X_83,X_84)) = least_upper_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_84))),bind(Y,$fot(X_83)),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_58,plain,
multiply(inverse(X_84),X_84) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_84))]]) ).
cnf(refute_0_59,plain,
( multiply(inverse(X_84),X_84) != identity
| multiply(inverse(X_84),least_upper_bound(X_83,X_84)) != least_upper_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))
| multiply(inverse(X_84),least_upper_bound(X_83,X_84)) = least_upper_bound(multiply(inverse(X_84),X_83),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_83,X_84)),least_upper_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_60,plain,
( multiply(inverse(X_84),least_upper_bound(X_83,X_84)) != least_upper_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))
| multiply(inverse(X_84),least_upper_bound(X_83,X_84)) = least_upper_bound(multiply(inverse(X_84),X_83),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),X_84),identity) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(inverse(X_84),least_upper_bound(X_83,X_84)) = least_upper_bound(multiply(inverse(X_84),X_83),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_83,X_84)),least_upper_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_63,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_62]) ).
cnf(refute_0_64,plain,
least_upper_bound(multiply(inverse(X_84),X_83),identity) = least_upper_bound(identity,multiply(inverse(X_84),X_83)),
inference(subst,[],[refute_0_63:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_65,plain,
( multiply(inverse(X_84),least_upper_bound(X_83,X_84)) != least_upper_bound(multiply(inverse(X_84),X_83),identity)
| least_upper_bound(multiply(inverse(X_84),X_83),identity) != least_upper_bound(identity,multiply(inverse(X_84),X_83))
| multiply(inverse(X_84),least_upper_bound(X_83,X_84)) = least_upper_bound(identity,multiply(inverse(X_84),X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_84),least_upper_bound(X_83,X_84)),least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),[0],$fot(least_upper_bound(multiply(inverse(X_84),X_83),identity))]]) ).
cnf(refute_0_66,plain,
( multiply(inverse(X_84),least_upper_bound(X_83,X_84)) != least_upper_bound(multiply(inverse(X_84),X_83),identity)
| multiply(inverse(X_84),least_upper_bound(X_83,X_84)) = least_upper_bound(identity,multiply(inverse(X_84),X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_84),X_83),identity),least_upper_bound(identity,multiply(inverse(X_84),X_83))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(inverse(X_84),least_upper_bound(X_83,X_84)) = least_upper_bound(identity,multiply(inverse(X_84),X_83)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_83,X_84)),least_upper_bound(multiply(inverse(X_84),X_83),identity)) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(inverse(X_86),least_upper_bound(identity,X_86)) = least_upper_bound(identity,multiply(inverse(X_86),identity)),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(identity)),bind(X_84,$fot(X_86))]]) ).
cnf(refute_0_69,plain,
inverse(X_86) = multiply(inverse(X_86),identity),
inference(subst,[],[refute_0_49:[bind(X_48,$fot(inverse(X_86)))]]) ).
cnf(refute_0_70,plain,
( inverse(X_86) != multiply(inverse(X_86),identity)
| multiply(inverse(X_86),identity) = inverse(X_86) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(X_86))),bind(Y0,$fot(multiply(inverse(X_86),identity)))]]) ).
cnf(refute_0_71,plain,
multiply(inverse(X_86),identity) = inverse(X_86),
inference(resolve,[$cnf( $equal(inverse(X_86),multiply(inverse(X_86),identity)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( multiply(inverse(X_86),identity) != inverse(X_86)
| multiply(inverse(X_86),least_upper_bound(identity,X_86)) != least_upper_bound(identity,multiply(inverse(X_86),identity))
| multiply(inverse(X_86),least_upper_bound(identity,X_86)) = least_upper_bound(identity,inverse(X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(identity,X_86)),least_upper_bound(identity,multiply(inverse(X_86),identity))) ),[1,1],$fot(inverse(X_86))]]) ).
cnf(refute_0_73,plain,
( multiply(inverse(X_86),least_upper_bound(identity,X_86)) != least_upper_bound(identity,multiply(inverse(X_86),identity))
| multiply(inverse(X_86),least_upper_bound(identity,X_86)) = least_upper_bound(identity,inverse(X_86)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),identity),inverse(X_86)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(X_86),least_upper_bound(identity,X_86)) = least_upper_bound(identity,inverse(X_86)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(identity,X_86)),least_upper_bound(identity,multiply(inverse(X_86),identity))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
( multiply(inverse(X_86),least_upper_bound(identity,X_86)) != least_upper_bound(identity,inverse(X_86))
| multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))) != inverse(inverse(X_86))
| multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = inverse(inverse(X_86)) ),
introduced(tautology,[equality,[$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_76,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( $equal(multiply(inverse(X_86),least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = inverse(inverse(X_86)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(multiply(inverse(X_86),least_upper_bound(identity,X_86)))),inverse(inverse(X_86))) )],[refute_0_56,refute_0_76]) ).
cnf(refute_0_78,plain,
inverse(inverse(X_50)) = multiply(inverse(inverse(X_50)),identity),
inference(subst,[],[refute_0_49:[bind(X_48,$fot(inverse(inverse(X_50))))]]) ).
cnf(refute_0_79,plain,
multiply(X_50,identity) = multiply(inverse(inverse(X_50)),identity),
inference(subst,[],[refute_0_22:[bind(X_47,$fot(X_50)),bind(X_48,$fot(identity))]]) ).
cnf(refute_0_80,plain,
( multiply(X_50,identity) != multiply(inverse(inverse(X_50)),identity)
| multiply(inverse(inverse(X_50)),identity) = multiply(X_50,identity) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_50,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_50)),identity)))]]) ).
cnf(refute_0_81,plain,
multiply(inverse(inverse(X_50)),identity) = multiply(X_50,identity),
inference(resolve,[$cnf( $equal(multiply(X_50,identity),multiply(inverse(inverse(X_50)),identity)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( multiply(inverse(inverse(X_50)),identity) != multiply(X_50,identity)
| inverse(inverse(X_50)) != multiply(inverse(inverse(X_50)),identity)
| inverse(inverse(X_50)) = multiply(X_50,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_50)),multiply(inverse(inverse(X_50)),identity)) ),[1],$fot(multiply(X_50,identity))]]) ).
cnf(refute_0_83,plain,
( inverse(inverse(X_50)) != multiply(inverse(inverse(X_50)),identity)
| inverse(inverse(X_50)) = multiply(X_50,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),identity),multiply(X_50,identity)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
inverse(inverse(X_50)) = multiply(X_50,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_50)),multiply(inverse(inverse(X_50)),identity)) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(X_50,identity) = X_50,
inference(subst,[],[refute_0_51:[bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_86,plain,
( multiply(X_50,identity) != X_50
| inverse(inverse(X_50)) != multiply(X_50,identity)
| inverse(inverse(X_50)) = X_50 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_50)),multiply(X_50,identity)) ),[1],$fot(X_50)]]) ).
cnf(refute_0_87,plain,
( inverse(inverse(X_50)) != multiply(X_50,identity)
| inverse(inverse(X_50)) = X_50 ),
inference(resolve,[$cnf( $equal(multiply(X_50,identity),X_50) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
inverse(inverse(X_50)) = X_50,
inference(resolve,[$cnf( $equal(inverse(inverse(X_50)),multiply(X_50,identity)) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
inverse(inverse(X_86)) = X_86,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_86))]]) ).
cnf(refute_0_90,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_91,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( $equal(inverse(inverse(X_86)),X_86) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))) = X_86,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),inverse(least_upper_bound(identity,inverse(X_86)))),inverse(inverse(X_86))) )],[refute_0_77,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b),
inference(subst,[],[refute_0_92:[bind(X_86,$fot(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))]]) ).
cnf(refute_0_94,plain,
multiply(least_upper_bound(inverse(X_89),X_91),X_89) = least_upper_bound(multiply(inverse(X_89),X_89),multiply(X_91,X_89)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_89)),bind(Y,$fot(inverse(X_89))),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_95,plain,
multiply(inverse(X_89),X_89) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_89))]]) ).
cnf(refute_0_96,plain,
( multiply(inverse(X_89),X_89) != identity
| multiply(least_upper_bound(inverse(X_89),X_91),X_89) != least_upper_bound(multiply(inverse(X_89),X_89),multiply(X_91,X_89))
| multiply(least_upper_bound(inverse(X_89),X_91),X_89) = least_upper_bound(identity,multiply(X_91,X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),X_91),X_89),least_upper_bound(multiply(inverse(X_89),X_89),multiply(X_91,X_89))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_97,plain,
( multiply(least_upper_bound(inverse(X_89),X_91),X_89) != least_upper_bound(multiply(inverse(X_89),X_89),multiply(X_91,X_89))
| multiply(least_upper_bound(inverse(X_89),X_91),X_89) = least_upper_bound(identity,multiply(X_91,X_89)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),X_89),identity) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(least_upper_bound(inverse(X_89),X_91),X_89) = least_upper_bound(identity,multiply(X_91,X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),X_91),X_89),least_upper_bound(multiply(inverse(X_89),X_89),multiply(X_91,X_89))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) = least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))),
inference(subst,[],[refute_0_98:[bind(X_89,$fot(greatest_lower_bound(X_162,X_163))),bind(X_91,$fot(inverse(X_163)))]]) ).
cnf(refute_0_100,plain,
multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(multiply(inverse(X_155),X_154),multiply(inverse(X_155),X_155)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_155))),bind(Y,$fot(X_154)),bind(Z,$fot(X_155))]]) ).
cnf(refute_0_101,plain,
multiply(inverse(X_155),X_155) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_155))]]) ).
cnf(refute_0_102,plain,
( multiply(inverse(X_155),X_155) != identity
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(multiply(inverse(X_155),X_154),multiply(inverse(X_155),X_155))
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(multiply(inverse(X_155),X_154),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)),greatest_lower_bound(multiply(inverse(X_155),X_154),multiply(inverse(X_155),X_155))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_103,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(multiply(inverse(X_155),X_154),multiply(inverse(X_155),X_155))
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(multiply(inverse(X_155),X_154),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),X_155),identity) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(multiply(inverse(X_155),X_154),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)),greatest_lower_bound(multiply(inverse(X_155),X_154),multiply(inverse(X_155),X_155))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_105]) ).
cnf(refute_0_107,plain,
greatest_lower_bound(multiply(inverse(X_155),X_154),identity) = greatest_lower_bound(identity,multiply(inverse(X_155),X_154)),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_155),X_154)))]]) ).
cnf(refute_0_108,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(multiply(inverse(X_155),X_154),identity)
| greatest_lower_bound(multiply(inverse(X_155),X_154),identity) != greatest_lower_bound(identity,multiply(inverse(X_155),X_154))
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_154)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)),greatest_lower_bound(identity,multiply(inverse(X_155),X_154))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_155),X_154),identity))]]) ).
cnf(refute_0_109,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(multiply(inverse(X_155),X_154),identity)
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_154)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_155),X_154),identity),greatest_lower_bound(identity,multiply(inverse(X_155),X_154))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_154)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)),greatest_lower_bound(multiply(inverse(X_155),X_154),identity)) )],[refute_0_104,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)) = greatest_lower_bound(identity,multiply(inverse(X_163),X_162)),
inference(subst,[],[refute_0_110:[bind(X_154,$fot(X_162)),bind(X_155,$fot(X_163))]]) ).
cnf(refute_0_112,plain,
( multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)) != greatest_lower_bound(identity,multiply(inverse(X_163),X_162))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) != least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)),least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))]]) ).
cnf(refute_0_113,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) != least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)),greatest_lower_bound(identity,multiply(inverse(X_163),X_162))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)),least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)))) )],[refute_0_99,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) != least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))
| least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))))]]) ).
cnf(refute_0_116,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))
| least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)),least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163)))) )],[refute_0_99,refute_0_115]) ).
cnf(refute_0_117,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_163),X_162)))]]) ).
cnf(refute_0_118,plain,
( least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))) != identity
| least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))),identity) ),[0],$fot(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))))]]) ).
cnf(refute_0_119,plain,
( least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))
| least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162))),identity) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))
| least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
least_upper_bound(identity,multiply(inverse(X_163),greatest_lower_bound(X_162,X_163))) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_162,X_163)),inverse(X_163)),greatest_lower_bound(X_162,X_163)),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_163),X_162)))) )],[refute_0_114,refute_0_120]) ).
cnf(refute_0_122,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))) = identity,
inference(subst,[],[refute_0_121:[bind(X_162,$fot(b)),bind(X_163,$fot(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(c,X_33))) = b,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_124,plain,
least_upper_bound(b,least_upper_bound(c,X_22)) = least_upper_bound(least_upper_bound(b,c),X_22),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_125,plain,
( least_upper_bound(a,c) != least_upper_bound(b,c)
| least_upper_bound(b,c) = least_upper_bound(a,c) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(a,c))),bind(Y0,$fot(least_upper_bound(b,c)))]]) ).
cnf(refute_0_126,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),least_upper_bound(b,c)) )],[p12_2,refute_0_125]) ).
cnf(refute_0_127,plain,
( least_upper_bound(b,c) != least_upper_bound(a,c)
| least_upper_bound(b,least_upper_bound(c,X_22)) != least_upper_bound(least_upper_bound(b,c),X_22)
| least_upper_bound(b,least_upper_bound(c,X_22)) = least_upper_bound(least_upper_bound(a,c),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_22)),least_upper_bound(least_upper_bound(b,c),X_22)) ),[1,0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_128,plain,
( least_upper_bound(b,least_upper_bound(c,X_22)) != least_upper_bound(least_upper_bound(b,c),X_22)
| least_upper_bound(b,least_upper_bound(c,X_22)) = least_upper_bound(least_upper_bound(a,c),X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
least_upper_bound(b,least_upper_bound(c,X_22)) = least_upper_bound(least_upper_bound(a,c),X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_22)),least_upper_bound(least_upper_bound(b,c),X_22)) )],[refute_0_124,refute_0_128]) ).
cnf(refute_0_130,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_131,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_130]) ).
cnf(refute_0_132,plain,
least_upper_bound(least_upper_bound(a,c),X_22) = least_upper_bound(a,least_upper_bound(c,X_22)),
inference(subst,[],[refute_0_131:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_133,plain,
( least_upper_bound(b,least_upper_bound(c,X_22)) != least_upper_bound(least_upper_bound(a,c),X_22)
| least_upper_bound(least_upper_bound(a,c),X_22) != least_upper_bound(a,least_upper_bound(c,X_22))
| least_upper_bound(b,least_upper_bound(c,X_22)) = least_upper_bound(a,least_upper_bound(c,X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(b,least_upper_bound(c,X_22)),least_upper_bound(a,least_upper_bound(c,X_22))) ),[0],$fot(least_upper_bound(least_upper_bound(a,c),X_22))]]) ).
cnf(refute_0_134,plain,
( least_upper_bound(b,least_upper_bound(c,X_22)) != least_upper_bound(least_upper_bound(a,c),X_22)
| least_upper_bound(b,least_upper_bound(c,X_22)) = least_upper_bound(a,least_upper_bound(c,X_22)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,c),X_22),least_upper_bound(a,least_upper_bound(c,X_22))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
least_upper_bound(b,least_upper_bound(c,X_22)) = least_upper_bound(a,least_upper_bound(c,X_22)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_22)),least_upper_bound(least_upper_bound(a,c),X_22)) )],[refute_0_129,refute_0_134]) ).
cnf(refute_0_136,plain,
least_upper_bound(b,least_upper_bound(c,X_33)) = least_upper_bound(a,least_upper_bound(c,X_33)),
inference(subst,[],[refute_0_135:[bind(X_22,$fot(X_33))]]) ).
cnf(refute_0_137,plain,
( greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(c,X_33))) != b
| least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(c,X_33))
| greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(c,X_33))),b) ),[0,1],$fot(least_upper_bound(a,least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_138,plain,
( greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(c,X_33))) != b
| greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(c,X_33))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,least_upper_bound(c,X_33))),b) )],[refute_0_123,refute_0_138]) ).
cnf(refute_0_140,plain,
greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(X_93,c)))) = b,
inference(subst,[],[refute_0_139:[bind(X_33,$fot(multiply(X_93,c)))]]) ).
cnf(refute_0_141,plain,
multiply(least_upper_bound(X_90,identity),X_89) = least_upper_bound(multiply(X_90,X_89),multiply(identity,X_89)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_89)),bind(Y,$fot(X_90)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_142,plain,
multiply(identity,X_89) = X_89,
inference(subst,[],[left_identity:[bind(X,$fot(X_89))]]) ).
cnf(refute_0_143,plain,
( multiply(identity,X_89) != X_89
| multiply(least_upper_bound(X_90,identity),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(identity,X_89))
| multiply(least_upper_bound(X_90,identity),X_89) = least_upper_bound(multiply(X_90,X_89),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),X_89),least_upper_bound(multiply(X_90,X_89),multiply(identity,X_89))) ),[1,1],$fot(X_89)]]) ).
cnf(refute_0_144,plain,
( multiply(least_upper_bound(X_90,identity),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(identity,X_89))
| multiply(least_upper_bound(X_90,identity),X_89) = least_upper_bound(multiply(X_90,X_89),X_89) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_89),X_89) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(least_upper_bound(X_90,identity),X_89) = least_upper_bound(multiply(X_90,X_89),X_89),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),X_89),least_upper_bound(multiply(X_90,X_89),multiply(identity,X_89))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
least_upper_bound(multiply(X_90,X_89),X_89) = least_upper_bound(X_89,multiply(X_90,X_89)),
inference(subst,[],[refute_0_63:[bind(X,$fot(X_89)),bind(Y,$fot(multiply(X_90,X_89)))]]) ).
cnf(refute_0_147,plain,
( multiply(least_upper_bound(X_90,identity),X_89) != least_upper_bound(multiply(X_90,X_89),X_89)
| least_upper_bound(multiply(X_90,X_89),X_89) != least_upper_bound(X_89,multiply(X_90,X_89))
| multiply(least_upper_bound(X_90,identity),X_89) = least_upper_bound(X_89,multiply(X_90,X_89)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_90,identity),X_89),least_upper_bound(X_89,multiply(X_90,X_89))) ),[0],$fot(least_upper_bound(multiply(X_90,X_89),X_89))]]) ).
cnf(refute_0_148,plain,
( multiply(least_upper_bound(X_90,identity),X_89) != least_upper_bound(multiply(X_90,X_89),X_89)
| multiply(least_upper_bound(X_90,identity),X_89) = least_upper_bound(X_89,multiply(X_90,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),X_89),least_upper_bound(X_89,multiply(X_90,X_89))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(least_upper_bound(X_90,identity),X_89) = least_upper_bound(X_89,multiply(X_90,X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),X_89),least_upper_bound(multiply(X_90,X_89),X_89)) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(least_upper_bound(X_93,identity),c) = least_upper_bound(c,multiply(X_93,c)),
inference(subst,[],[refute_0_149:[bind(X_89,$fot(c)),bind(X_90,$fot(X_93))]]) ).
cnf(refute_0_151,plain,
( multiply(least_upper_bound(X_93,identity),c) != least_upper_bound(c,multiply(X_93,c))
| least_upper_bound(c,multiply(X_93,c)) = multiply(least_upper_bound(X_93,identity),c) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_93,identity),c))),bind(Y0,$fot(least_upper_bound(c,multiply(X_93,c))))]]) ).
cnf(refute_0_152,plain,
least_upper_bound(c,multiply(X_93,c)) = multiply(least_upper_bound(X_93,identity),c),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_93,identity),c),least_upper_bound(c,multiply(X_93,c))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
( greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(X_93,c)))) != b
| least_upper_bound(c,multiply(X_93,c)) != multiply(least_upper_bound(X_93,identity),c)
| greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_93,identity),c))) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(X_93,c)))),b) ),[0,1,1],$fot(multiply(least_upper_bound(X_93,identity),c))]]) ).
cnf(refute_0_154,plain,
( greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(X_93,c)))) != b
| greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_93,identity),c))) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,multiply(X_93,c)),multiply(least_upper_bound(X_93,identity),c)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_93,identity),c))) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(X_93,c)))),b) )],[refute_0_140,refute_0_154]) ).
cnf(refute_0_156,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_102,identity),c))) = b,
inference(subst,[],[refute_0_155:[bind(X_93,$fot(X_102))]]) ).
cnf(refute_0_157,plain,
least_upper_bound(identity,X_102) = least_upper_bound(X_102,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_102))]]) ).
cnf(refute_0_158,plain,
( least_upper_bound(identity,X_102) != least_upper_bound(X_102,identity)
| least_upper_bound(X_102,identity) = least_upper_bound(identity,X_102) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(identity,X_102))),bind(Y0,$fot(least_upper_bound(X_102,identity)))]]) ).
cnf(refute_0_159,plain,
least_upper_bound(X_102,identity) = least_upper_bound(identity,X_102),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_102),least_upper_bound(X_102,identity)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_102,identity),c))) != b
| least_upper_bound(X_102,identity) != least_upper_bound(identity,X_102)
| greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,X_102),c))) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_102,identity),c))),b) ),[0,1,1,0],$fot(least_upper_bound(identity,X_102))]]) ).
cnf(refute_0_161,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_102,identity),c))) != b
| greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,X_102),c))) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_102,identity),least_upper_bound(identity,X_102)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,X_102),c))) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(X_102,identity),c))),b) )],[refute_0_156,refute_0_161]) ).
cnf(refute_0_163,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),c))) = b,
inference(subst,[],[refute_0_162:[bind(X_102,$fot(multiply(b,inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_164,plain,
multiply(least_upper_bound(X_90,X_91),inverse(X_91)) = least_upper_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_91))),bind(Y,$fot(X_90)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_165,plain,
multiply(X_91,inverse(X_91)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_91))]]) ).
cnf(refute_0_166,plain,
( multiply(X_91,inverse(X_91)) != identity
| multiply(least_upper_bound(X_90,X_91),inverse(X_91)) != least_upper_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))
| multiply(least_upper_bound(X_90,X_91),inverse(X_91)) = least_upper_bound(multiply(X_90,inverse(X_91)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),least_upper_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_167,plain,
( multiply(least_upper_bound(X_90,X_91),inverse(X_91)) != least_upper_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))
| multiply(least_upper_bound(X_90,X_91),inverse(X_91)) = least_upper_bound(multiply(X_90,inverse(X_91)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_91,inverse(X_91)),identity) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(least_upper_bound(X_90,X_91),inverse(X_91)) = least_upper_bound(multiply(X_90,inverse(X_91)),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),least_upper_bound(multiply(X_90,inverse(X_91)),multiply(X_91,inverse(X_91)))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
least_upper_bound(multiply(X_90,inverse(X_91)),identity) = least_upper_bound(identity,multiply(X_90,inverse(X_91))),
inference(subst,[],[refute_0_63:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_90,inverse(X_91))))]]) ).
cnf(refute_0_170,plain,
( multiply(least_upper_bound(X_90,X_91),inverse(X_91)) != least_upper_bound(multiply(X_90,inverse(X_91)),identity)
| least_upper_bound(multiply(X_90,inverse(X_91)),identity) != least_upper_bound(identity,multiply(X_90,inverse(X_91)))
| multiply(least_upper_bound(X_90,X_91),inverse(X_91)) = least_upper_bound(identity,multiply(X_90,inverse(X_91))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),least_upper_bound(identity,multiply(X_90,inverse(X_91)))) ),[0],$fot(least_upper_bound(multiply(X_90,inverse(X_91)),identity))]]) ).
cnf(refute_0_171,plain,
( multiply(least_upper_bound(X_90,X_91),inverse(X_91)) != least_upper_bound(multiply(X_90,inverse(X_91)),identity)
| multiply(least_upper_bound(X_90,X_91),inverse(X_91)) = least_upper_bound(identity,multiply(X_90,inverse(X_91))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,inverse(X_91)),identity),least_upper_bound(identity,multiply(X_90,inverse(X_91)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
multiply(least_upper_bound(X_90,X_91),inverse(X_91)) = least_upper_bound(identity,multiply(X_90,inverse(X_91))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),least_upper_bound(multiply(X_90,inverse(X_91)),identity)) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(b)),bind(X_91,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_174,plain,
least_upper_bound(b,greatest_lower_bound(b,c)) = b,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_175,plain,
( greatest_lower_bound(a,c) != greatest_lower_bound(b,c)
| greatest_lower_bound(b,c) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(a,c))),bind(Y0,$fot(greatest_lower_bound(b,c)))]]) ).
cnf(refute_0_176,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),greatest_lower_bound(b,c)) )],[p12_1,refute_0_175]) ).
cnf(refute_0_177,plain,
( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
| least_upper_bound(b,greatest_lower_bound(b,c)) != b
| least_upper_bound(b,greatest_lower_bound(a,c)) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,c)),b) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_178,plain,
( least_upper_bound(b,greatest_lower_bound(b,c)) != b
| least_upper_bound(b,greatest_lower_bound(a,c)) = b ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
least_upper_bound(b,greatest_lower_bound(a,c)) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,c)),b) )],[refute_0_174,refute_0_178]) ).
cnf(refute_0_180,plain,
( multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
| least_upper_bound(b,greatest_lower_bound(a,c)) != b
| multiply(b,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_181,plain,
( multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
| multiply(b,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
multiply(b,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) )],[refute_0_173,refute_0_181]) ).
cnf(refute_0_183,plain,
( multiply(b,inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_184,plain,
least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),c))) != b
| least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(greatest_lower_bound(a,c)))
| greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),c))),b) ),[0,1,1,0],$fot(multiply(b,inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_186,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),c))) != b
| greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),c))),b) )],[refute_0_163,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c) = multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(inverse(greatest_lower_bound(a,c)))),bind(Z,$fot(c))]]) ).
cnf(refute_0_189,plain,
least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)) = least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)),
introduced(tautology,[refl,[$fot(least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)))]]) ).
cnf(refute_0_190,plain,
( multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c) != multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)) != least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))
| least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)) = least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)),least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) ),[1,1],$fot(multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_191,plain,
( multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c) != multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)) = least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)),least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)) = least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c),multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_188,refute_0_191]) ).
cnf(refute_0_193,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) = greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))))]]) ).
cnf(refute_0_194,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) != greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)))
| least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)) != least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))
| greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) = greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))),greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)))) ),[1,1],$fot(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_195,plain,
( least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)) != least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))
| greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) = greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))),greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) = greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c)),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) != b
| greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) != greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))
| greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))),b) ),[0],$fot(greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_198,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))) != b
| greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) = b ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))),greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(multiply(b,inverse(greatest_lower_bound(a,c))),c))),b) )],[refute_0_187,refute_0_198]) ).
cnf(refute_0_200,plain,
( greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) != b
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))) != identity
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))),identity) ),[0,1,1],$fot(b)]]) ).
cnf(refute_0_201,plain,
( least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))) != identity
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),greatest_lower_bound(b,least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))),identity) )],[refute_0_122,refute_0_201]) ).
cnf(refute_0_203,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != identity
| multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_204,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)
| multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) )],[refute_0_93,refute_0_204]) ).
cnf(refute_0_206,plain,
multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(identity)),bind(X_91,$fot(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))]]) ).
cnf(refute_0_207,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != identity
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_208,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity) )],[refute_0_202,refute_0_207]) ).
cnf(refute_0_209,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) )],[refute_0_206,refute_0_208]) ).
cnf(refute_0_210,plain,
multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_83),multiply(inverse(X_45),multiply(X_45,X_46))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_83)),bind(Z,$fot(multiply(X_45,X_46)))]]) ).
cnf(refute_0_211,plain,
( X_46 != multiply(inverse(X_45),multiply(X_45,X_46))
| multiply(inverse(X_45),multiply(X_45,X_46)) = X_46 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(inverse(X_45),multiply(X_45,X_46))))]]) ).
cnf(refute_0_212,plain,
multiply(inverse(X_45),multiply(X_45,X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_8,refute_0_211]) ).
cnf(refute_0_213,plain,
( multiply(inverse(X_45),multiply(X_45,X_46)) != X_46
| multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))) != least_upper_bound(multiply(inverse(X_45),X_83),multiply(inverse(X_45),multiply(X_45,X_46)))
| multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_83),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))),least_upper_bound(multiply(inverse(X_45),X_83),multiply(inverse(X_45),multiply(X_45,X_46)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_214,plain,
( multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))) != least_upper_bound(multiply(inverse(X_45),X_83),multiply(inverse(X_45),multiply(X_45,X_46)))
| multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_83),X_46) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),multiply(X_45,X_46)),X_46) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))) = least_upper_bound(multiply(inverse(X_45),X_83),X_46),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),least_upper_bound(X_83,multiply(X_45,X_46))),least_upper_bound(multiply(inverse(X_45),X_83),multiply(inverse(X_45),multiply(X_45,X_46)))) )],[refute_0_210,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(subst,[],[refute_0_215:[bind(X_45,$fot(b)),bind(X_46,$fot(multiply(inverse(greatest_lower_bound(a,c)),c))),bind(X_83,$fot(a))]]) ).
cnf(refute_0_217,plain,
X_48 = multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_48)),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(multiply(X,Y))),bind(X_46,$fot(X_48))]]) ).
cnf(refute_0_218,plain,
multiply(multiply(X,Y),X_48) = multiply(X,multiply(Y,X_48)),
inference(subst,[],[associativity:[bind(Z,$fot(X_48))]]) ).
cnf(refute_0_219,plain,
( X_48 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_48))
| multiply(multiply(X,Y),X_48) != multiply(X,multiply(Y,X_48))
| X_48 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(X_48,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_48))) ),[1,1],$fot(multiply(X,multiply(Y,X_48)))]]) ).
cnf(refute_0_220,plain,
( X_48 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_48))
| X_48 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_48))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_48),multiply(X,multiply(Y,X_48))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
X_48 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_48))),
inference(resolve,[$cnf( $equal(X_48,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_48))) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
inverse(X_69) = multiply(inverse(multiply(X_68,X_69)),multiply(X_68,multiply(X_69,inverse(X_69)))),
inference(subst,[],[refute_0_221:[bind(X,$fot(X_68)),bind(Y,$fot(X_69)),bind(X_48,$fot(inverse(X_69)))]]) ).
cnf(refute_0_223,plain,
multiply(X_69,inverse(X_69)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_69))]]) ).
cnf(refute_0_224,plain,
( multiply(X_69,inverse(X_69)) != identity
| inverse(X_69) != multiply(inverse(multiply(X_68,X_69)),multiply(X_68,multiply(X_69,inverse(X_69))))
| inverse(X_69) = multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_69),multiply(inverse(multiply(X_68,X_69)),multiply(X_68,multiply(X_69,inverse(X_69))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_225,plain,
( inverse(X_69) != multiply(inverse(multiply(X_68,X_69)),multiply(X_68,multiply(X_69,inverse(X_69))))
| inverse(X_69) = multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_69,inverse(X_69)),identity) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
inverse(X_69) = multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)),
inference(resolve,[$cnf( $equal(inverse(X_69),multiply(inverse(multiply(X_68,X_69)),multiply(X_68,multiply(X_69,inverse(X_69))))) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
multiply(X_68,identity) = X_68,
inference(subst,[],[refute_0_51:[bind(X_48,$fot(X_68))]]) ).
cnf(refute_0_228,plain,
multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) = multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)))]]) ).
cnf(refute_0_229,plain,
( multiply(X_68,identity) != X_68
| multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) != multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity))
| multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) = multiply(inverse(multiply(X_68,X_69)),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)),multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity))) ),[1,1],$fot(X_68)]]) ).
cnf(refute_0_230,plain,
( multiply(X_68,identity) != X_68
| multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) = multiply(inverse(multiply(X_68,X_69)),X_68) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)),multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) = multiply(inverse(multiply(X_68,X_69)),X_68),
inference(resolve,[$cnf( $equal(multiply(X_68,identity),X_68) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
( multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)) != multiply(inverse(multiply(X_68,X_69)),X_68)
| inverse(X_69) != multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity))
| inverse(X_69) = multiply(inverse(multiply(X_68,X_69)),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_69),multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity))) ),[1],$fot(multiply(inverse(multiply(X_68,X_69)),X_68))]]) ).
cnf(refute_0_233,plain,
( inverse(X_69) != multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity))
| inverse(X_69) = multiply(inverse(multiply(X_68,X_69)),X_68) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity)),multiply(inverse(multiply(X_68,X_69)),X_68)) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
inverse(X_69) = multiply(inverse(multiply(X_68,X_69)),X_68),
inference(resolve,[$cnf( $equal(inverse(X_69),multiply(inverse(multiply(X_68,X_69)),multiply(X_68,identity))) )],[refute_0_226,refute_0_233]) ).
cnf(refute_0_235,plain,
inverse(multiply(X_45,X_46)) = multiply(inverse(multiply(inverse(X_45),multiply(X_45,X_46))),inverse(X_45)),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(X_45))),bind(X_69,$fot(multiply(X_45,X_46)))]]) ).
cnf(refute_0_236,plain,
( multiply(inverse(X_45),multiply(X_45,X_46)) != X_46
| inverse(multiply(X_45,X_46)) != multiply(inverse(multiply(inverse(X_45),multiply(X_45,X_46))),inverse(X_45))
| inverse(multiply(X_45,X_46)) = multiply(inverse(X_46),inverse(X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_45,X_46)),multiply(inverse(multiply(inverse(X_45),multiply(X_45,X_46))),inverse(X_45))) ),[1,0,0],$fot(X_46)]]) ).
cnf(refute_0_237,plain,
( inverse(multiply(X_45,X_46)) != multiply(inverse(multiply(inverse(X_45),multiply(X_45,X_46))),inverse(X_45))
| inverse(multiply(X_45,X_46)) = multiply(inverse(X_46),inverse(X_45)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),multiply(X_45,X_46)),X_46) )],[refute_0_212,refute_0_236]) ).
cnf(refute_0_238,plain,
inverse(multiply(X_45,X_46)) = multiply(inverse(X_46),inverse(X_45)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_45,X_46)),multiply(inverse(multiply(inverse(X_45),multiply(X_45,X_46))),inverse(X_45))) )],[refute_0_235,refute_0_237]) ).
cnf(refute_0_239,plain,
inverse(multiply(inverse(X_50),X_74)) = multiply(inverse(X_74),inverse(inverse(X_50))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(inverse(X_50))),bind(X_46,$fot(X_74))]]) ).
cnf(refute_0_240,plain,
( inverse(multiply(inverse(X_50),X_74)) != multiply(inverse(X_74),inverse(inverse(X_50)))
| inverse(inverse(X_50)) != X_50
| inverse(multiply(inverse(X_50),X_74)) = multiply(inverse(X_74),X_50) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_50),X_74)),multiply(inverse(X_74),inverse(inverse(X_50)))) ),[1,1],$fot(X_50)]]) ).
cnf(refute_0_241,plain,
( inverse(multiply(inverse(X_50),X_74)) != multiply(inverse(X_74),inverse(inverse(X_50)))
| inverse(multiply(inverse(X_50),X_74)) = multiply(inverse(X_74),X_50) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_50)),X_50) )],[refute_0_88,refute_0_240]) ).
cnf(refute_0_242,plain,
inverse(multiply(inverse(X_50),X_74)) = multiply(inverse(X_74),X_50),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_50),X_74)),multiply(inverse(X_74),inverse(inverse(X_50)))) )],[refute_0_239,refute_0_241]) ).
cnf(refute_0_243,plain,
inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),bind(X_74,$fot(b))]]) ).
cnf(refute_0_244,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_245,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_17,refute_0_244]) ).
cnf(refute_0_246,plain,
( multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))
| inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),bind(Y0,$fot(multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))),bind(Z0,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_247,plain,
( multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(resolve,[$cnf( $equal(multiply(inverse(b),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_216,refute_0_247]) ).
cnf(refute_0_249,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))]]) ).
cnf(refute_0_250,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))
| inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),bind(Y0,$fot(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),bind(Z0,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_251,plain,
( inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) ),[0],$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_254,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))]]) ).
cnf(refute_0_256,plain,
( inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) ),[1,1],$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_257,plain,
( inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_248,refute_0_257]) ).
cnf(refute_0_259,plain,
multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))]]) ).
cnf(refute_0_260,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_261,plain,
( greatest_lower_bound(X,least_upper_bound(X,Y)) != X
| greatest_lower_bound(X,least_upper_bound(Y,X)) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_260]) ).
cnf(refute_0_262,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X) )],[glb_absorbtion,refute_0_261]) ).
cnf(refute_0_263,plain,
greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_262:[bind(X,$fot(least_upper_bound(X_18,Y)))]]) ).
cnf(refute_0_264,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_265,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_266,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_17:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_267,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$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_269,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( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_264,refute_0_269]) ).
cnf(refute_0_271,plain,
least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) = least_upper_bound(X_13,Y),
inference(subst,[],[refute_0_270:[bind(X_10,$fot(least_upper_bound(X_13,Y))),bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_272,plain,
greatest_lower_bound(X_13,least_upper_bound(X_13,Y)) = X_13,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_273,plain,
( greatest_lower_bound(X_13,least_upper_bound(X_13,Y)) != X_13
| least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))),least_upper_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_274,plain,
( least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,least_upper_bound(X_13,Y)),X_13) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))),least_upper_bound(X_13,Y)) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,least_upper_bound(Y,X_13)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_277,plain,
( least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,least_upper_bound(Y,X_13))
| least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,Y)) ),[0],$fot(least_upper_bound(X_13,least_upper_bound(Y,X_13)))]]) ).
cnf(refute_0_278,plain,
( least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,Y)
| least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,least_upper_bound(Y,X_13))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,Y)) )],[refute_0_275,refute_0_278]) ).
cnf(refute_0_280,plain,
least_upper_bound(Y,least_upper_bound(X_18,Y)) = least_upper_bound(Y,X_18),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_18)),bind(X_13,$fot(Y))]]) ).
cnf(refute_0_281,plain,
( greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))) != least_upper_bound(X_18,Y)
| least_upper_bound(Y,least_upper_bound(X_18,Y)) != least_upper_bound(Y,X_18)
| greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y) ),
introduced(tautology,[equality,[$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_282,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( $equal(least_upper_bound(Y,least_upper_bound(X_18,Y)),least_upper_bound(Y,X_18)) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_18,Y),least_upper_bound(Y,least_upper_bound(X_18,Y))),least_upper_bound(X_18,Y)) )],[refute_0_263,refute_0_282]) ).
cnf(refute_0_284,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_283:[bind(Y,$fot(multiply(X,Y))),bind(X_18,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_285,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_286,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_285]) ).
cnf(refute_0_287,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_288,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_284,refute_0_288]) ).
cnf(refute_0_290,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_283:[bind(Y,$fot(Z)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_291,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_292,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_293,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_296,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_295]) ).
cnf(refute_0_297,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
inference(subst,[],[refute_0_296:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_298,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_299,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_294,refute_0_299]) ).
cnf(refute_0_301,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_286:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_302,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_303,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_304,plain,
( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_301,refute_0_304]) ).
cnf(refute_0_306,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_307,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_300,refute_0_307]) ).
cnf(refute_0_309,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_106:[bind(X,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_310,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_311,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_308,refute_0_311]) ).
cnf(refute_0_313,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_314,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_316,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_301,refute_0_315]) ).
cnf(refute_0_317,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_314,refute_0_316]) ).
cnf(refute_0_318,plain,
multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_289,refute_0_317]) ).
cnf(refute_0_319,plain,
( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_320,plain,
multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)) = multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),
inference(subst,[],[refute_0_320:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))]]) ).
cnf(refute_0_322,plain,
( multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)) != multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))]]) ).
cnf(refute_0_323,plain,
( multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)),multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) )],[refute_0_259,refute_0_323]) ).
cnf(refute_0_325,plain,
multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_326,plain,
X_82 = multiply(X_82,identity),
inference(subst,[],[refute_0_49:[bind(X_48,$fot(X_82))]]) ).
cnf(refute_0_327,plain,
( X_82 != multiply(X_82,identity)
| multiply(X_82,identity) = X_82 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_82)),bind(Y0,$fot(multiply(X_82,identity)))]]) ).
cnf(refute_0_328,plain,
multiply(X_82,identity) = X_82,
inference(resolve,[$cnf( $equal(X_82,multiply(X_82,identity)) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
( multiply(X_82,identity) != X_82
| multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))
| multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),X_82) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))) ),[1,1],$fot(X_82)]]) ).
cnf(refute_0_330,plain,
( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))
| multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),X_82) ),
inference(resolve,[$cnf( $equal(multiply(X_82,identity),X_82) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),X_82),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))) )],[refute_0_325,refute_0_330]) ).
cnf(refute_0_332,plain,
least_upper_bound(multiply(X_82,X_83),X_82) = least_upper_bound(X_82,multiply(X_82,X_83)),
inference(subst,[],[refute_0_63:[bind(X,$fot(X_82)),bind(Y,$fot(multiply(X_82,X_83)))]]) ).
cnf(refute_0_333,plain,
( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),X_82)
| least_upper_bound(multiply(X_82,X_83),X_82) != least_upper_bound(X_82,multiply(X_82,X_83))
| multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(X_82,multiply(X_82,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(X_82,multiply(X_82,X_83))) ),[0],$fot(least_upper_bound(multiply(X_82,X_83),X_82))]]) ).
cnf(refute_0_334,plain,
( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),X_82)
| multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(X_82,multiply(X_82,X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),X_82),least_upper_bound(X_82,multiply(X_82,X_83))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(X_82,multiply(X_82,X_83)),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(multiply(X_82,X_83),X_82)) )],[refute_0_331,refute_0_334]) ).
cnf(refute_0_336,plain,
( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(X_82,multiply(X_82,X_83))
| least_upper_bound(X_82,multiply(X_82,X_83)) = multiply(X_82,least_upper_bound(X_83,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_82,least_upper_bound(X_83,identity)))),bind(Y0,$fot(least_upper_bound(X_82,multiply(X_82,X_83))))]]) ).
cnf(refute_0_337,plain,
least_upper_bound(X_82,multiply(X_82,X_83)) = multiply(X_82,least_upper_bound(X_83,identity)),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(X_82,multiply(X_82,X_83))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)),
inference(subst,[],[refute_0_337:[bind(X_82,$fot(identity)),bind(X_83,$fot(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))]]) ).
cnf(refute_0_339,plain,
( multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))]]) ).
cnf(refute_0_340,plain,
( multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),identity)),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) )],[refute_0_324,refute_0_340]) ).
cnf(refute_0_342,plain,
( least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_343,plain,
( least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_258,refute_0_343]) ).
cnf(refute_0_345,plain,
( least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))]]) ).
cnf(refute_0_346,plain,
( least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) )],[refute_0_254,refute_0_346]) ).
cnf(refute_0_348,plain,
least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) )],[refute_0_209,refute_0_347]) ).
cnf(refute_0_349,plain,
( least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) != least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_350,plain,
least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b),
inference(subst,[],[left_identity:[bind(X,$fot(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))]]) ).
cnf(refute_0_352,plain,
inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))]]) ).
cnf(refute_0_353,plain,
( multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)
| inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))
| inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) ),[1,0],$fot(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))]]) ).
cnf(refute_0_354,plain,
( multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)
| inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),
inference(resolve,[$cnf( $equal(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) )],[refute_0_351,refute_0_354]) ).
cnf(refute_0_356,plain,
( inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))
| inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),bind(Y0,$fot(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),bind(Z0,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_357,plain,
( inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_248,refute_0_357]) ).
cnf(refute_0_359,plain,
least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))]]) ).
cnf(refute_0_360,plain,
( inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))
| least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) ),[1,1],$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_361,plain,
( inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_358,refute_0_361]) ).
cnf(refute_0_363,plain,
( least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))),bind(Z0,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_364,plain,
( least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_350,refute_0_364]) ).
cnf(refute_0_366,plain,
inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))))]]) ).
cnf(refute_0_367,plain,
( inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))
| least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))) ),[1,0],$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_368,plain,
( least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_365,refute_0_368]) ).
cnf(refute_0_370,plain,
multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))) = multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))),
inference(subst,[],[associativity:[bind(Z,$fot(inverse(least_upper_bound(multiply(X,Y),identity))))]]) ).
cnf(refute_0_371,plain,
inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))) = multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(least_upper_bound(X_103,identity))),bind(X_46,$fot(inverse(X_103)))]]) ).
cnf(refute_0_372,plain,
multiply(least_upper_bound(X_93,identity),inverse(X_93)) = least_upper_bound(inverse(X_93),multiply(X_93,inverse(X_93))),
inference(subst,[],[refute_0_149:[bind(X_89,$fot(inverse(X_93))),bind(X_90,$fot(X_93))]]) ).
cnf(refute_0_373,plain,
multiply(X_93,inverse(X_93)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_93))]]) ).
cnf(refute_0_374,plain,
( multiply(X_93,inverse(X_93)) != identity
| multiply(least_upper_bound(X_93,identity),inverse(X_93)) != least_upper_bound(inverse(X_93),multiply(X_93,inverse(X_93)))
| multiply(least_upper_bound(X_93,identity),inverse(X_93)) = least_upper_bound(inverse(X_93),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_93,identity),inverse(X_93)),least_upper_bound(inverse(X_93),multiply(X_93,inverse(X_93)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_375,plain,
( multiply(least_upper_bound(X_93,identity),inverse(X_93)) != least_upper_bound(inverse(X_93),multiply(X_93,inverse(X_93)))
| multiply(least_upper_bound(X_93,identity),inverse(X_93)) = least_upper_bound(inverse(X_93),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_93,inverse(X_93)),identity) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
multiply(least_upper_bound(X_93,identity),inverse(X_93)) = least_upper_bound(inverse(X_93),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_93,identity),inverse(X_93)),least_upper_bound(inverse(X_93),multiply(X_93,inverse(X_93)))) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
least_upper_bound(inverse(X_93),identity) = least_upper_bound(identity,inverse(X_93)),
inference(subst,[],[refute_0_63:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_93)))]]) ).
cnf(refute_0_378,plain,
( multiply(least_upper_bound(X_93,identity),inverse(X_93)) != least_upper_bound(inverse(X_93),identity)
| least_upper_bound(inverse(X_93),identity) != least_upper_bound(identity,inverse(X_93))
| multiply(least_upper_bound(X_93,identity),inverse(X_93)) = least_upper_bound(identity,inverse(X_93)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_93,identity),inverse(X_93)),least_upper_bound(identity,inverse(X_93))) ),[0],$fot(least_upper_bound(inverse(X_93),identity))]]) ).
cnf(refute_0_379,plain,
( multiply(least_upper_bound(X_93,identity),inverse(X_93)) != least_upper_bound(inverse(X_93),identity)
| multiply(least_upper_bound(X_93,identity),inverse(X_93)) = least_upper_bound(identity,inverse(X_93)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_93),identity),least_upper_bound(identity,inverse(X_93))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
multiply(least_upper_bound(X_93,identity),inverse(X_93)) = least_upper_bound(identity,inverse(X_93)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_93,identity),inverse(X_93)),least_upper_bound(inverse(X_93),identity)) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
multiply(least_upper_bound(X_103,identity),inverse(X_103)) = least_upper_bound(identity,inverse(X_103)),
inference(subst,[],[refute_0_380:[bind(X_93,$fot(X_103))]]) ).
cnf(refute_0_382,plain,
( multiply(least_upper_bound(X_103,identity),inverse(X_103)) != least_upper_bound(identity,inverse(X_103))
| inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))) != multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))
| inverse(least_upper_bound(identity,inverse(X_103))) = multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_103)))]]) ).
cnf(refute_0_383,plain,
( inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))) != multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))
| inverse(least_upper_bound(identity,inverse(X_103))) = multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_103,identity),inverse(X_103)),least_upper_bound(identity,inverse(X_103))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
inverse(least_upper_bound(identity,inverse(X_103))) = multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))) )],[refute_0_371,refute_0_383]) ).
cnf(refute_0_385,plain,
inverse(multiply(X_73,inverse(X_50))) = multiply(inverse(inverse(X_50)),inverse(X_73)),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(X_73)),bind(X_46,$fot(inverse(X_50)))]]) ).
cnf(refute_0_386,plain,
( inverse(multiply(X_73,inverse(X_50))) != multiply(inverse(inverse(X_50)),inverse(X_73))
| inverse(inverse(X_50)) != X_50
| inverse(multiply(X_73,inverse(X_50))) = multiply(X_50,inverse(X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_73,inverse(X_50))),multiply(inverse(inverse(X_50)),inverse(X_73))) ),[1,0],$fot(X_50)]]) ).
cnf(refute_0_387,plain,
( inverse(multiply(X_73,inverse(X_50))) != multiply(inverse(inverse(X_50)),inverse(X_73))
| inverse(multiply(X_73,inverse(X_50))) = multiply(X_50,inverse(X_73)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_50)),X_50) )],[refute_0_88,refute_0_386]) ).
cnf(refute_0_388,plain,
inverse(multiply(X_73,inverse(X_50))) = multiply(X_50,inverse(X_73)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_73,inverse(X_50))),multiply(inverse(inverse(X_50)),inverse(X_73))) )],[refute_0_385,refute_0_387]) ).
cnf(refute_0_389,plain,
inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))) = multiply(X_103,inverse(least_upper_bound(X_103,identity))),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(X_103)),bind(X_73,$fot(least_upper_bound(X_103,identity)))]]) ).
cnf(refute_0_390,plain,
( inverse(multiply(X_45,X_46)) != multiply(inverse(X_46),inverse(X_45))
| multiply(inverse(X_46),inverse(X_45)) = inverse(multiply(X_45,X_46)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(multiply(X_45,X_46)))),bind(Y0,$fot(multiply(inverse(X_46),inverse(X_45))))]]) ).
cnf(refute_0_391,plain,
multiply(inverse(X_46),inverse(X_45)) = inverse(multiply(X_45,X_46)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_45,X_46)),multiply(inverse(X_46),inverse(X_45))) )],[refute_0_238,refute_0_390]) ).
cnf(refute_0_392,plain,
multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) = inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(least_upper_bound(X_103,identity))),bind(X_46,$fot(inverse(X_103)))]]) ).
cnf(refute_0_393,plain,
( multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) != inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103)))
| inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))) != multiply(X_103,inverse(least_upper_bound(X_103,identity)))
| multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) = multiply(X_103,inverse(least_upper_bound(X_103,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))))),bind(Z0,$fot(multiply(X_103,inverse(least_upper_bound(X_103,identity)))))]]) ).
cnf(refute_0_394,plain,
( inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))) != multiply(X_103,inverse(least_upper_bound(X_103,identity)))
| multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) = multiply(X_103,inverse(least_upper_bound(X_103,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))),inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) = multiply(X_103,inverse(least_upper_bound(X_103,identity))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),multiply(X_103,inverse(least_upper_bound(X_103,identity)))) )],[refute_0_389,refute_0_394]) ).
cnf(refute_0_396,plain,
( multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))) != multiply(X_103,inverse(least_upper_bound(X_103,identity)))
| inverse(least_upper_bound(identity,inverse(X_103))) != multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))
| inverse(least_upper_bound(identity,inverse(X_103))) = multiply(X_103,inverse(least_upper_bound(X_103,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_103))),multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))) ),[1],$fot(multiply(X_103,inverse(least_upper_bound(X_103,identity))))]]) ).
cnf(refute_0_397,plain,
( inverse(least_upper_bound(identity,inverse(X_103))) != multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))
| inverse(least_upper_bound(identity,inverse(X_103))) = multiply(X_103,inverse(least_upper_bound(X_103,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity))),multiply(X_103,inverse(least_upper_bound(X_103,identity)))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
inverse(least_upper_bound(identity,inverse(X_103))) = multiply(X_103,inverse(least_upper_bound(X_103,identity))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_103))),multiply(inverse(inverse(X_103)),inverse(least_upper_bound(X_103,identity)))) )],[refute_0_384,refute_0_397]) ).
cnf(refute_0_399,plain,
inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))),
inference(subst,[],[refute_0_398:[bind(X_103,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_400,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) != multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity)))
| multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))) = inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))))),bind(Y0,$fot(multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity)))))]]) ).
cnf(refute_0_401,plain,
multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))) = inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity)))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
( multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))) != multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))
| multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))) != inverse(least_upper_bound(identity,inverse(multiply(X,Y))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))),multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))) ),[0],$fot(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_403,plain,
( multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))) != multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))),inverse(least_upper_bound(identity,inverse(multiply(X,Y))))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(least_upper_bound(multiply(X,Y),identity))),multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))) )],[refute_0_370,refute_0_403]) ).
cnf(refute_0_405,plain,
X_46 = multiply(inverse(least_upper_bound(X_95,inverse(X_46))),multiply(least_upper_bound(X_95,inverse(X_46)),X_46)),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(least_upper_bound(X_95,inverse(X_46))))]]) ).
cnf(refute_0_406,plain,
multiply(least_upper_bound(X_90,inverse(X_89)),X_89) = least_upper_bound(multiply(X_90,X_89),multiply(inverse(X_89),X_89)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_89)),bind(Y,$fot(X_90)),bind(Z,$fot(inverse(X_89)))]]) ).
cnf(refute_0_407,plain,
( multiply(inverse(X_89),X_89) != identity
| multiply(least_upper_bound(X_90,inverse(X_89)),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(inverse(X_89),X_89))
| multiply(least_upper_bound(X_90,inverse(X_89)),X_89) = least_upper_bound(multiply(X_90,X_89),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(X_89)),X_89),least_upper_bound(multiply(X_90,X_89),multiply(inverse(X_89),X_89))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_408,plain,
( multiply(least_upper_bound(X_90,inverse(X_89)),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(inverse(X_89),X_89))
| multiply(least_upper_bound(X_90,inverse(X_89)),X_89) = least_upper_bound(multiply(X_90,X_89),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),X_89),identity) )],[refute_0_95,refute_0_407]) ).
cnf(refute_0_409,plain,
multiply(least_upper_bound(X_90,inverse(X_89)),X_89) = least_upper_bound(multiply(X_90,X_89),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(X_89)),X_89),least_upper_bound(multiply(X_90,X_89),multiply(inverse(X_89),X_89))) )],[refute_0_406,refute_0_408]) ).
cnf(refute_0_410,plain,
least_upper_bound(multiply(X_90,X_89),identity) = least_upper_bound(identity,multiply(X_90,X_89)),
inference(subst,[],[refute_0_63:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_90,X_89)))]]) ).
cnf(refute_0_411,plain,
( multiply(least_upper_bound(X_90,inverse(X_89)),X_89) != least_upper_bound(multiply(X_90,X_89),identity)
| least_upper_bound(multiply(X_90,X_89),identity) != least_upper_bound(identity,multiply(X_90,X_89))
| multiply(least_upper_bound(X_90,inverse(X_89)),X_89) = least_upper_bound(identity,multiply(X_90,X_89)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_90,inverse(X_89)),X_89),least_upper_bound(identity,multiply(X_90,X_89))) ),[0],$fot(least_upper_bound(multiply(X_90,X_89),identity))]]) ).
cnf(refute_0_412,plain,
( multiply(least_upper_bound(X_90,inverse(X_89)),X_89) != least_upper_bound(multiply(X_90,X_89),identity)
| multiply(least_upper_bound(X_90,inverse(X_89)),X_89) = least_upper_bound(identity,multiply(X_90,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),identity),least_upper_bound(identity,multiply(X_90,X_89))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
multiply(least_upper_bound(X_90,inverse(X_89)),X_89) = least_upper_bound(identity,multiply(X_90,X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(X_89)),X_89),least_upper_bound(multiply(X_90,X_89),identity)) )],[refute_0_409,refute_0_412]) ).
cnf(refute_0_414,plain,
multiply(least_upper_bound(X_95,inverse(X_46)),X_46) = least_upper_bound(identity,multiply(X_95,X_46)),
inference(subst,[],[refute_0_413:[bind(X_89,$fot(X_46)),bind(X_90,$fot(X_95))]]) ).
cnf(refute_0_415,plain,
( X_46 != multiply(inverse(least_upper_bound(X_95,inverse(X_46))),multiply(least_upper_bound(X_95,inverse(X_46)),X_46))
| multiply(least_upper_bound(X_95,inverse(X_46)),X_46) != least_upper_bound(identity,multiply(X_95,X_46))
| X_46 = multiply(inverse(least_upper_bound(X_95,inverse(X_46))),least_upper_bound(identity,multiply(X_95,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,multiply(inverse(least_upper_bound(X_95,inverse(X_46))),multiply(least_upper_bound(X_95,inverse(X_46)),X_46))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_95,X_46)))]]) ).
cnf(refute_0_416,plain,
( X_46 != multiply(inverse(least_upper_bound(X_95,inverse(X_46))),multiply(least_upper_bound(X_95,inverse(X_46)),X_46))
| X_46 = multiply(inverse(least_upper_bound(X_95,inverse(X_46))),least_upper_bound(identity,multiply(X_95,X_46))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_95,inverse(X_46)),X_46),least_upper_bound(identity,multiply(X_95,X_46))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
X_46 = multiply(inverse(least_upper_bound(X_95,inverse(X_46))),least_upper_bound(identity,multiply(X_95,X_46))),
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(least_upper_bound(X_95,inverse(X_46))),multiply(least_upper_bound(X_95,inverse(X_46)),X_46))) )],[refute_0_405,refute_0_416]) ).
cnf(refute_0_418,plain,
inverse(least_upper_bound(X_98,X_207)) = multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207))))),
inference(subst,[],[refute_0_417:[bind(X_46,$fot(inverse(least_upper_bound(X_98,X_207)))),bind(X_95,$fot(X_207))]]) ).
cnf(refute_0_419,plain,
multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),
inference(subst,[],[refute_0_74:[bind(X_86,$fot(least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_420,plain,
least_upper_bound(X_19,least_upper_bound(X_18,X_19)) = least_upper_bound(X_19,X_18),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_18)),bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_421,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_422,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_17:[bind(X0,$fot(least_upper_bound(X_19,X_18))),bind(Y0,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_423,plain,
least_upper_bound(X_18,X_19) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,X_18),least_upper_bound(X_18,X_19)) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
( least_upper_bound(X_18,X_19) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,X_18)
| least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18) ),
introduced(tautology,[equality,[$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_425,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( $equal(least_upper_bound(X_18,X_19),least_upper_bound(X_19,X_18)) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
least_upper_bound(X_19,least_upper_bound(X_19,X_18)) = least_upper_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,X_18)) )],[refute_0_420,refute_0_425]) ).
cnf(refute_0_427,plain,
least_upper_bound(identity,least_upper_bound(identity,X_18)) = least_upper_bound(identity,X_18),
inference(subst,[],[refute_0_426:[bind(X_19,$fot(identity))]]) ).
cnf(refute_0_428,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| least_upper_bound(identity,least_upper_bound(identity,X_18)) != least_upper_bound(identity,X_18)
| multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) ),[0,1],$fot(least_upper_bound(identity,X_18))]]) ).
cnf(refute_0_429,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,least_upper_bound(identity,X_18))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) )],[refute_0_419,refute_0_429]) ).
cnf(refute_0_431,plain,
multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(identity,X_18)))]]) ).
cnf(refute_0_432,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) != identity
| multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_433,plain,
( multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)),identity) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_18))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_18)),least_upper_bound(identity,X_18)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_18)))) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99))))),
inference(subst,[],[refute_0_434:[bind(X_18,$fot(multiply(X_98,inverse(X_99))))]]) ).
cnf(refute_0_436,plain,
multiply(least_upper_bound(X_98,X_99),inverse(X_99)) = least_upper_bound(identity,multiply(X_98,inverse(X_99))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(X_98)),bind(X_91,$fot(X_99))]]) ).
cnf(refute_0_437,plain,
( multiply(least_upper_bound(X_98,X_99),inverse(X_99)) != least_upper_bound(identity,multiply(X_98,inverse(X_99)))
| least_upper_bound(identity,multiply(X_98,inverse(X_99))) = multiply(least_upper_bound(X_98,X_99),inverse(X_99)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_98,inverse(X_99)))))]]) ).
cnf(refute_0_438,plain,
least_upper_bound(identity,multiply(X_98,inverse(X_99))) = multiply(least_upper_bound(X_98,X_99),inverse(X_99)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_98,X_99),inverse(X_99)),least_upper_bound(identity,multiply(X_98,inverse(X_99)))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))))
| least_upper_bound(identity,multiply(X_98,inverse(X_99))) != multiply(least_upper_bound(X_98,X_99),inverse(X_99))
| identity = least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))))) ),[1,1,0],$fot(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))]]) ).
cnf(refute_0_440,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))))
| identity = least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_98,inverse(X_99))),multiply(least_upper_bound(X_98,X_99),inverse(X_99))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
identity = least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))))) )],[refute_0_435,refute_0_440]) ).
cnf(refute_0_442,plain,
inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) = multiply(X_99,inverse(least_upper_bound(X_98,X_99))),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(X_99)),bind(X_73,$fot(least_upper_bound(X_98,X_99)))]]) ).
cnf(refute_0_443,plain,
least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))))]]) ).
cnf(refute_0_444,plain,
( inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) != multiply(X_99,inverse(least_upper_bound(X_98,X_99)))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) != least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) = least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))),least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))))) ),[1,1],$fot(multiply(X_99,inverse(least_upper_bound(X_98,X_99))))]]) ).
cnf(refute_0_445,plain,
( inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) != multiply(X_99,inverse(least_upper_bound(X_98,X_99)))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) = least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))),least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) = least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99)))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))),multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) )],[refute_0_442,refute_0_445]) ).
cnf(refute_0_447,plain,
( identity != least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))))
| least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) != least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99))))
| identity = least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99))))) ),[0],$fot(least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))))]]) ).
cnf(refute_0_448,plain,
( identity != least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))))
| identity = least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))),least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99))))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
identity = least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(X_98,X_99)))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))))) )],[refute_0_441,refute_0_448]) ).
cnf(refute_0_450,plain,
identity = least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))),
inference(subst,[],[refute_0_449:[bind(X_99,$fot(X_207))]]) ).
cnf(refute_0_451,plain,
( identity != least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207))))
| least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207))))))]]) ).
cnf(refute_0_452,plain,
least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207))))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
( inverse(least_upper_bound(X_98,X_207)) != multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))))
| least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))) != identity
| inverse(least_upper_bound(X_98,X_207)) = multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_98,X_207)),multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_454,plain,
( inverse(least_upper_bound(X_98,X_207)) != multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))))
| inverse(least_upper_bound(X_98,X_207)) = multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))),identity) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
inverse(least_upper_bound(X_98,X_207)) = multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_98,X_207)),multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),least_upper_bound(identity,multiply(X_207,inverse(least_upper_bound(X_98,X_207)))))) )],[refute_0_418,refute_0_454]) ).
cnf(refute_0_456,plain,
least_upper_bound(X_207,least_upper_bound(X_98,X_207)) = least_upper_bound(X_207,X_98),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_98)),bind(X_13,$fot(X_207))]]) ).
cnf(refute_0_457,plain,
inverse(inverse(least_upper_bound(X_98,X_207))) = least_upper_bound(X_98,X_207),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(least_upper_bound(X_98,X_207)))]]) ).
cnf(refute_0_458,plain,
least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) = least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))]]) ).
cnf(refute_0_459,plain,
( inverse(inverse(least_upper_bound(X_98,X_207))) != least_upper_bound(X_98,X_207)
| least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) != least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))
| least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) = least_upper_bound(X_207,least_upper_bound(X_98,X_207)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))),least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) ),[1,1],$fot(least_upper_bound(X_98,X_207))]]) ).
cnf(refute_0_460,plain,
( inverse(inverse(least_upper_bound(X_98,X_207))) != least_upper_bound(X_98,X_207)
| least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) = least_upper_bound(X_207,least_upper_bound(X_98,X_207)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))),least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) = least_upper_bound(X_207,least_upper_bound(X_98,X_207)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_98,X_207))),least_upper_bound(X_98,X_207)) )],[refute_0_457,refute_0_460]) ).
cnf(refute_0_462,plain,
( least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) != least_upper_bound(X_207,least_upper_bound(X_98,X_207))
| least_upper_bound(X_207,least_upper_bound(X_98,X_207)) != least_upper_bound(X_207,X_98)
| least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) = least_upper_bound(X_207,X_98) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))),bind(Y0,$fot(least_upper_bound(X_207,least_upper_bound(X_98,X_207)))),bind(Z0,$fot(least_upper_bound(X_207,X_98)))]]) ).
cnf(refute_0_463,plain,
( least_upper_bound(X_207,least_upper_bound(X_98,X_207)) != least_upper_bound(X_207,X_98)
| least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) = least_upper_bound(X_207,X_98) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))),least_upper_bound(X_207,least_upper_bound(X_98,X_207))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) = least_upper_bound(X_207,X_98),
inference(resolve,[$cnf( $equal(least_upper_bound(X_207,least_upper_bound(X_98,X_207)),least_upper_bound(X_207,X_98)) )],[refute_0_456,refute_0_463]) ).
cnf(refute_0_465,plain,
inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) = inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))))]]) ).
cnf(refute_0_466,plain,
( inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) != inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))
| least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) != least_upper_bound(X_207,X_98)
| inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) = inverse(least_upper_bound(X_207,X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))) ),[1,0],$fot(least_upper_bound(X_207,X_98))]]) ).
cnf(refute_0_467,plain,
( least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))) != least_upper_bound(X_207,X_98)
| inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) = inverse(least_upper_bound(X_207,X_98)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) = inverse(least_upper_bound(X_207,X_98)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))),least_upper_bound(X_207,X_98)) )],[refute_0_464,refute_0_467]) ).
cnf(refute_0_469,plain,
multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) = inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))))]]) ).
cnf(refute_0_470,plain,
( multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) != inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))
| inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) != inverse(least_upper_bound(X_207,X_98))
| multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) = inverse(least_upper_bound(X_207,X_98)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity))),bind(Y0,$fot(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))))),bind(Z0,$fot(inverse(least_upper_bound(X_207,X_98))))]]) ).
cnf(refute_0_471,plain,
( inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))) != inverse(least_upper_bound(X_207,X_98))
| multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) = inverse(least_upper_bound(X_207,X_98)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity),inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207)))))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) = inverse(least_upper_bound(X_207,X_98)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),inverse(least_upper_bound(X_207,X_98))) )],[refute_0_468,refute_0_471]) ).
cnf(refute_0_473,plain,
( multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity) != inverse(least_upper_bound(X_207,X_98))
| inverse(least_upper_bound(X_98,X_207)) != multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity)
| inverse(least_upper_bound(X_98,X_207)) = inverse(least_upper_bound(X_207,X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_98,X_207)),multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity)) ),[1],$fot(inverse(least_upper_bound(X_207,X_98)))]]) ).
cnf(refute_0_474,plain,
( inverse(least_upper_bound(X_98,X_207)) != multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity)
| inverse(least_upper_bound(X_98,X_207)) = inverse(least_upper_bound(X_207,X_98)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity),inverse(least_upper_bound(X_207,X_98))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
inverse(least_upper_bound(X_98,X_207)) = inverse(least_upper_bound(X_207,X_98)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_98,X_207)),multiply(inverse(least_upper_bound(X_207,inverse(inverse(least_upper_bound(X_98,X_207))))),identity)) )],[refute_0_455,refute_0_474]) ).
cnf(refute_0_476,plain,
( inverse(least_upper_bound(X_98,X_207)) != inverse(least_upper_bound(X_207,X_98))
| inverse(least_upper_bound(X_207,X_98)) = inverse(least_upper_bound(X_98,X_207)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_98,X_207)))),bind(Y0,$fot(inverse(least_upper_bound(X_207,X_98))))]]) ).
cnf(refute_0_477,plain,
inverse(least_upper_bound(X_207,X_98)) = inverse(least_upper_bound(X_98,X_207)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_98,X_207)),inverse(least_upper_bound(X_207,X_98))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
inverse(least_upper_bound(multiply(X,Y),identity)) = inverse(least_upper_bound(identity,multiply(X,Y))),
inference(subst,[],[refute_0_477:[bind(X_207,$fot(multiply(X,Y))),bind(X_98,$fot(identity))]]) ).
cnf(refute_0_479,plain,
multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))) = multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))),
introduced(tautology,[refl,[$fot(multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))]]) ).
cnf(refute_0_480,plain,
( multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))) != multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))
| inverse(least_upper_bound(multiply(X,Y),identity)) != inverse(least_upper_bound(identity,multiply(X,Y)))
| multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))) = multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))),multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) ),[1,1],$fot(inverse(least_upper_bound(identity,multiply(X,Y))))]]) ).
cnf(refute_0_481,plain,
( inverse(least_upper_bound(multiply(X,Y),identity)) != inverse(least_upper_bound(identity,multiply(X,Y)))
| multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))) = multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))) ),
inference(resolve,[$cnf( $equal(multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))),multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))) = multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X,Y),identity)),inverse(least_upper_bound(identity,multiply(X,Y)))) )],[refute_0_478,refute_0_481]) ).
cnf(refute_0_483,plain,
multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) = multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))),
introduced(tautology,[refl,[$fot(multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))))]]) ).
cnf(refute_0_484,plain,
( multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) != multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))
| multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))) != multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))
| multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) = multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))),multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))) ),[1,1],$fot(multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))]]) ).
cnf(refute_0_485,plain,
( multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))) != multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))
| multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) = multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))),multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) = multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))),
inference(resolve,[$cnf( $equal(multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))),multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) )],[refute_0_482,refute_0_485]) ).
cnf(refute_0_487,plain,
( multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))) != multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) != multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))) ),[1],$fot(multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))))]]) ).
cnf(refute_0_488,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) != multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity)))),multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),multiply(X,multiply(Y,inverse(least_upper_bound(multiply(X,Y),identity))))) )],[refute_0_404,refute_0_488]) ).
cnf(refute_0_490,plain,
inverse(least_upper_bound(X_241,inverse(X_240))) = multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))),inverse(least_upper_bound(identity,multiply(X_241,X_240)))),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(least_upper_bound(identity,multiply(X_241,X_240))))),bind(X_69,$fot(least_upper_bound(X_241,inverse(X_240))))]]) ).
cnf(refute_0_491,plain,
inverse(X_69) = multiply(inverse(multiply(least_upper_bound(X_95,inverse(X_69)),X_69)),least_upper_bound(X_95,inverse(X_69))),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(least_upper_bound(X_95,inverse(X_69))))]]) ).
cnf(refute_0_492,plain,
multiply(least_upper_bound(X_95,inverse(X_69)),X_69) = least_upper_bound(identity,multiply(X_95,X_69)),
inference(subst,[],[refute_0_413:[bind(X_89,$fot(X_69)),bind(X_90,$fot(X_95))]]) ).
cnf(refute_0_493,plain,
( multiply(least_upper_bound(X_95,inverse(X_69)),X_69) != least_upper_bound(identity,multiply(X_95,X_69))
| inverse(X_69) != multiply(inverse(multiply(least_upper_bound(X_95,inverse(X_69)),X_69)),least_upper_bound(X_95,inverse(X_69)))
| inverse(X_69) = multiply(inverse(least_upper_bound(identity,multiply(X_95,X_69))),least_upper_bound(X_95,inverse(X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_69),multiply(inverse(multiply(least_upper_bound(X_95,inverse(X_69)),X_69)),least_upper_bound(X_95,inverse(X_69)))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_95,X_69)))]]) ).
cnf(refute_0_494,plain,
( inverse(X_69) != multiply(inverse(multiply(least_upper_bound(X_95,inverse(X_69)),X_69)),least_upper_bound(X_95,inverse(X_69)))
| inverse(X_69) = multiply(inverse(least_upper_bound(identity,multiply(X_95,X_69))),least_upper_bound(X_95,inverse(X_69))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_95,inverse(X_69)),X_69),least_upper_bound(identity,multiply(X_95,X_69))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
inverse(X_69) = multiply(inverse(least_upper_bound(identity,multiply(X_95,X_69))),least_upper_bound(X_95,inverse(X_69))),
inference(resolve,[$cnf( $equal(inverse(X_69),multiply(inverse(multiply(least_upper_bound(X_95,inverse(X_69)),X_69)),least_upper_bound(X_95,inverse(X_69)))) )],[refute_0_491,refute_0_494]) ).
cnf(refute_0_496,plain,
inverse(X_240) = multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240))),
inference(subst,[],[refute_0_495:[bind(X_69,$fot(X_240)),bind(X_95,$fot(X_241))]]) ).
cnf(refute_0_497,plain,
( inverse(X_240) != multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))
| multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240))) = inverse(X_240) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(X_240))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))))]]) ).
cnf(refute_0_498,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240))) = inverse(X_240),
inference(resolve,[$cnf( $equal(inverse(X_240),multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
( multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240))) != inverse(X_240)
| inverse(least_upper_bound(X_241,inverse(X_240))) != multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))),inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| inverse(least_upper_bound(X_241,inverse(X_240))) = multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_241,inverse(X_240))),multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))),inverse(least_upper_bound(identity,multiply(X_241,X_240))))) ),[1,0,0],$fot(inverse(X_240))]]) ).
cnf(refute_0_500,plain,
( inverse(least_upper_bound(X_241,inverse(X_240))) != multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))),inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| inverse(least_upper_bound(X_241,inverse(X_240))) = multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240))),inverse(X_240)) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
inverse(least_upper_bound(X_241,inverse(X_240))) = multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_241,inverse(X_240))),multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_241,X_240))),least_upper_bound(X_241,inverse(X_240)))),inverse(least_upper_bound(identity,multiply(X_241,X_240))))) )],[refute_0_490,refute_0_500]) ).
cnf(refute_0_502,plain,
inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240))) = multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(X_240)),bind(X_73,$fot(least_upper_bound(identity,multiply(X_241,X_240))))]]) ).
cnf(refute_0_503,plain,
multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) = inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(least_upper_bound(identity,multiply(X_241,X_240)))),bind(X_46,$fot(inverse(X_240)))]]) ).
cnf(refute_0_504,plain,
( multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) != inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240)))
| inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240))) != multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) = multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240))))),bind(Z0,$fot(multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))))]]) ).
cnf(refute_0_505,plain,
( inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240))) != multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) = multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))),inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240)))) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) = multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(X_241,X_240)),inverse(X_240))),multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))) )],[refute_0_502,refute_0_505]) ).
cnf(refute_0_507,plain,
( multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))) != multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| inverse(least_upper_bound(X_241,inverse(X_240))) != multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| inverse(least_upper_bound(X_241,inverse(X_240))) = multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_241,inverse(X_240))),multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240))))) ),[1],$fot(multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))))]]) ).
cnf(refute_0_508,plain,
( inverse(least_upper_bound(X_241,inverse(X_240))) != multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| inverse(least_upper_bound(X_241,inverse(X_240))) = multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240)))),multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
inverse(least_upper_bound(X_241,inverse(X_240))) = multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_241,inverse(X_240))),multiply(inverse(inverse(X_240)),inverse(least_upper_bound(identity,multiply(X_241,X_240))))) )],[refute_0_501,refute_0_508]) ).
cnf(refute_0_510,plain,
( inverse(least_upper_bound(X_241,inverse(X_240))) != multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))
| multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))) = inverse(least_upper_bound(X_241,inverse(X_240))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_241,inverse(X_240))))),bind(Y0,$fot(multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))))]]) ).
cnf(refute_0_511,plain,
multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240)))) = inverse(least_upper_bound(X_241,inverse(X_240))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_241,inverse(X_240))),multiply(X_240,inverse(least_upper_bound(identity,multiply(X_241,X_240))))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))) = inverse(least_upper_bound(X,inverse(Y))),
inference(subst,[],[refute_0_511:[bind(X_240,$fot(Y)),bind(X_241,$fot(X))]]) ).
cnf(refute_0_513,plain,
multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) = multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))),
introduced(tautology,[refl,[$fot(multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))))]]) ).
cnf(refute_0_514,plain,
( multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) != multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))
| multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))) != inverse(least_upper_bound(X,inverse(Y)))
| multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) = multiply(X,inverse(least_upper_bound(X,inverse(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))),multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))) ),[1,1],$fot(inverse(least_upper_bound(X,inverse(Y))))]]) ).
cnf(refute_0_515,plain,
( multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))) != inverse(least_upper_bound(X,inverse(Y)))
| multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) = multiply(X,inverse(least_upper_bound(X,inverse(Y)))) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))),multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) = multiply(X,inverse(least_upper_bound(X,inverse(Y)))),
inference(resolve,[$cnf( $equal(multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))),inverse(least_upper_bound(X,inverse(Y)))) )],[refute_0_512,refute_0_515]) ).
cnf(refute_0_517,plain,
( multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))) != multiply(X,inverse(least_upper_bound(X,inverse(Y))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) != multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,inverse(least_upper_bound(X,inverse(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))) ),[1],$fot(multiply(X,inverse(least_upper_bound(X,inverse(Y)))))]]) ).
cnf(refute_0_518,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) != multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))
| inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,inverse(least_upper_bound(X,inverse(Y)))) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y))))),multiply(X,inverse(least_upper_bound(X,inverse(Y))))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) = multiply(X,inverse(least_upper_bound(X,inverse(Y)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),multiply(X,multiply(Y,inverse(least_upper_bound(identity,multiply(X,Y)))))) )],[refute_0_489,refute_0_518]) ).
cnf(refute_0_520,plain,
( inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) != multiply(X,inverse(least_upper_bound(X,inverse(Y))))
| multiply(X,inverse(least_upper_bound(X,inverse(Y)))) = inverse(least_upper_bound(identity,inverse(multiply(X,Y)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))))),bind(Y0,$fot(multiply(X,inverse(least_upper_bound(X,inverse(Y))))))]]) ).
cnf(refute_0_521,plain,
multiply(X,inverse(least_upper_bound(X,inverse(Y)))) = inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(X,Y)))),multiply(X,inverse(least_upper_bound(X,inverse(Y))))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),
inference(subst,[],[refute_0_521:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))]]) ).
cnf(refute_0_523,plain,
( multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))
| inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))))),bind(Z0,$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_524,plain,
( inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(multiply(identity,multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_369,refute_0_524]) ).
cnf(refute_0_526,plain,
( multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)
| multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) ),[0],$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_527,plain,
( multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))) != multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) )],[refute_0_205,refute_0_527]) ).
cnf(refute_0_529,plain,
( inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) != multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)
| multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)))]]) ).
cnf(refute_0_530,plain,
multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b)) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
( multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| b != multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))
| b = multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) ),[1,1],$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_532,plain,
( b != multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))
| b = multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
b = multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),
inference(resolve,[$cnf( $equal(b,multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),multiply(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))),b))) )],[refute_0_9,refute_0_532]) ).
cnf(refute_0_534,plain,
inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),bind(X_73,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_535,plain,
multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),bind(X_46,$fot(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))))]]) ).
cnf(refute_0_536,plain,
( multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))))
| inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))))),bind(Z0,$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))))]]) ).
cnf(refute_0_537,plain,
( inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))))) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_534,refute_0_537]) ).
cnf(refute_0_539,plain,
( multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| b != multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) ),[1],$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_540,plain,
( b != multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),
inference(resolve,[$cnf( $equal(b,multiply(inverse(inverse(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_533,refute_0_540]) ).
cnf(refute_0_542,plain,
multiply(inverse(greatest_lower_bound(a,c)),c) = multiply(inverse(a),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(a)),bind(X_46,$fot(multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_543,plain,
inverse(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_544,plain,
multiply(inverse(c),inverse(multiply(least_upper_bound(a,c),inverse(c)))) = inverse(least_upper_bound(a,c)),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(least_upper_bound(a,c))),bind(X_55,$fot(inverse(c)))]]) ).
cnf(refute_0_545,plain,
least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)) = least_upper_bound(least_upper_bound(X_20,greatest_lower_bound(X_20,Y)),X_22),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(greatest_lower_bound(X_20,Y))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_546,plain,
least_upper_bound(X_20,greatest_lower_bound(X_20,Y)) = X_20,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_547,plain,
( least_upper_bound(X_20,greatest_lower_bound(X_20,Y)) != X_20
| least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)) != least_upper_bound(least_upper_bound(X_20,greatest_lower_bound(X_20,Y)),X_22)
| least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)) = least_upper_bound(X_20,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)),least_upper_bound(least_upper_bound(X_20,greatest_lower_bound(X_20,Y)),X_22)) ),[1,0],$fot(X_20)]]) ).
cnf(refute_0_548,plain,
( least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)) != least_upper_bound(least_upper_bound(X_20,greatest_lower_bound(X_20,Y)),X_22)
| least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)) = least_upper_bound(X_20,X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,greatest_lower_bound(X_20,Y)),X_20) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)) = least_upper_bound(X_20,X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_20,Y),X_22)),least_upper_bound(least_upper_bound(X_20,greatest_lower_bound(X_20,Y)),X_22)) )],[refute_0_545,refute_0_548]) ).
cnf(refute_0_550,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),
inference(subst,[],[refute_0_549:[bind(X_20,$fot(identity)),bind(X_22,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_551,plain,
multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) = least_upper_bound(identity,multiply(inverse(X_86),inverse(X_45))),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(inverse(X_45))),bind(X_84,$fot(X_86))]]) ).
cnf(refute_0_552,plain,
inverse(multiply(X_45,X_86)) = multiply(inverse(X_86),inverse(X_45)),
inference(subst,[],[refute_0_238:[bind(X_46,$fot(X_86))]]) ).
cnf(refute_0_553,plain,
( inverse(multiply(X_45,X_86)) != multiply(inverse(X_86),inverse(X_45))
| multiply(inverse(X_86),inverse(X_45)) = inverse(multiply(X_45,X_86)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(multiply(X_45,X_86)))),bind(Y0,$fot(multiply(inverse(X_86),inverse(X_45))))]]) ).
cnf(refute_0_554,plain,
multiply(inverse(X_86),inverse(X_45)) = inverse(multiply(X_45,X_86)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_45,X_86)),multiply(inverse(X_86),inverse(X_45))) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
( multiply(inverse(X_86),inverse(X_45)) != inverse(multiply(X_45,X_86))
| multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) != least_upper_bound(identity,multiply(inverse(X_86),inverse(X_45)))
| multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) = least_upper_bound(identity,inverse(multiply(X_45,X_86))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)),least_upper_bound(identity,multiply(inverse(X_86),inverse(X_45)))) ),[1,1],$fot(inverse(multiply(X_45,X_86)))]]) ).
cnf(refute_0_556,plain,
( multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) != least_upper_bound(identity,multiply(inverse(X_86),inverse(X_45)))
| multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) = least_upper_bound(identity,inverse(multiply(X_45,X_86))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),inverse(X_45)),inverse(multiply(X_45,X_86))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) = least_upper_bound(identity,inverse(multiply(X_45,X_86))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)),least_upper_bound(identity,multiply(inverse(X_86),inverse(X_45)))) )],[refute_0_551,refute_0_556]) ).
cnf(refute_0_558,plain,
inverse(greatest_lower_bound(X_200,X_199)) = multiply(inverse(multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199))),inverse(greatest_lower_bound(X_199,X_200))),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(greatest_lower_bound(X_199,X_200)))),bind(X_69,$fot(greatest_lower_bound(X_200,X_199)))]]) ).
cnf(refute_0_559,plain,
multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)),
inference(subst,[],[refute_0_110:[bind(X_154,$fot(X_162)),bind(X_155,$fot(greatest_lower_bound(Y,X_162)))]]) ).
cnf(refute_0_560,plain,
greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))) = greatest_lower_bound(X_15,Y),
inference(subst,[],[refute_0_262:[bind(X,$fot(greatest_lower_bound(X_15,Y))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_561,plain,
least_upper_bound(X_15,greatest_lower_bound(X_15,Y)) = X_15,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_562,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))) != greatest_lower_bound(X_15,Y)
| least_upper_bound(X_15,greatest_lower_bound(X_15,Y)) != X_15
| greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))),greatest_lower_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_563,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))) != greatest_lower_bound(X_15,Y)
| greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,greatest_lower_bound(X_15,Y)),X_15) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),least_upper_bound(X_15,greatest_lower_bound(X_15,Y))),greatest_lower_bound(X_15,Y)) )],[refute_0_560,refute_0_563]) ).
cnf(refute_0_565,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_566,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_565]) ).
cnf(refute_0_567,plain,
greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) = greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_568,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) != greatest_lower_bound(X_15,Y)
| greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) != greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15))
| greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)) = greatest_lower_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15),greatest_lower_bound(X_15,Y)) ),[0],$fot(greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)))]]) ).
cnf(refute_0_569,plain,
( greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15) != greatest_lower_bound(X_15,Y)
| greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)) = greatest_lower_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15),greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15))) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
greatest_lower_bound(X_15,greatest_lower_bound(Y,X_15)) = greatest_lower_bound(X_15,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_15,Y),X_15),greatest_lower_bound(X_15,Y)) )],[refute_0_564,refute_0_569]) ).
cnf(refute_0_571,plain,
greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162)) = greatest_lower_bound(X_162,Y),
inference(subst,[],[refute_0_570:[bind(X_15,$fot(X_162))]]) ).
cnf(refute_0_572,plain,
( multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162))
| greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162)) != greatest_lower_bound(X_162,Y)
| multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162))) ),[0,1],$fot(greatest_lower_bound(X_162,Y))]]) ).
cnf(refute_0_573,plain,
( multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162))
| multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,greatest_lower_bound(Y,X_162))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162))) )],[refute_0_559,refute_0_573]) ).
cnf(refute_0_575,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_86),X_85))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_86),X_85)))]]) ).
cnf(refute_0_576,plain,
multiply(inverse(X_86),least_upper_bound(X_85,X_86)) = least_upper_bound(identity,multiply(inverse(X_86),X_85)),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(X_85)),bind(X_84,$fot(X_86))]]) ).
cnf(refute_0_577,plain,
( multiply(inverse(X_86),least_upper_bound(X_85,X_86)) != least_upper_bound(identity,multiply(inverse(X_86),X_85))
| least_upper_bound(identity,multiply(inverse(X_86),X_85)) = multiply(inverse(X_86),least_upper_bound(X_85,X_86)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(X_86),least_upper_bound(X_85,X_86)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_86),X_85))))]]) ).
cnf(refute_0_578,plain,
least_upper_bound(identity,multiply(inverse(X_86),X_85)) = multiply(inverse(X_86),least_upper_bound(X_85,X_86)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(X_85,X_86)),least_upper_bound(identity,multiply(inverse(X_86),X_85))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_86),X_85))) != identity
| least_upper_bound(identity,multiply(inverse(X_86),X_85)) != multiply(inverse(X_86),least_upper_bound(X_85,X_86))
| greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_86),X_85))),identity) ),[0,1],$fot(multiply(inverse(X_86),least_upper_bound(X_85,X_86)))]]) ).
cnf(refute_0_580,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_86),X_85))) != identity
| greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_86),X_85)),multiply(inverse(X_86),least_upper_bound(X_85,X_86))) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_86),X_85))),identity) )],[refute_0_575,refute_0_580]) ).
cnf(refute_0_582,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)))) = identity,
inference(subst,[],[refute_0_581:[bind(X_85,$fot(X_130)),bind(X_86,$fot(greatest_lower_bound(X_11,X_130)))]]) ).
cnf(refute_0_583,plain,
least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)) = X_130,
inference(subst,[],[refute_0_270:[bind(X_10,$fot(X_130))]]) ).
cnf(refute_0_584,plain,
( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)))) != identity
| least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)) != X_130
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),X_130)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)))),identity) ),[0,1,1],$fot(X_130)]]) ).
cnf(refute_0_585,plain,
( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)))) != identity
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),X_130)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)),X_130) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),X_130)) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_130)),least_upper_bound(X_130,greatest_lower_bound(X_11,X_130)))),identity) )],[refute_0_582,refute_0_585]) ).
cnf(refute_0_587,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)) = identity,
inference(subst,[],[refute_0_586:[bind(X_11,$fot(Y)),bind(X_130,$fot(X_162))]]) ).
cnf(refute_0_588,plain,
( multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)) != identity
| multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)))]]) ).
cnf(refute_0_589,plain,
( multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162))
| multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162)),identity) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_162)),greatest_lower_bound(X_162,Y)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_162)),X_162))) )],[refute_0_574,refute_0_589]) ).
cnf(refute_0_591,plain,
multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199)) = identity,
inference(subst,[],[refute_0_590:[bind(Y,$fot(X_199)),bind(X_162,$fot(X_200))]]) ).
cnf(refute_0_592,plain,
( multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199)) != identity
| inverse(greatest_lower_bound(X_200,X_199)) != multiply(inverse(multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199))),inverse(greatest_lower_bound(X_199,X_200)))
| inverse(greatest_lower_bound(X_200,X_199)) = multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_200,X_199)),multiply(inverse(multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199))),inverse(greatest_lower_bound(X_199,X_200)))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_593,plain,
( inverse(greatest_lower_bound(X_200,X_199)) != multiply(inverse(multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199))),inverse(greatest_lower_bound(X_199,X_200)))
| inverse(greatest_lower_bound(X_200,X_199)) = multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199)),identity) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
inverse(greatest_lower_bound(X_200,X_199)) = multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_200,X_199)),multiply(inverse(multiply(inverse(greatest_lower_bound(X_199,X_200)),greatest_lower_bound(X_200,X_199))),inverse(greatest_lower_bound(X_199,X_200)))) )],[refute_0_558,refute_0_593]) ).
cnf(refute_0_595,plain,
multiply(greatest_lower_bound(X_199,X_200),identity) = greatest_lower_bound(X_199,X_200),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(greatest_lower_bound(X_199,X_200)))]]) ).
cnf(refute_0_596,plain,
inverse(multiply(greatest_lower_bound(X_199,X_200),identity)) = inverse(multiply(greatest_lower_bound(X_199,X_200),identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(X_199,X_200),identity)))]]) ).
cnf(refute_0_597,plain,
( multiply(greatest_lower_bound(X_199,X_200),identity) != greatest_lower_bound(X_199,X_200)
| inverse(multiply(greatest_lower_bound(X_199,X_200),identity)) != inverse(multiply(greatest_lower_bound(X_199,X_200),identity))
| inverse(multiply(greatest_lower_bound(X_199,X_200),identity)) = inverse(greatest_lower_bound(X_199,X_200)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_199,X_200),identity)),inverse(multiply(greatest_lower_bound(X_199,X_200),identity))) ),[1,0],$fot(greatest_lower_bound(X_199,X_200))]]) ).
cnf(refute_0_598,plain,
( multiply(greatest_lower_bound(X_199,X_200),identity) != greatest_lower_bound(X_199,X_200)
| inverse(multiply(greatest_lower_bound(X_199,X_200),identity)) = inverse(greatest_lower_bound(X_199,X_200)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_199,X_200),identity)),inverse(multiply(greatest_lower_bound(X_199,X_200),identity))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
inverse(multiply(greatest_lower_bound(X_199,X_200),identity)) = inverse(greatest_lower_bound(X_199,X_200)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_199,X_200),identity),greatest_lower_bound(X_199,X_200)) )],[refute_0_595,refute_0_598]) ).
cnf(refute_0_600,plain,
multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) = inverse(multiply(greatest_lower_bound(X_199,X_200),identity)),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(greatest_lower_bound(X_199,X_200))),bind(X_46,$fot(identity))]]) ).
cnf(refute_0_601,plain,
( multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) != inverse(multiply(greatest_lower_bound(X_199,X_200),identity))
| inverse(multiply(greatest_lower_bound(X_199,X_200),identity)) != inverse(greatest_lower_bound(X_199,X_200))
| multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) = inverse(greatest_lower_bound(X_199,X_200)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(X_199,X_200),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_199,X_200))))]]) ).
cnf(refute_0_602,plain,
( inverse(multiply(greatest_lower_bound(X_199,X_200),identity)) != inverse(greatest_lower_bound(X_199,X_200))
| multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) = inverse(greatest_lower_bound(X_199,X_200)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))),inverse(multiply(greatest_lower_bound(X_199,X_200),identity))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) = inverse(greatest_lower_bound(X_199,X_200)),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_199,X_200),identity)),inverse(greatest_lower_bound(X_199,X_200))) )],[refute_0_599,refute_0_602]) ).
cnf(refute_0_604,plain,
( multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))) != inverse(greatest_lower_bound(X_199,X_200))
| inverse(greatest_lower_bound(X_200,X_199)) != multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200)))
| inverse(greatest_lower_bound(X_200,X_199)) = inverse(greatest_lower_bound(X_199,X_200)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_200,X_199)),multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200)))) ),[1],$fot(inverse(greatest_lower_bound(X_199,X_200)))]]) ).
cnf(refute_0_605,plain,
( inverse(greatest_lower_bound(X_200,X_199)) != multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200)))
| inverse(greatest_lower_bound(X_200,X_199)) = inverse(greatest_lower_bound(X_199,X_200)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200))),inverse(greatest_lower_bound(X_199,X_200))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
inverse(greatest_lower_bound(X_200,X_199)) = inverse(greatest_lower_bound(X_199,X_200)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_200,X_199)),multiply(inverse(identity),inverse(greatest_lower_bound(X_199,X_200)))) )],[refute_0_594,refute_0_605]) ).
cnf(refute_0_607,plain,
( inverse(greatest_lower_bound(X_200,X_199)) != inverse(greatest_lower_bound(X_199,X_200))
| inverse(greatest_lower_bound(X_199,X_200)) = inverse(greatest_lower_bound(X_200,X_199)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(X_200,X_199)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_199,X_200))))]]) ).
cnf(refute_0_608,plain,
inverse(greatest_lower_bound(X_199,X_200)) = inverse(greatest_lower_bound(X_200,X_199)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_200,X_199)),inverse(greatest_lower_bound(X_199,X_200))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
inverse(greatest_lower_bound(multiply(X_45,X_86),identity)) = inverse(greatest_lower_bound(identity,multiply(X_45,X_86))),
inference(subst,[],[refute_0_608:[bind(X_199,$fot(multiply(X_45,X_86))),bind(X_200,$fot(identity))]]) ).
cnf(refute_0_610,plain,
inverse(greatest_lower_bound(X_364,identity)) = multiply(inverse(multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))),least_upper_bound(identity,inverse(X_364))),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(least_upper_bound(identity,inverse(X_364)))),bind(X_69,$fot(greatest_lower_bound(X_364,identity)))]]) ).
cnf(refute_0_611,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))) = multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),
inference(subst,[],[refute_0_262:[bind(X,$fot(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))),bind(Y,$fot(identity))]]) ).
cnf(refute_0_612,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = least_upper_bound(X_89,multiply(least_upper_bound(inverse(X_89),X_97),X_89)),
inference(subst,[],[refute_0_149:[bind(X_90,$fot(least_upper_bound(inverse(X_89),X_97)))]]) ).
cnf(refute_0_613,plain,
multiply(least_upper_bound(inverse(X_89),X_97),X_89) = least_upper_bound(identity,multiply(X_97,X_89)),
inference(subst,[],[refute_0_98:[bind(X_91,$fot(X_97))]]) ).
cnf(refute_0_614,plain,
( multiply(least_upper_bound(inverse(X_89),X_97),X_89) != least_upper_bound(identity,multiply(X_97,X_89))
| multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) != least_upper_bound(X_89,multiply(least_upper_bound(inverse(X_89),X_97),X_89))
| multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89),least_upper_bound(X_89,multiply(least_upper_bound(inverse(X_89),X_97),X_89))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_97,X_89)))]]) ).
cnf(refute_0_615,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) != least_upper_bound(X_89,multiply(least_upper_bound(inverse(X_89),X_97),X_89))
| multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),X_97),X_89),least_upper_bound(identity,multiply(X_97,X_89))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89),least_upper_bound(X_89,multiply(least_upper_bound(inverse(X_89),X_97),X_89))) )],[refute_0_612,refute_0_615]) ).
cnf(refute_0_617,plain,
multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = least_upper_bound(multiply(least_upper_bound(X_95,inverse(X)),X),multiply(Z,X)),
inference(subst,[],[monotony_lub2:[bind(Y,$fot(least_upper_bound(X_95,inverse(X))))]]) ).
cnf(refute_0_618,plain,
multiply(least_upper_bound(X_95,inverse(X)),X) = least_upper_bound(identity,multiply(X_95,X)),
inference(subst,[],[refute_0_413:[bind(X_89,$fot(X)),bind(X_90,$fot(X_95))]]) ).
cnf(refute_0_619,plain,
( multiply(least_upper_bound(X_95,inverse(X)),X) != least_upper_bound(identity,multiply(X_95,X))
| multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_95,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_95,inverse(X)),X),multiply(Z,X))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_95,X)))]]) ).
cnf(refute_0_620,plain,
( multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_95,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_95,inverse(X)),X),least_upper_bound(identity,multiply(X_95,X))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_95,inverse(X)),X),multiply(Z,X))) )],[refute_0_617,refute_0_620]) ).
cnf(refute_0_622,plain,
least_upper_bound(least_upper_bound(X_95,inverse(X)),Z) = least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_95)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_623,plain,
multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X))]]) ).
cnf(refute_0_624,plain,
( multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) != multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X)
| least_upper_bound(least_upper_bound(X_95,inverse(X)),Z) != least_upper_bound(X_95,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X)) ),[1,0],$fot(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_625,plain,
( least_upper_bound(least_upper_bound(X_95,inverse(X)),Z) != least_upper_bound(X_95,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X)) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) = multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),least_upper_bound(X_95,least_upper_bound(inverse(X),Z))) )],[refute_0_622,refute_0_625]) ).
cnf(refute_0_627,plain,
( multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) != multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X)
| multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))
| multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))) ),[0],$fot(multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X))]]) ).
cnf(refute_0_628,plain,
( multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))
| multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X)) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_630,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_629]) ).
cnf(refute_0_631,plain,
least_upper_bound(multiply(X_95,X),multiply(Z,X)) = multiply(least_upper_bound(X_95,Z),X),
inference(subst,[],[refute_0_630:[bind(Y,$fot(X_95))]]) ).
cnf(refute_0_632,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))) = least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))))]]) ).
cnf(refute_0_633,plain,
( least_upper_bound(multiply(X_95,X),multiply(Z,X)) != multiply(least_upper_bound(X_95,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))) != least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X)))
| least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X)))) ),[1,1],$fot(multiply(least_upper_bound(X_95,Z),X))]]) ).
cnf(refute_0_634,plain,
( least_upper_bound(multiply(X_95,X),multiply(Z,X)) != multiply(least_upper_bound(X_95,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X)))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_95,X),multiply(Z,X)),multiply(least_upper_bound(X_95,Z),X)) )],[refute_0_631,refute_0_634]) ).
cnf(refute_0_636,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) = least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))),
inference(subst,[],[refute_0_131:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_95,X))),bind(Z,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_637,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) != least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X)))
| least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X))))]]) ).
cnf(refute_0_638,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)),least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X)))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_95,X),multiply(Z,X))),least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X))) )],[refute_0_635,refute_0_638]) ).
cnf(refute_0_640,plain,
( multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))
| least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)) != least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X))
| multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X),least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)))]]) ).
cnf(refute_0_641,plain,
( multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))
| multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X)),least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
( multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))
| multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X),least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))) )],[refute_0_628,refute_0_641]) ).
cnf(refute_0_643,plain,
multiply(least_upper_bound(X_95,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_95,Z),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_95,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_95,X)),multiply(Z,X))) )],[refute_0_621,refute_0_642]) ).
cnf(refute_0_644,plain,
multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)),
inference(subst,[],[refute_0_643:[bind(X,$fot(X_89)),bind(Z,$fot(X_97)),bind(X_95,$fot(identity))]]) ).
cnf(refute_0_645,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = least_upper_bound(X_19,multiply(X_93,X_19)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(multiply(X_93,X_19)))]]) ).
cnf(refute_0_646,plain,
multiply(least_upper_bound(X_93,identity),X_19) = least_upper_bound(X_19,multiply(X_93,X_19)),
inference(subst,[],[refute_0_149:[bind(X_89,$fot(X_19)),bind(X_90,$fot(X_93))]]) ).
cnf(refute_0_647,plain,
( multiply(least_upper_bound(X_93,identity),X_19) != least_upper_bound(X_19,multiply(X_93,X_19))
| least_upper_bound(X_19,multiply(X_93,X_19)) = multiply(least_upper_bound(X_93,identity),X_19) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_93,identity),X_19))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_93,X_19))))]]) ).
cnf(refute_0_648,plain,
least_upper_bound(X_19,multiply(X_93,X_19)) = multiply(least_upper_bound(X_93,identity),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_93,identity),X_19),least_upper_bound(X_19,multiply(X_93,X_19))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
( least_upper_bound(X_19,multiply(X_93,X_19)) != multiply(least_upper_bound(X_93,identity),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) != least_upper_bound(X_19,multiply(X_93,X_19))
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(X_93,identity),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))),least_upper_bound(X_19,multiply(X_93,X_19))) ),[1],$fot(multiply(least_upper_bound(X_93,identity),X_19))]]) ).
cnf(refute_0_650,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) != least_upper_bound(X_19,multiply(X_93,X_19))
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(X_93,identity),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_93,X_19)),multiply(least_upper_bound(X_93,identity),X_19)) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(X_93,identity),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))),least_upper_bound(X_19,multiply(X_93,X_19))) )],[refute_0_645,refute_0_650]) ).
cnf(refute_0_652,plain,
least_upper_bound(identity,least_upper_bound(X_93,identity)) = least_upper_bound(identity,X_93),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_93)),bind(X_13,$fot(identity))]]) ).
cnf(refute_0_653,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19))]]) ).
cnf(refute_0_654,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)
| least_upper_bound(identity,least_upper_bound(X_93,identity)) != least_upper_bound(identity,X_93)
| multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) = multiply(least_upper_bound(identity,X_93),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)) ),[1,0],$fot(least_upper_bound(identity,X_93))]]) ).
cnf(refute_0_655,plain,
( least_upper_bound(identity,least_upper_bound(X_93,identity)) != least_upper_bound(identity,X_93)
| multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) = multiply(least_upper_bound(identity,X_93),X_19) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) = multiply(least_upper_bound(identity,X_93),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_93,identity)),least_upper_bound(identity,X_93)) )],[refute_0_652,refute_0_655]) ).
cnf(refute_0_657,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(multiply(X_91,X_89))),bind(X_19,$fot(multiply(X_90,X_89)))]]) ).
cnf(refute_0_658,plain,
multiply(least_upper_bound(X_90,X_91),X_89) = least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_89)),bind(Y,$fot(X_90)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_659,plain,
( multiply(least_upper_bound(X_90,X_91),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))
| least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)) = multiply(least_upper_bound(X_90,X_91),X_89) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_90,X_91),X_89))),bind(Y0,$fot(least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))))]]) ).
cnf(refute_0_660,plain,
least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)) = multiply(least_upper_bound(X_90,X_91),X_89),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
( least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)) != multiply(least_upper_bound(X_90,X_91),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_90,X_91),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) ),[1],$fot(multiply(least_upper_bound(X_90,X_91),X_89))]]) ).
cnf(refute_0_662,plain,
( least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_90,X_91),X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)),multiply(least_upper_bound(X_90,X_91),X_89)) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_90,X_91),X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) )],[refute_0_657,refute_0_662]) ).
cnf(refute_0_664,plain,
least_upper_bound(X_90,X_90) = X_90,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_90))]]) ).
cnf(refute_0_665,plain,
least_upper_bound(X_91,least_upper_bound(X_90,X_90)) = least_upper_bound(X_91,least_upper_bound(X_90,X_90)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_91,least_upper_bound(X_90,X_90)))]]) ).
cnf(refute_0_666,plain,
( least_upper_bound(X_90,X_90) != X_90
| least_upper_bound(X_91,least_upper_bound(X_90,X_90)) != least_upper_bound(X_91,least_upper_bound(X_90,X_90))
| least_upper_bound(X_91,least_upper_bound(X_90,X_90)) = least_upper_bound(X_91,X_90) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),least_upper_bound(X_91,least_upper_bound(X_90,X_90))) ),[1,1],$fot(X_90)]]) ).
cnf(refute_0_667,plain,
( least_upper_bound(X_90,X_90) != X_90
| least_upper_bound(X_91,least_upper_bound(X_90,X_90)) = least_upper_bound(X_91,X_90) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),least_upper_bound(X_91,least_upper_bound(X_90,X_90))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
least_upper_bound(X_91,least_upper_bound(X_90,X_90)) = least_upper_bound(X_91,X_90),
inference(resolve,[$cnf( $equal(least_upper_bound(X_90,X_90),X_90) )],[refute_0_664,refute_0_667]) ).
cnf(refute_0_669,plain,
multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) = multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89))]]) ).
cnf(refute_0_670,plain,
( multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) != multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)
| least_upper_bound(X_91,least_upper_bound(X_90,X_90)) != least_upper_bound(X_91,X_90)
| multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) = multiply(least_upper_bound(X_91,X_90),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89),multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)) ),[1,0],$fot(least_upper_bound(X_91,X_90))]]) ).
cnf(refute_0_671,plain,
( least_upper_bound(X_91,least_upper_bound(X_90,X_90)) != least_upper_bound(X_91,X_90)
| multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) = multiply(least_upper_bound(X_91,X_90),X_89) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89),multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) = multiply(least_upper_bound(X_91,X_90),X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),least_upper_bound(X_91,X_90)) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89)) = multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89),
inference(subst,[],[refute_0_630:[bind(X,$fot(X_89)),bind(Y,$fot(X_91)),bind(Z,$fot(least_upper_bound(X_90,X_90)))]]) ).
cnf(refute_0_674,plain,
least_upper_bound(X,least_upper_bound(X_20,X_21)) = least_upper_bound(least_upper_bound(X_20,X_21),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_675,plain,
least_upper_bound(X_20,least_upper_bound(X_21,X)) = least_upper_bound(least_upper_bound(X_20,X_21),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X))]]) ).
cnf(refute_0_676,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,X)) != least_upper_bound(least_upper_bound(X_20,X_21),X)
| least_upper_bound(least_upper_bound(X_20,X_21),X) = least_upper_bound(X_20,least_upper_bound(X_21,X)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_20,X_21),X)))]]) ).
cnf(refute_0_677,plain,
least_upper_bound(least_upper_bound(X_20,X_21),X) = least_upper_bound(X_20,least_upper_bound(X_21,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,X)),least_upper_bound(least_upper_bound(X_20,X_21),X)) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_21)) != least_upper_bound(least_upper_bound(X_20,X_21),X)
| least_upper_bound(least_upper_bound(X_20,X_21),X) != least_upper_bound(X_20,least_upper_bound(X_21,X))
| least_upper_bound(X,least_upper_bound(X_20,X_21)) = least_upper_bound(X_20,least_upper_bound(X_21,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_20,X_21)),least_upper_bound(X_20,least_upper_bound(X_21,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_20,X_21),X))]]) ).
cnf(refute_0_679,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_21)) != least_upper_bound(least_upper_bound(X_20,X_21),X)
| least_upper_bound(X,least_upper_bound(X_20,X_21)) = least_upper_bound(X_20,least_upper_bound(X_21,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),X),least_upper_bound(X_20,least_upper_bound(X_21,X))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
least_upper_bound(X,least_upper_bound(X_20,X_21)) = least_upper_bound(X_20,least_upper_bound(X_21,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,X_21)),least_upper_bound(least_upper_bound(X_20,X_21),X)) )],[refute_0_674,refute_0_679]) ).
cnf(refute_0_681,plain,
least_upper_bound(X,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X)),
inference(subst,[],[refute_0_680:[bind(X_20,$fot(multiply(X_90,X_89))),bind(X_21,$fot(multiply(X_91,X_89)))]]) ).
cnf(refute_0_682,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X))
| least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)) != multiply(least_upper_bound(X_90,X_91),X_89)
| least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)) = least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X))) ),[0,1],$fot(multiply(least_upper_bound(X_90,X_91),X_89))]]) ).
cnf(refute_0_683,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X))
| least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)) = least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)),multiply(least_upper_bound(X_90,X_91),X_89)) )],[refute_0_660,refute_0_682]) ).
cnf(refute_0_684,plain,
least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)) = least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X))) )],[refute_0_681,refute_0_683]) ).
cnf(refute_0_685,plain,
( least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)) != least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X))
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X)) = least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)))),bind(Y0,$fot(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X))))]]) ).
cnf(refute_0_686,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X)) = least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(least_upper_bound(X_90,X_91),X_89)),least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_91,X_89),X))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89)),
inference(subst,[],[refute_0_686:[bind(X,$fot(multiply(X_91,X_89))),bind(X_91,$fot(X_90))]]) ).
cnf(refute_0_688,plain,
( least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89))
| least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89)) != multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))))),bind(Y0,$fot(least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89)))),bind(Z0,$fot(multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)))]]) ).
cnf(refute_0_689,plain,
( least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89)) != multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89))) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_91,X_89),multiply(least_upper_bound(X_90,X_90),X_89)),multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)) )],[refute_0_673,refute_0_689]) ).
cnf(refute_0_691,plain,
( multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) != multiply(least_upper_bound(X_91,X_90),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_91,X_90),X_89) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))))),bind(Y0,$fot(multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89))),bind(Z0,$fot(multiply(least_upper_bound(X_91,X_90),X_89)))]]) ).
cnf(refute_0_692,plain,
( multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89) != multiply(least_upper_bound(X_91,X_90),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_91,X_90),X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89)) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) = multiply(least_upper_bound(X_91,X_90),X_89),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,least_upper_bound(X_90,X_90)),X_89),multiply(least_upper_bound(X_91,X_90),X_89)) )],[refute_0_672,refute_0_692]) ).
cnf(refute_0_694,plain,
( least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != multiply(least_upper_bound(X_90,X_91),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != multiply(least_upper_bound(X_91,X_90),X_89)
| multiply(least_upper_bound(X_91,X_90),X_89) = multiply(least_upper_bound(X_90,X_91),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),multiply(least_upper_bound(X_90,X_91),X_89)) ),[0],$fot(multiply(least_upper_bound(X_91,X_90),X_89))]]) ).
cnf(refute_0_695,plain,
( least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))) != multiply(least_upper_bound(X_90,X_91),X_89)
| multiply(least_upper_bound(X_91,X_90),X_89) = multiply(least_upper_bound(X_90,X_91),X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),multiply(least_upper_bound(X_91,X_90),X_89)) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
multiply(least_upper_bound(X_91,X_90),X_89) = multiply(least_upper_bound(X_90,X_91),X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),multiply(least_upper_bound(X_90,X_91),X_89)) )],[refute_0_663,refute_0_695]) ).
cnf(refute_0_697,plain,
( multiply(least_upper_bound(X_91,X_90),X_89) != multiply(least_upper_bound(X_90,X_91),X_89)
| multiply(least_upper_bound(X_90,X_91),X_89) = multiply(least_upper_bound(X_91,X_90),X_89) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_91,X_90),X_89))),bind(Y0,$fot(multiply(least_upper_bound(X_90,X_91),X_89)))]]) ).
cnf(refute_0_698,plain,
multiply(least_upper_bound(X_90,X_91),X_89) = multiply(least_upper_bound(X_91,X_90),X_89),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,X_90),X_89),multiply(least_upper_bound(X_90,X_91),X_89)) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19),
inference(subst,[],[refute_0_698:[bind(X_89,$fot(X_19)),bind(X_90,$fot(least_upper_bound(X_93,identity))),bind(X_91,$fot(identity))]]) ).
cnf(refute_0_700,plain,
( multiply(least_upper_bound(X_90,identity),X_89) != least_upper_bound(X_89,multiply(X_90,X_89))
| least_upper_bound(X_89,multiply(X_90,X_89)) = multiply(least_upper_bound(X_90,identity),X_89) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_90,identity),X_89))),bind(Y0,$fot(least_upper_bound(X_89,multiply(X_90,X_89))))]]) ).
cnf(refute_0_701,plain,
least_upper_bound(X_89,multiply(X_90,X_89)) = multiply(least_upper_bound(X_90,identity),X_89),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),X_89),least_upper_bound(X_89,multiply(X_90,X_89))) )],[refute_0_149,refute_0_700]) ).
cnf(refute_0_702,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)) = multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19),
inference(subst,[],[refute_0_701:[bind(X_89,$fot(X_19)),bind(X_90,$fot(least_upper_bound(X_93,identity)))]]) ).
cnf(refute_0_703,plain,
( multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)) != multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)))]]) ).
cnf(refute_0_704,plain,
( multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)),multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19)) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_93,identity),identity),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)) )],[refute_0_699,refute_0_704]) ).
cnf(refute_0_706,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(least_upper_bound(X_20,least_upper_bound(Y,X_20)),X_22),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(least_upper_bound(Y,X_20))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_707,plain,
least_upper_bound(X_20,least_upper_bound(Y,X_20)) = least_upper_bound(X_20,Y),
inference(subst,[],[refute_0_279:[bind(X_13,$fot(X_20))]]) ).
cnf(refute_0_708,plain,
( least_upper_bound(X_20,least_upper_bound(Y,X_20)) != least_upper_bound(X_20,Y)
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(least_upper_bound(X_20,least_upper_bound(Y,X_20)),X_22)
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(least_upper_bound(X_20,Y),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(least_upper_bound(X_20,least_upper_bound(Y,X_20)),X_22)) ),[1,0],$fot(least_upper_bound(X_20,Y))]]) ).
cnf(refute_0_709,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(least_upper_bound(X_20,least_upper_bound(Y,X_20)),X_22)
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(least_upper_bound(X_20,Y),X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(Y,X_20)),least_upper_bound(X_20,Y)) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(least_upper_bound(X_20,Y),X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(least_upper_bound(X_20,least_upper_bound(Y,X_20)),X_22)) )],[refute_0_706,refute_0_709]) ).
cnf(refute_0_711,plain,
least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(Y,X_21))) = least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(least_upper_bound(Y,X_21)))]]) ).
cnf(refute_0_712,plain,
least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y),
inference(subst,[],[refute_0_279:[bind(X_13,$fot(X_21))]]) ).
cnf(refute_0_713,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(Y,X_21))) != least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21))
| least_upper_bound(X_21,least_upper_bound(Y,X_21)) != least_upper_bound(X_21,Y)
| least_upper_bound(X_20,least_upper_bound(X_21,Y)) = least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(Y,X_21))),least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21))) ),[0,1],$fot(least_upper_bound(X_21,Y))]]) ).
cnf(refute_0_714,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(Y,X_21))) != least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21))
| least_upper_bound(X_20,least_upper_bound(X_21,Y)) = least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(Y,X_21)),least_upper_bound(X_21,Y)) )],[refute_0_712,refute_0_713]) ).
cnf(refute_0_715,plain,
least_upper_bound(X_20,least_upper_bound(X_21,Y)) = least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(Y,X_21))),least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21))) )],[refute_0_711,refute_0_714]) ).
cnf(refute_0_716,plain,
least_upper_bound(least_upper_bound(X_20,X_21),Y) = least_upper_bound(X_20,least_upper_bound(X_21,Y)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_717,plain,
least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)))]]) ).
cnf(refute_0_718,plain,
( least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y))
| least_upper_bound(least_upper_bound(X_20,X_21),Y) != least_upper_bound(X_20,least_upper_bound(X_21,Y))
| least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y))) ),[1,1],$fot(least_upper_bound(X_20,least_upper_bound(X_21,Y)))]]) ).
cnf(refute_0_719,plain,
( least_upper_bound(least_upper_bound(X_20,X_21),Y) != least_upper_bound(X_20,least_upper_bound(X_21,Y))
| least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y))) )],[refute_0_717,refute_0_718]) ).
cnf(refute_0_720,plain,
least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),Y),least_upper_bound(X_20,least_upper_bound(X_21,Y))) )],[refute_0_716,refute_0_719]) ).
cnf(refute_0_721,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_21)) != least_upper_bound(X_20,least_upper_bound(X_21,X))
| least_upper_bound(X_20,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(X_20,X_21)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_20,X_21)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,X))))]]) ).
cnf(refute_0_722,plain,
least_upper_bound(X_20,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,X_21)),least_upper_bound(X_20,least_upper_bound(X_21,X))) )],[refute_0_680,refute_0_721]) ).
cnf(refute_0_723,plain,
least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) = least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)),
inference(subst,[],[refute_0_722:[bind(X,$fot(X_21)),bind(X_20,$fot(least_upper_bound(X_20,X_21))),bind(X_21,$fot(Y))]]) ).
cnf(refute_0_724,plain,
( least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))
| least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) != least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y))
| least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)))),bind(Z0,$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))))]]) ).
cnf(refute_0_725,plain,
( least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))
| least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)),least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))) )],[refute_0_720,refute_0_725]) ).
cnf(refute_0_727,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,Y)) != least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21))
| least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))
| least_upper_bound(X_20,least_upper_bound(X_21,Y)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_20,least_upper_bound(X_21,Y)),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)))]]) ).
cnf(refute_0_728,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,Y)) != least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21))
| least_upper_bound(X_20,least_upper_bound(X_21,Y)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21)),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
least_upper_bound(X_20,least_upper_bound(X_21,Y)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,Y)),least_upper_bound(least_upper_bound(X_20,X_21),least_upper_bound(Y,X_21))) )],[refute_0_715,refute_0_728]) ).
cnf(refute_0_730,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,Y)) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) = least_upper_bound(X_20,least_upper_bound(X_21,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,Y)))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))))]]) ).
cnf(refute_0_731,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y))) = least_upper_bound(X_20,least_upper_bound(X_21,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,Y)),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,Y)))) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))) = least_upper_bound(Y,least_upper_bound(X_20,X_22)),
inference(subst,[],[refute_0_731:[bind(Y,$fot(X_22)),bind(X_20,$fot(Y)),bind(X_21,$fot(X_20))]]) ).
cnf(refute_0_733,plain,
least_upper_bound(least_upper_bound(Y,X_20),X_22) = least_upper_bound(Y,least_upper_bound(X_20,X_22)),
inference(subst,[],[refute_0_131:[bind(X,$fot(Y)),bind(Y,$fot(X_20)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_734,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)))]]) ).
cnf(refute_0_735,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22))
| least_upper_bound(least_upper_bound(Y,X_20),X_22) != least_upper_bound(Y,least_upper_bound(X_20,X_22))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_20,X_22)))]]) ).
cnf(refute_0_736,plain,
( least_upper_bound(least_upper_bound(Y,X_20),X_22) != least_upper_bound(Y,least_upper_bound(X_20,X_22))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_20),X_22),least_upper_bound(Y,least_upper_bound(X_20,X_22))) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
( least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))) != least_upper_bound(Y,least_upper_bound(X_20,X_22))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(Y,least_upper_bound(X_20,X_22)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_20,X_22))))]]) ).
cnf(refute_0_739,plain,
( least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))) != least_upper_bound(Y,least_upper_bound(X_20,X_22))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(Y,least_upper_bound(X_20,X_22)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22)))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) = least_upper_bound(Y,least_upper_bound(X_20,X_22)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_20,X_22))),least_upper_bound(Y,least_upper_bound(X_20,X_22))) )],[refute_0_732,refute_0_739]) ).
cnf(refute_0_741,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(Y,least_upper_bound(X_20,X_22))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(least_upper_bound(X_20,Y),X_22)
| least_upper_bound(Y,least_upper_bound(X_20,X_22)) = least_upper_bound(least_upper_bound(X_20,Y),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(least_upper_bound(X_20,Y),X_22)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_20,X_22)))]]) ).
cnf(refute_0_742,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(least_upper_bound(X_20,Y),X_22)
| least_upper_bound(Y,least_upper_bound(X_20,X_22)) = least_upper_bound(least_upper_bound(X_20,Y),X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(Y,least_upper_bound(X_20,X_22))) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
least_upper_bound(least_upper_bound(X_20,Y),X_22) = least_upper_bound(X_20,least_upper_bound(Y,X_22)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_20)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_744,plain,
( least_upper_bound(Y,least_upper_bound(X_20,X_22)) != least_upper_bound(least_upper_bound(X_20,Y),X_22)
| least_upper_bound(least_upper_bound(X_20,Y),X_22) != least_upper_bound(X_20,least_upper_bound(Y,X_22))
| least_upper_bound(Y,least_upper_bound(X_20,X_22)) = least_upper_bound(X_20,least_upper_bound(Y,X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_20,X_22)),least_upper_bound(X_20,least_upper_bound(Y,X_22))) ),[0],$fot(least_upper_bound(least_upper_bound(X_20,Y),X_22))]]) ).
cnf(refute_0_745,plain,
( least_upper_bound(Y,least_upper_bound(X_20,X_22)) != least_upper_bound(least_upper_bound(X_20,Y),X_22)
| least_upper_bound(Y,least_upper_bound(X_20,X_22)) = least_upper_bound(X_20,least_upper_bound(Y,X_22)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,Y),X_22),least_upper_bound(X_20,least_upper_bound(Y,X_22))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)) != least_upper_bound(least_upper_bound(X_20,Y),X_22)
| least_upper_bound(Y,least_upper_bound(X_20,X_22)) = least_upper_bound(X_20,least_upper_bound(Y,X_22)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_20,X_22)),least_upper_bound(least_upper_bound(X_20,Y),X_22)) )],[refute_0_742,refute_0_745]) ).
cnf(refute_0_747,plain,
least_upper_bound(Y,least_upper_bound(X_20,X_22)) = least_upper_bound(X_20,least_upper_bound(Y,X_22)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(Y,X_20),X_22)),least_upper_bound(least_upper_bound(X_20,Y),X_22)) )],[refute_0_710,refute_0_746]) ).
cnf(refute_0_748,plain,
least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))) = least_upper_bound(X_20,least_upper_bound(Y,multiply(X_93,Y))),
inference(subst,[],[refute_0_747:[bind(X_22,$fot(multiply(X_93,Y)))]]) ).
cnf(refute_0_749,plain,
multiply(least_upper_bound(X_93,identity),Y) = least_upper_bound(Y,multiply(X_93,Y)),
inference(subst,[],[refute_0_149:[bind(X_89,$fot(Y)),bind(X_90,$fot(X_93))]]) ).
cnf(refute_0_750,plain,
( multiply(least_upper_bound(X_93,identity),Y) != least_upper_bound(Y,multiply(X_93,Y))
| least_upper_bound(Y,multiply(X_93,Y)) = multiply(least_upper_bound(X_93,identity),Y) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_93,identity),Y))),bind(Y0,$fot(least_upper_bound(Y,multiply(X_93,Y))))]]) ).
cnf(refute_0_751,plain,
least_upper_bound(Y,multiply(X_93,Y)) = multiply(least_upper_bound(X_93,identity),Y),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_93,identity),Y),least_upper_bound(Y,multiply(X_93,Y))) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
( least_upper_bound(Y,multiply(X_93,Y)) != multiply(least_upper_bound(X_93,identity),Y)
| least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))) != least_upper_bound(X_20,least_upper_bound(Y,multiply(X_93,Y)))
| least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))) = least_upper_bound(X_20,multiply(least_upper_bound(X_93,identity),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))),least_upper_bound(X_20,least_upper_bound(Y,multiply(X_93,Y)))) ),[1,1],$fot(multiply(least_upper_bound(X_93,identity),Y))]]) ).
cnf(refute_0_753,plain,
( least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))) != least_upper_bound(X_20,least_upper_bound(Y,multiply(X_93,Y)))
| least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))) = least_upper_bound(X_20,multiply(least_upper_bound(X_93,identity),Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,multiply(X_93,Y)),multiply(least_upper_bound(X_93,identity),Y)) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))) = least_upper_bound(X_20,multiply(least_upper_bound(X_93,identity),Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_20,multiply(X_93,Y))),least_upper_bound(X_20,least_upper_bound(Y,multiply(X_93,Y)))) )],[refute_0_748,refute_0_753]) ).
cnf(refute_0_755,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)),
inference(subst,[],[refute_0_754:[bind(Y,$fot(X_19)),bind(X_20,$fot(X_19))]]) ).
cnf(refute_0_756,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)) != multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) != least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19))
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))))),bind(Y0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)))]]) ).
cnf(refute_0_757,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)) != multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))),least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19))) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_93,identity),X_19)),multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)) )],[refute_0_705,refute_0_757]) ).
cnf(refute_0_759,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) != multiply(least_upper_bound(identity,X_93),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) != multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(identity,X_93),X_19) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_93),X_19)))]]) ).
cnf(refute_0_760,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19) != multiply(least_upper_bound(identity,X_93),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(identity,X_93),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))),multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19)) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) = multiply(least_upper_bound(identity,X_93),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_93,identity)),X_19),multiply(least_upper_bound(identity,X_93),X_19)) )],[refute_0_656,refute_0_760]) ).
cnf(refute_0_762,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) != multiply(least_upper_bound(X_93,identity),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) != multiply(least_upper_bound(identity,X_93),X_19)
| multiply(least_upper_bound(identity,X_93),X_19) = multiply(least_upper_bound(X_93,identity),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))),multiply(least_upper_bound(X_93,identity),X_19)) ),[0],$fot(multiply(least_upper_bound(identity,X_93),X_19))]]) ).
cnf(refute_0_763,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))) != multiply(least_upper_bound(X_93,identity),X_19)
| multiply(least_upper_bound(identity,X_93),X_19) = multiply(least_upper_bound(X_93,identity),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))),multiply(least_upper_bound(identity,X_93),X_19)) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
multiply(least_upper_bound(identity,X_93),X_19) = multiply(least_upper_bound(X_93,identity),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_93,X_19))),multiply(least_upper_bound(X_93,identity),X_19)) )],[refute_0_651,refute_0_763]) ).
cnf(refute_0_765,plain,
( multiply(least_upper_bound(identity,X_93),X_19) != multiply(least_upper_bound(X_93,identity),X_19)
| multiply(least_upper_bound(X_93,identity),X_19) = multiply(least_upper_bound(identity,X_93),X_19) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(identity,X_93),X_19))),bind(Y0,$fot(multiply(least_upper_bound(X_93,identity),X_19)))]]) ).
cnf(refute_0_766,plain,
multiply(least_upper_bound(X_93,identity),X_19) = multiply(least_upper_bound(identity,X_93),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_93),X_19),multiply(least_upper_bound(X_93,identity),X_19)) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89),
inference(subst,[],[refute_0_766:[bind(X_19,$fot(X_89)),bind(X_93,$fot(least_upper_bound(inverse(X_89),X_97)))]]) ).
cnf(refute_0_768,plain,
( multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89))
| multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) != multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89)
| multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89))))]]) ).
cnf(refute_0_769,plain,
( multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89))
| multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89),multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89)) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(inverse(X_89),X_97)),X_89),least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89))) )],[refute_0_644,refute_0_769]) ).
cnf(refute_0_771,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) != least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89)))
| multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89))
| least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)) = least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89),least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89)))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)))]]) ).
cnf(refute_0_772,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89) != least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89)))
| least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)) = least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89),least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89))) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,X_97),X_89)) = least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_89),X_97),identity),X_89),least_upper_bound(X_89,least_upper_bound(identity,multiply(X_97,X_89)))) )],[refute_0_616,refute_0_772]) ).
cnf(refute_0_774,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) = least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,multiply(inverse(X_157),greatest_lower_bound(X_157,identity)))),
inference(subst,[],[refute_0_773:[bind(X_89,$fot(greatest_lower_bound(X_157,identity))),bind(X_97,$fot(inverse(X_157)))]]) ).
cnf(refute_0_775,plain,
multiply(X_153,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_153)),bind(Y,$fot(X_154)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_776,plain,
X_153 = multiply(X_153,identity),
inference(subst,[],[refute_0_49:[bind(X_48,$fot(X_153))]]) ).
cnf(refute_0_777,plain,
( X_153 != multiply(X_153,identity)
| multiply(X_153,identity) = X_153 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_153)),bind(Y0,$fot(multiply(X_153,identity)))]]) ).
cnf(refute_0_778,plain,
multiply(X_153,identity) = X_153,
inference(resolve,[$cnf( $equal(X_153,multiply(X_153,identity)) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
( multiply(X_153,greatest_lower_bound(X_154,identity)) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,identity))
| multiply(X_153,identity) != X_153
| multiply(X_153,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(multiply(X_153,X_154),X_153) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,identity)),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,identity))) ),[1,1],$fot(X_153)]]) ).
cnf(refute_0_780,plain,
( multiply(X_153,greatest_lower_bound(X_154,identity)) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,identity))
| multiply(X_153,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(multiply(X_153,X_154),X_153) ),
inference(resolve,[$cnf( $equal(multiply(X_153,identity),X_153) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
multiply(X_153,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(multiply(X_153,X_154),X_153),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,identity)),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,identity))) )],[refute_0_775,refute_0_780]) ).
cnf(refute_0_782,plain,
greatest_lower_bound(multiply(X_153,X_154),X_153) = greatest_lower_bound(X_153,multiply(X_153,X_154)),
inference(subst,[],[refute_0_106:[bind(X,$fot(X_153)),bind(Y,$fot(multiply(X_153,X_154)))]]) ).
cnf(refute_0_783,plain,
( multiply(X_153,greatest_lower_bound(X_154,identity)) != greatest_lower_bound(multiply(X_153,X_154),X_153)
| greatest_lower_bound(multiply(X_153,X_154),X_153) != greatest_lower_bound(X_153,multiply(X_153,X_154))
| multiply(X_153,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(X_153,multiply(X_153,X_154)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_153,greatest_lower_bound(X_154,identity)),greatest_lower_bound(X_153,multiply(X_153,X_154))) ),[0],$fot(greatest_lower_bound(multiply(X_153,X_154),X_153))]]) ).
cnf(refute_0_784,plain,
( multiply(X_153,greatest_lower_bound(X_154,identity)) != greatest_lower_bound(multiply(X_153,X_154),X_153)
| multiply(X_153,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(X_153,multiply(X_153,X_154)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),X_153),greatest_lower_bound(X_153,multiply(X_153,X_154))) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
multiply(X_153,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(X_153,multiply(X_153,X_154)),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,identity)),greatest_lower_bound(multiply(X_153,X_154),X_153)) )],[refute_0_781,refute_0_784]) ).
cnf(refute_0_786,plain,
multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) = greatest_lower_bound(inverse(X_157),multiply(inverse(X_157),X_157)),
inference(subst,[],[refute_0_785:[bind(X_153,$fot(inverse(X_157))),bind(X_154,$fot(X_157))]]) ).
cnf(refute_0_787,plain,
multiply(inverse(X_157),X_157) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_157))]]) ).
cnf(refute_0_788,plain,
( multiply(inverse(X_157),X_157) != identity
| multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) != greatest_lower_bound(inverse(X_157),multiply(inverse(X_157),X_157))
| multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) = greatest_lower_bound(inverse(X_157),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_157),greatest_lower_bound(X_157,identity)),greatest_lower_bound(inverse(X_157),multiply(inverse(X_157),X_157))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_789,plain,
( multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) != greatest_lower_bound(inverse(X_157),multiply(inverse(X_157),X_157))
| multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) = greatest_lower_bound(inverse(X_157),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_157),X_157),identity) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) = greatest_lower_bound(inverse(X_157),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_157),greatest_lower_bound(X_157,identity)),greatest_lower_bound(inverse(X_157),multiply(inverse(X_157),X_157))) )],[refute_0_786,refute_0_789]) ).
cnf(refute_0_791,plain,
greatest_lower_bound(inverse(X_157),identity) = greatest_lower_bound(identity,inverse(X_157)),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_157)))]]) ).
cnf(refute_0_792,plain,
( multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) != greatest_lower_bound(inverse(X_157),identity)
| greatest_lower_bound(inverse(X_157),identity) != greatest_lower_bound(identity,inverse(X_157))
| multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) = greatest_lower_bound(identity,inverse(X_157)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_157),greatest_lower_bound(X_157,identity)),greatest_lower_bound(identity,inverse(X_157))) ),[0],$fot(greatest_lower_bound(inverse(X_157),identity))]]) ).
cnf(refute_0_793,plain,
( multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) != greatest_lower_bound(inverse(X_157),identity)
| multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) = greatest_lower_bound(identity,inverse(X_157)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_157),identity),greatest_lower_bound(identity,inverse(X_157))) )],[refute_0_791,refute_0_792]) ).
cnf(refute_0_794,plain,
multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) = greatest_lower_bound(identity,inverse(X_157)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_157),greatest_lower_bound(X_157,identity)),greatest_lower_bound(inverse(X_157),identity)) )],[refute_0_790,refute_0_793]) ).
cnf(refute_0_795,plain,
( multiply(inverse(X_157),greatest_lower_bound(X_157,identity)) != greatest_lower_bound(identity,inverse(X_157))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) != least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,multiply(inverse(X_157),greatest_lower_bound(X_157,identity))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) = least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))),least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,multiply(inverse(X_157),greatest_lower_bound(X_157,identity))))) ),[1,1,1],$fot(greatest_lower_bound(identity,inverse(X_157)))]]) ).
cnf(refute_0_796,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) != least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,multiply(inverse(X_157),greatest_lower_bound(X_157,identity))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) = least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_157),greatest_lower_bound(X_157,identity)),greatest_lower_bound(identity,inverse(X_157))) )],[refute_0_794,refute_0_795]) ).
cnf(refute_0_797,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) = least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))),least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,multiply(inverse(X_157),greatest_lower_bound(X_157,identity))))) )],[refute_0_774,refute_0_796]) ).
cnf(refute_0_798,plain,
least_upper_bound(identity,greatest_lower_bound(X_157,identity)) = identity,
inference(subst,[],[refute_0_270:[bind(X_10,$fot(identity)),bind(X_11,$fot(X_157))]]) ).
cnf(refute_0_799,plain,
least_upper_bound(X_83,X_84) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),
inference(subst,[],[refute_0_417:[bind(X_46,$fot(least_upper_bound(X_83,X_84))),bind(X_95,$fot(inverse(X_84)))]]) ).
cnf(refute_0_800,plain,
( multiply(inverse(X_84),least_upper_bound(X_83,X_84)) != least_upper_bound(identity,multiply(inverse(X_84),X_83))
| least_upper_bound(X_83,X_84) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(X_83,X_84))))
| least_upper_bound(X_83,X_84) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_83,X_84),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(X_83,X_84))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_801,plain,
( least_upper_bound(X_83,X_84) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(X_83,X_84))))
| least_upper_bound(X_83,X_84) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_83,X_84)),least_upper_bound(identity,multiply(inverse(X_84),X_83))) )],[refute_0_67,refute_0_800]) ).
cnf(refute_0_802,plain,
least_upper_bound(X_83,X_84) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_83,X_84),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(X_83,X_84))))) )],[refute_0_799,refute_0_801]) ).
cnf(refute_0_803,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(identity,multiply(inverse(X_84),X_83)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(multiply(inverse(X_84),X_83))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_804,plain,
multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))))]]) ).
cnf(refute_0_805,plain,
( multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))) != least_upper_bound(identity,multiply(inverse(X_84),X_83))
| multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_806,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))) != least_upper_bound(identity,multiply(inverse(X_84),X_83))
| multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) )],[refute_0_803,refute_0_806]) ).
cnf(refute_0_808,plain,
( multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| least_upper_bound(X_83,X_84) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))))
| least_upper_bound(X_83,X_84) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_83,X_84),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))))) ),[1],$fot(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))))]]) ).
cnf(refute_0_809,plain,
( least_upper_bound(X_83,X_84) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))))
| least_upper_bound(X_83,X_84) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83)))),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
least_upper_bound(X_83,X_84) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_83,X_84),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_84),X_83))))) )],[refute_0_802,refute_0_809]) ).
cnf(refute_0_811,plain,
multiply(X_84,identity) = X_84,
inference(subst,[],[refute_0_51:[bind(X_48,$fot(X_84))]]) ).
cnf(refute_0_812,plain,
least_upper_bound(multiply(X_84,identity),X_83) = least_upper_bound(multiply(X_84,identity),X_83),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_84,identity),X_83))]]) ).
cnf(refute_0_813,plain,
( multiply(X_84,identity) != X_84
| least_upper_bound(multiply(X_84,identity),X_83) != least_upper_bound(multiply(X_84,identity),X_83)
| least_upper_bound(multiply(X_84,identity),X_83) = least_upper_bound(X_84,X_83) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_84,identity),X_83),least_upper_bound(multiply(X_84,identity),X_83)) ),[1,0],$fot(X_84)]]) ).
cnf(refute_0_814,plain,
( multiply(X_84,identity) != X_84
| least_upper_bound(multiply(X_84,identity),X_83) = least_upper_bound(X_84,X_83) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,identity),X_83),least_upper_bound(multiply(X_84,identity),X_83)) )],[refute_0_812,refute_0_813]) ).
cnf(refute_0_815,plain,
least_upper_bound(multiply(X_84,identity),X_83) = least_upper_bound(X_84,X_83),
inference(resolve,[$cnf( $equal(multiply(X_84,identity),X_84) )],[refute_0_811,refute_0_814]) ).
cnf(refute_0_816,plain,
multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))) = least_upper_bound(multiply(X_82,X_83),multiply(X_82,multiply(inverse(X_82),X_46))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(multiply(inverse(X_82),X_46)))]]) ).
cnf(refute_0_817,plain,
X_46 = multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46)),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(inverse(X_50)))]]) ).
cnf(refute_0_818,plain,
multiply(X_50,multiply(inverse(X_50),X_46)) = multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46)),
inference(subst,[],[refute_0_22:[bind(X_47,$fot(X_50)),bind(X_48,$fot(multiply(inverse(X_50),X_46)))]]) ).
cnf(refute_0_819,plain,
( multiply(X_50,multiply(inverse(X_50),X_46)) != multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46))
| multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46)) = multiply(X_50,multiply(inverse(X_50),X_46)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_50,multiply(inverse(X_50),X_46)))),bind(Y0,$fot(multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46))))]]) ).
cnf(refute_0_820,plain,
multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46)) = multiply(X_50,multiply(inverse(X_50),X_46)),
inference(resolve,[$cnf( $equal(multiply(X_50,multiply(inverse(X_50),X_46)),multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46))) )],[refute_0_818,refute_0_819]) ).
cnf(refute_0_821,plain,
( X_46 != multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46))
| multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46)) != multiply(X_50,multiply(inverse(X_50),X_46))
| X_46 = multiply(X_50,multiply(inverse(X_50),X_46)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_46,multiply(X_50,multiply(inverse(X_50),X_46))) ),[0],$fot(multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46)))]]) ).
cnf(refute_0_822,plain,
( X_46 != multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46))
| X_46 = multiply(X_50,multiply(inverse(X_50),X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46)),multiply(X_50,multiply(inverse(X_50),X_46))) )],[refute_0_820,refute_0_821]) ).
cnf(refute_0_823,plain,
X_46 = multiply(X_50,multiply(inverse(X_50),X_46)),
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(inverse(X_50)),multiply(inverse(X_50),X_46))) )],[refute_0_817,refute_0_822]) ).
cnf(refute_0_824,plain,
X_46 = multiply(X_82,multiply(inverse(X_82),X_46)),
inference(subst,[],[refute_0_823:[bind(X_50,$fot(X_82))]]) ).
cnf(refute_0_825,plain,
( X_46 != multiply(X_82,multiply(inverse(X_82),X_46))
| multiply(X_82,multiply(inverse(X_82),X_46)) = X_46 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(X_82,multiply(inverse(X_82),X_46))))]]) ).
cnf(refute_0_826,plain,
multiply(X_82,multiply(inverse(X_82),X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(X_82,multiply(inverse(X_82),X_46))) )],[refute_0_824,refute_0_825]) ).
cnf(refute_0_827,plain,
( multiply(X_82,multiply(inverse(X_82),X_46)) != X_46
| multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,multiply(inverse(X_82),X_46)))
| multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))) = least_upper_bound(multiply(X_82,X_83),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))),least_upper_bound(multiply(X_82,X_83),multiply(X_82,multiply(inverse(X_82),X_46)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_828,plain,
( multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,multiply(inverse(X_82),X_46)))
| multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))) = least_upper_bound(multiply(X_82,X_83),X_46) ),
inference(resolve,[$cnf( $equal(multiply(X_82,multiply(inverse(X_82),X_46)),X_46) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))) = least_upper_bound(multiply(X_82,X_83),X_46),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,multiply(inverse(X_82),X_46))),least_upper_bound(multiply(X_82,X_83),multiply(X_82,multiply(inverse(X_82),X_46)))) )],[refute_0_816,refute_0_828]) ).
cnf(refute_0_830,plain,
multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(multiply(X_84,identity),X_83),
inference(subst,[],[refute_0_829:[bind(X_46,$fot(X_83)),bind(X_82,$fot(X_84)),bind(X_83,$fot(identity))]]) ).
cnf(refute_0_831,plain,
( multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) != least_upper_bound(multiply(X_84,identity),X_83)
| least_upper_bound(multiply(X_84,identity),X_83) != least_upper_bound(X_84,X_83)
| multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(X_84,X_83) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))))),bind(Y0,$fot(least_upper_bound(multiply(X_84,identity),X_83))),bind(Z0,$fot(least_upper_bound(X_84,X_83)))]]) ).
cnf(refute_0_832,plain,
( least_upper_bound(multiply(X_84,identity),X_83) != least_upper_bound(X_84,X_83)
| multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(X_84,X_83) ),
inference(resolve,[$cnf( $equal(multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))),least_upper_bound(multiply(X_84,identity),X_83)) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(X_84,X_83),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,identity),X_83),least_upper_bound(X_84,X_83)) )],[refute_0_815,refute_0_832]) ).
cnf(refute_0_834,plain,
inverse(inverse(X_84)) = X_84,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_84))]]) ).
cnf(refute_0_835,plain,
inverse(X_240) = multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))),
inference(subst,[],[refute_0_495:[bind(X_69,$fot(X_240)),bind(X_95,$fot(inverse(least_upper_bound(X_240,X_18))))]]) ).
cnf(refute_0_836,plain,
multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,least_upper_bound(X_85,X_18))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85)),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(X_85)),bind(X_84,$fot(least_upper_bound(X_85,X_18)))]]) ).
cnf(refute_0_837,plain,
least_upper_bound(X_85,least_upper_bound(X_85,X_18)) = least_upper_bound(X_85,X_18),
inference(subst,[],[refute_0_426:[bind(X_19,$fot(X_85))]]) ).
cnf(refute_0_838,plain,
( multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,least_upper_bound(X_85,X_18))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))
| least_upper_bound(X_85,least_upper_bound(X_85,X_18)) != least_upper_bound(X_85,X_18)
| multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,least_upper_bound(X_85,X_18))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))) ),[0,1],$fot(least_upper_bound(X_85,X_18))]]) ).
cnf(refute_0_839,plain,
( multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,least_upper_bound(X_85,X_18))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))
| multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_85,least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) )],[refute_0_837,refute_0_838]) ).
cnf(refute_0_840,plain,
multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,least_upper_bound(X_85,X_18))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))) )],[refute_0_836,refute_0_839]) ).
cnf(refute_0_841,plain,
multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_85,X_18)))]]) ).
cnf(refute_0_842,plain,
( multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) != identity
| multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))) ),[0],$fot(identity)]]) ).
cnf(refute_0_843,plain,
( multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)),identity) )],[refute_0_841,refute_0_842]) ).
cnf(refute_0_844,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_18)),least_upper_bound(X_85,X_18)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_85,X_18)),X_85))) )],[refute_0_840,refute_0_843]) ).
cnf(refute_0_845,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240)),
inference(subst,[],[refute_0_844:[bind(X_85,$fot(X_240))]]) ).
cnf(refute_0_846,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240)) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))))]]) ).
cnf(refute_0_847,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
( inverse(X_240) != multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240)) != identity
| inverse(X_240) = multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_240),multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_849,plain,
( inverse(X_240) != multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))
| inverse(X_240) = multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240)),identity) )],[refute_0_847,refute_0_848]) ).
cnf(refute_0_850,plain,
inverse(X_240) = multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))),
inference(resolve,[$cnf( $equal(inverse(X_240),multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_240,X_18)),X_240))),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))) )],[refute_0_835,refute_0_849]) ).
cnf(refute_0_851,plain,
multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))))]]) ).
cnf(refute_0_852,plain,
multiply(inverse(identity),identity) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_853,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_49:[bind(X_48,$fot(inverse(identity)))]]) ).
cnf(refute_0_854,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_855,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
( multiply(inverse(identity),identity) != identity
| multiply(inverse(identity),identity) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_857,plain,
( multiply(inverse(identity),identity) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_852,refute_0_857]) ).
cnf(refute_0_859,plain,
multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))))]]) ).
cnf(refute_0_860,plain,
( multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) != multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_861,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_861]) ).
cnf(refute_0_863,plain,
( multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) != least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))
| multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) != multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))
| multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))))),bind(Z0,$fot(least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))))]]) ).
cnf(refute_0_864,plain,
( multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) != least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))
| multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) )],[refute_0_851,refute_0_864]) ).
cnf(refute_0_866,plain,
multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) = multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),
inference(subst,[],[refute_0_320:[bind(X,$fot(inverse(identity))),bind(Y,$fot(inverse(X_240))),bind(Z,$fot(inverse(least_upper_bound(X_240,X_18))))]]) ).
cnf(refute_0_867,plain,
( multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) != least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))
| multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) != multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))
| multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))))),bind(Z0,$fot(least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))))]]) ).
cnf(refute_0_868,plain,
( multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) != least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))
| multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))),multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))) )],[refute_0_866,refute_0_867]) ).
cnf(refute_0_869,plain,
multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) )],[refute_0_865,refute_0_868]) ).
cnf(refute_0_870,plain,
( multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))) != least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))
| inverse(X_240) != multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))
| inverse(X_240) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_240),multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))) ),[1],$fot(least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))))]]) ).
cnf(refute_0_871,plain,
( inverse(X_240) != multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))
| inverse(X_240) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240))),least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18)))) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
inverse(X_240) = least_upper_bound(inverse(X_240),inverse(least_upper_bound(X_240,X_18))),
inference(resolve,[$cnf( $equal(inverse(X_240),multiply(inverse(identity),least_upper_bound(inverse(least_upper_bound(X_240,X_18)),inverse(X_240)))) )],[refute_0_850,refute_0_871]) ).
cnf(refute_0_873,plain,
inverse(X_332) = least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_332,X_331))),
inference(subst,[],[refute_0_872:[bind(X_18,$fot(X_331)),bind(X_240,$fot(X_332))]]) ).
cnf(refute_0_874,plain,
least_upper_bound(X_331,X_332) = least_upper_bound(X_332,X_331),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_331)),bind(Y,$fot(X_332))]]) ).
cnf(refute_0_875,plain,
( least_upper_bound(X_331,X_332) != least_upper_bound(X_332,X_331)
| least_upper_bound(X_332,X_331) = least_upper_bound(X_331,X_332) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_331,X_332))),bind(Y0,$fot(least_upper_bound(X_332,X_331)))]]) ).
cnf(refute_0_876,plain,
least_upper_bound(X_332,X_331) = least_upper_bound(X_331,X_332),
inference(resolve,[$cnf( $equal(least_upper_bound(X_331,X_332),least_upper_bound(X_332,X_331)) )],[refute_0_874,refute_0_875]) ).
cnf(refute_0_877,plain,
( inverse(X_332) != least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_332,X_331)))
| least_upper_bound(X_332,X_331) != least_upper_bound(X_331,X_332)
| inverse(X_332) = least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_332),least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_332,X_331)))) ),[1,1,0],$fot(least_upper_bound(X_331,X_332))]]) ).
cnf(refute_0_878,plain,
( inverse(X_332) != least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_332,X_331)))
| inverse(X_332) = least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_332,X_331),least_upper_bound(X_331,X_332)) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
inverse(X_332) = least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332))),
inference(resolve,[$cnf( $equal(inverse(X_332),least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_332,X_331)))) )],[refute_0_873,refute_0_878]) ).
cnf(refute_0_880,plain,
( inverse(X_332) != least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332)))
| least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332))) = inverse(X_332) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(X_332))),bind(Y0,$fot(least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332)))))]]) ).
cnf(refute_0_881,plain,
least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332))) = inverse(X_332),
inference(resolve,[$cnf( $equal(inverse(X_332),least_upper_bound(inverse(X_332),inverse(least_upper_bound(X_331,X_332)))) )],[refute_0_879,refute_0_880]) ).
cnf(refute_0_882,plain,
least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84))) = inverse(X_84),
inference(subst,[],[refute_0_881:[bind(X_331,$fot(X_83)),bind(X_332,$fot(X_84))]]) ).
cnf(refute_0_883,plain,
inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) = inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))))]]) ).
cnf(refute_0_884,plain,
( inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) != inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84))))
| least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84))) != inverse(X_84)
| inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) = inverse(inverse(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84))))) ),[1,0],$fot(inverse(X_84))]]) ).
cnf(refute_0_885,plain,
( least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84))) != inverse(X_84)
| inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) = inverse(inverse(X_84)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84))))) )],[refute_0_883,refute_0_884]) ).
cnf(refute_0_886,plain,
inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) = inverse(inverse(X_84)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84))),inverse(X_84)) )],[refute_0_882,refute_0_885]) ).
cnf(refute_0_887,plain,
( inverse(inverse(X_84)) != X_84
| inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) != inverse(inverse(X_84))
| inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) = X_84 ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))))),bind(Y0,$fot(inverse(inverse(X_84)))),bind(Z0,$fot(X_84))]]) ).
cnf(refute_0_888,plain,
( inverse(inverse(X_84)) != X_84
| inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) = X_84 ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),inverse(inverse(X_84))) )],[refute_0_886,refute_0_887]) ).
cnf(refute_0_889,plain,
inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) = X_84,
inference(resolve,[$cnf( $equal(inverse(inverse(X_84)),X_84) )],[refute_0_834,refute_0_888]) ).
cnf(refute_0_890,plain,
multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))))]]) ).
cnf(refute_0_891,plain,
( multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) != X_84
| multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))) ),[1,0],$fot(X_84)]]) ).
cnf(refute_0_892,plain,
( inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))) != X_84
| multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),X_84) )],[refute_0_889,refute_0_892]) ).
cnf(refute_0_894,plain,
( multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) != least_upper_bound(X_84,X_83)
| multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) != multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(X_84,X_83) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))))),bind(Y0,$fot(multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))))),bind(Z0,$fot(least_upper_bound(X_84,X_83)))]]) ).
cnf(refute_0_895,plain,
( multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))) != least_upper_bound(X_84,X_83)
| multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(X_84,X_83) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83)))) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) = least_upper_bound(X_84,X_83),
inference(resolve,[$cnf( $equal(multiply(X_84,least_upper_bound(identity,multiply(inverse(X_84),X_83))),least_upper_bound(X_84,X_83)) )],[refute_0_833,refute_0_895]) ).
cnf(refute_0_897,plain,
( multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))) != least_upper_bound(X_84,X_83)
| least_upper_bound(X_83,X_84) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| least_upper_bound(X_83,X_84) = least_upper_bound(X_84,X_83) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_83,X_84),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))) ),[1],$fot(least_upper_bound(X_84,X_83))]]) ).
cnf(refute_0_898,plain,
( least_upper_bound(X_83,X_84) != multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| least_upper_bound(X_83,X_84) = least_upper_bound(X_84,X_83) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83))),least_upper_bound(X_84,X_83)) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
least_upper_bound(X_83,X_84) = least_upper_bound(X_84,X_83),
inference(resolve,[$cnf( $equal(least_upper_bound(X_83,X_84),multiply(inverse(least_upper_bound(inverse(X_84),inverse(least_upper_bound(X_83,X_84)))),least_upper_bound(identity,multiply(inverse(X_84),X_83)))) )],[refute_0_810,refute_0_898]) ).
cnf(refute_0_900,plain,
( least_upper_bound(X_83,X_84) != least_upper_bound(X_84,X_83)
| least_upper_bound(X_84,X_83) = least_upper_bound(X_83,X_84) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_83,X_84))),bind(Y0,$fot(least_upper_bound(X_84,X_83)))]]) ).
cnf(refute_0_901,plain,
least_upper_bound(X_84,X_83) = least_upper_bound(X_83,X_84),
inference(resolve,[$cnf( $equal(least_upper_bound(X_83,X_84),least_upper_bound(X_84,X_83)) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
least_upper_bound(greatest_lower_bound(X_157,identity),identity) = least_upper_bound(identity,greatest_lower_bound(X_157,identity)),
inference(subst,[],[refute_0_901:[bind(X_83,$fot(identity)),bind(X_84,$fot(greatest_lower_bound(X_157,identity)))]]) ).
cnf(refute_0_903,plain,
( least_upper_bound(greatest_lower_bound(X_157,identity),identity) != least_upper_bound(identity,greatest_lower_bound(X_157,identity))
| least_upper_bound(identity,greatest_lower_bound(X_157,identity)) != identity
| least_upper_bound(greatest_lower_bound(X_157,identity),identity) = identity ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_157,identity),identity))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(X_157,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_904,plain,
( least_upper_bound(identity,greatest_lower_bound(X_157,identity)) != identity
| least_upper_bound(greatest_lower_bound(X_157,identity),identity) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_157,identity),identity),least_upper_bound(identity,greatest_lower_bound(X_157,identity))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
least_upper_bound(greatest_lower_bound(X_157,identity),identity) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_157,identity)),identity) )],[refute_0_798,refute_0_904]) ).
cnf(refute_0_906,plain,
least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_32,Y))),
inference(subst,[],[refute_0_680:[bind(X,$fot(greatest_lower_bound(X_32,Y))),bind(X_20,$fot(X_31)),bind(X_21,$fot(X_32))]]) ).
cnf(refute_0_907,plain,
least_upper_bound(X_32,greatest_lower_bound(X_32,Y)) = X_32,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_908,plain,
( least_upper_bound(X_32,greatest_lower_bound(X_32,Y)) != X_32
| least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_32,Y)))
| least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_32,Y)))) ),[1,1],$fot(X_32)]]) ).
cnf(refute_0_909,plain,
( least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_32,Y)))
| least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,X_32) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,greatest_lower_bound(X_32,Y)),X_32) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,X_32),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,greatest_lower_bound(X_32,Y)))) )],[refute_0_906,refute_0_909]) ).
cnf(refute_0_911,plain,
least_upper_bound(X_30,least_upper_bound(X_31,least_upper_bound(Y,X_31))) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)),
inference(subst,[],[refute_0_680:[bind(X,$fot(X_30)),bind(X_20,$fot(X_31)),bind(X_21,$fot(least_upper_bound(Y,X_31)))]]) ).
cnf(refute_0_912,plain,
least_upper_bound(X_31,least_upper_bound(Y,X_31)) = least_upper_bound(X_31,Y),
inference(subst,[],[refute_0_279:[bind(X_13,$fot(X_31))]]) ).
cnf(refute_0_913,plain,
( least_upper_bound(X_30,least_upper_bound(X_31,least_upper_bound(Y,X_31))) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))
| least_upper_bound(X_31,least_upper_bound(Y,X_31)) != least_upper_bound(X_31,Y)
| least_upper_bound(X_30,least_upper_bound(X_31,Y)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_31,least_upper_bound(Y,X_31))),least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))) ),[0,1],$fot(least_upper_bound(X_31,Y))]]) ).
cnf(refute_0_914,plain,
( least_upper_bound(X_30,least_upper_bound(X_31,least_upper_bound(Y,X_31))) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))
| least_upper_bound(X_30,least_upper_bound(X_31,Y)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(Y,X_31)),least_upper_bound(X_31,Y)) )],[refute_0_912,refute_0_913]) ).
cnf(refute_0_915,plain,
least_upper_bound(X_30,least_upper_bound(X_31,Y)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_31,least_upper_bound(Y,X_31))),least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))) )],[refute_0_911,refute_0_914]) ).
cnf(refute_0_916,plain,
least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))) = least_upper_bound(Y,least_upper_bound(X_31,X_30)),
inference(subst,[],[refute_0_731:[bind(Y,$fot(X_30)),bind(X_20,$fot(Y)),bind(X_21,$fot(X_31))]]) ).
cnf(refute_0_917,plain,
least_upper_bound(least_upper_bound(Y,X_31),X_30) = least_upper_bound(Y,least_upper_bound(X_31,X_30)),
inference(subst,[],[refute_0_131:[bind(X,$fot(Y)),bind(Y,$fot(X_31)),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_918,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) = least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)))]]) ).
cnf(refute_0_919,plain,
( least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))
| least_upper_bound(least_upper_bound(Y,X_31),X_30) != least_upper_bound(Y,least_upper_bound(X_31,X_30))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) = least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)),least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_31,X_30)))]]) ).
cnf(refute_0_920,plain,
( least_upper_bound(least_upper_bound(Y,X_31),X_30) != least_upper_bound(Y,least_upper_bound(X_31,X_30))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) = least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)),least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))) )],[refute_0_918,refute_0_919]) ).
cnf(refute_0_921,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) = least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_31),X_30),least_upper_bound(Y,least_upper_bound(X_31,X_30))) )],[refute_0_917,refute_0_920]) ).
cnf(refute_0_922,plain,
( least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))) != least_upper_bound(Y,least_upper_bound(X_31,X_30))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) != least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30)))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) = least_upper_bound(Y,least_upper_bound(X_31,X_30)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)))),bind(Y0,$fot(least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_31,X_30))))]]) ).
cnf(refute_0_923,plain,
( least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))) != least_upper_bound(Y,least_upper_bound(X_31,X_30))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) = least_upper_bound(Y,least_upper_bound(X_31,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)),least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30)))) )],[refute_0_921,refute_0_922]) ).
cnf(refute_0_924,plain,
least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) = least_upper_bound(Y,least_upper_bound(X_31,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(Y,least_upper_bound(X_31,X_30))),least_upper_bound(Y,least_upper_bound(X_31,X_30))) )],[refute_0_916,refute_0_923]) ).
cnf(refute_0_925,plain,
( least_upper_bound(X_30,least_upper_bound(X_31,Y)) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))
| least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)) != least_upper_bound(Y,least_upper_bound(X_31,X_30))
| least_upper_bound(X_30,least_upper_bound(X_31,Y)) = least_upper_bound(Y,least_upper_bound(X_31,X_30)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_30,least_upper_bound(X_31,Y)),least_upper_bound(Y,least_upper_bound(X_31,X_30))) ),[0],$fot(least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)))]]) ).
cnf(refute_0_926,plain,
( least_upper_bound(X_30,least_upper_bound(X_31,Y)) != least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))
| least_upper_bound(X_30,least_upper_bound(X_31,Y)) = least_upper_bound(Y,least_upper_bound(X_31,X_30)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30)),least_upper_bound(Y,least_upper_bound(X_31,X_30))) )],[refute_0_924,refute_0_925]) ).
cnf(refute_0_927,plain,
least_upper_bound(X_30,least_upper_bound(X_31,Y)) = least_upper_bound(Y,least_upper_bound(X_31,X_30)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_31,Y)),least_upper_bound(X_31,least_upper_bound(least_upper_bound(Y,X_31),X_30))) )],[refute_0_915,refute_0_926]) ).
cnf(refute_0_928,plain,
( least_upper_bound(X_30,least_upper_bound(X_31,Y)) != least_upper_bound(Y,least_upper_bound(X_31,X_30))
| least_upper_bound(Y,least_upper_bound(X_31,X_30)) = least_upper_bound(X_30,least_upper_bound(X_31,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_30,least_upper_bound(X_31,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_31,X_30))))]]) ).
cnf(refute_0_929,plain,
least_upper_bound(Y,least_upper_bound(X_31,X_30)) = least_upper_bound(X_30,least_upper_bound(X_31,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_31,Y)),least_upper_bound(Y,least_upper_bound(X_31,X_30))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,greatest_lower_bound(X_32,Y))),
inference(subst,[],[refute_0_929:[bind(Y,$fot(greatest_lower_bound(X_32,Y))),bind(X_30,$fot(X_32))]]) ).
cnf(refute_0_931,plain,
( least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,X_32)
| least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,least_upper_bound(X_31,greatest_lower_bound(X_32,Y)))
| least_upper_bound(X_32,least_upper_bound(X_31,greatest_lower_bound(X_32,Y))) = least_upper_bound(X_31,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,X_32)) ),[0],$fot(least_upper_bound(X_32,least_upper_bound(X_31,greatest_lower_bound(X_32,Y))))]]) ).
cnf(refute_0_932,plain,
( least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,X_32)
| least_upper_bound(X_32,least_upper_bound(X_31,greatest_lower_bound(X_32,Y))) = least_upper_bound(X_31,X_32) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)),least_upper_bound(X_32,least_upper_bound(X_31,greatest_lower_bound(X_32,Y)))) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
least_upper_bound(X_32,least_upper_bound(X_31,greatest_lower_bound(X_32,Y))) = least_upper_bound(X_31,X_32),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_32,Y),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,X_32)) )],[refute_0_910,refute_0_932]) ).
cnf(refute_0_934,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))) = least_upper_bound(greatest_lower_bound(X_157,identity),identity),
inference(subst,[],[refute_0_933:[bind(Y,$fot(inverse(X_157))),bind(X_31,$fot(greatest_lower_bound(X_157,identity))),bind(X_32,$fot(identity))]]) ).
cnf(refute_0_935,plain,
( least_upper_bound(greatest_lower_bound(X_157,identity),identity) != identity
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))) != least_upper_bound(greatest_lower_bound(X_157,identity),identity)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))) = identity ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_157,identity),identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_936,plain,
( least_upper_bound(greatest_lower_bound(X_157,identity),identity) != identity
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))),least_upper_bound(greatest_lower_bound(X_157,identity),identity)) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_157,identity),identity),identity) )],[refute_0_905,refute_0_936]) ).
cnf(refute_0_938,plain,
least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_20,X_21),X_13)) = least_upper_bound(X_13,least_upper_bound(X_20,X_21)),
inference(subst,[],[refute_0_279:[bind(Y,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_939,plain,
least_upper_bound(X_20,least_upper_bound(X_21,X_13)) = least_upper_bound(least_upper_bound(X_20,X_21),X_13),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_940,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,X_13)) != least_upper_bound(least_upper_bound(X_20,X_21),X_13)
| least_upper_bound(least_upper_bound(X_20,X_21),X_13) = least_upper_bound(X_20,least_upper_bound(X_21,X_13)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,X_13)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_20,X_21),X_13)))]]) ).
cnf(refute_0_941,plain,
least_upper_bound(least_upper_bound(X_20,X_21),X_13) = least_upper_bound(X_20,least_upper_bound(X_21,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,X_13)),least_upper_bound(least_upper_bound(X_20,X_21),X_13)) )],[refute_0_939,refute_0_940]) ).
cnf(refute_0_942,plain,
( least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_20,X_21),X_13)) != least_upper_bound(X_13,least_upper_bound(X_20,X_21))
| least_upper_bound(least_upper_bound(X_20,X_21),X_13) != least_upper_bound(X_20,least_upper_bound(X_21,X_13))
| least_upper_bound(X_13,least_upper_bound(X_20,least_upper_bound(X_21,X_13))) = least_upper_bound(X_13,least_upper_bound(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_20,X_21),X_13)),least_upper_bound(X_13,least_upper_bound(X_20,X_21))) ),[0,1],$fot(least_upper_bound(X_20,least_upper_bound(X_21,X_13)))]]) ).
cnf(refute_0_943,plain,
( least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_20,X_21),X_13)) != least_upper_bound(X_13,least_upper_bound(X_20,X_21))
| least_upper_bound(X_13,least_upper_bound(X_20,least_upper_bound(X_21,X_13))) = least_upper_bound(X_13,least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),X_13),least_upper_bound(X_20,least_upper_bound(X_21,X_13))) )],[refute_0_941,refute_0_942]) ).
cnf(refute_0_944,plain,
least_upper_bound(X_13,least_upper_bound(X_20,least_upper_bound(X_21,X_13))) = least_upper_bound(X_13,least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(least_upper_bound(X_20,X_21),X_13)),least_upper_bound(X_13,least_upper_bound(X_20,X_21))) )],[refute_0_938,refute_0_943]) ).
cnf(refute_0_945,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))]]) ).
cnf(refute_0_946,plain,
least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)) = least_upper_bound(X_21,X_312),
inference(subst,[],[refute_0_549:[bind(Y,$fot(X_310)),bind(X_20,$fot(X_21)),bind(X_22,$fot(X_312))]]) ).
cnf(refute_0_947,plain,
( least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)) != least_upper_bound(X_21,X_312)
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))) ),[0,1,1],$fot(least_upper_bound(X_21,X_312))]]) ).
cnf(refute_0_948,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)),least_upper_bound(X_21,X_312)) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))) )],[refute_0_945,refute_0_948]) ).
cnf(refute_0_950,plain,
least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)) = least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)),
inference(subst,[],[refute_0_279:[bind(Y,$fot(greatest_lower_bound(X_21,X_310))),bind(X_13,$fot(X_312))]]) ).
cnf(refute_0_951,plain,
least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))))]]) ).
cnf(refute_0_952,plain,
( least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) != least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)) != least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))
| least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) ),[1,1],$fot(least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))]]) ).
cnf(refute_0_953,plain,
( least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)) != least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))
| least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)),least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))) )],[refute_0_950,refute_0_953]) ).
cnf(refute_0_955,plain,
least_upper_bound(X_296,least_upper_bound(X_297,X_295)) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))),
inference(subst,[],[refute_0_729:[bind(Y,$fot(X_295)),bind(X_20,$fot(X_296)),bind(X_21,$fot(X_297))]]) ).
cnf(refute_0_956,plain,
least_upper_bound(X_295,X_297) = least_upper_bound(X_297,X_295),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_295)),bind(Y,$fot(X_297))]]) ).
cnf(refute_0_957,plain,
( least_upper_bound(X_295,X_297) != least_upper_bound(X_297,X_295)
| least_upper_bound(X_297,X_295) = least_upper_bound(X_295,X_297) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_295,X_297))),bind(Y0,$fot(least_upper_bound(X_297,X_295)))]]) ).
cnf(refute_0_958,plain,
least_upper_bound(X_297,X_295) = least_upper_bound(X_295,X_297),
inference(resolve,[$cnf( $equal(least_upper_bound(X_295,X_297),least_upper_bound(X_297,X_295)) )],[refute_0_956,refute_0_957]) ).
cnf(refute_0_959,plain,
( least_upper_bound(X_296,least_upper_bound(X_297,X_295)) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295)))
| least_upper_bound(X_297,X_295) != least_upper_bound(X_295,X_297)
| least_upper_bound(X_296,least_upper_bound(X_295,X_297)) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) ),[0,1],$fot(least_upper_bound(X_295,X_297))]]) ).
cnf(refute_0_960,plain,
( least_upper_bound(X_296,least_upper_bound(X_297,X_295)) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295)))
| least_upper_bound(X_296,least_upper_bound(X_295,X_297)) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,X_295),least_upper_bound(X_295,X_297)) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
least_upper_bound(X_296,least_upper_bound(X_295,X_297)) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) )],[refute_0_955,refute_0_960]) ).
cnf(refute_0_962,plain,
least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))) = least_upper_bound(X_296,least_upper_bound(X_297,X_295)),
inference(subst,[],[refute_0_731:[bind(Y,$fot(X_295)),bind(X_20,$fot(X_296)),bind(X_21,$fot(X_297))]]) ).
cnf(refute_0_963,plain,
( least_upper_bound(X_296,least_upper_bound(X_295,X_297)) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295)))
| least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))) != least_upper_bound(X_296,least_upper_bound(X_297,X_295))
| least_upper_bound(X_296,least_upper_bound(X_295,X_297)) = least_upper_bound(X_296,least_upper_bound(X_297,X_295)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_296,least_upper_bound(X_295,X_297)),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) ),[0],$fot(least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))))]]) ).
cnf(refute_0_964,plain,
( least_upper_bound(X_296,least_upper_bound(X_295,X_297)) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295)))
| least_upper_bound(X_296,least_upper_bound(X_295,X_297)) = least_upper_bound(X_296,least_upper_bound(X_297,X_295)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295))),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) )],[refute_0_962,refute_0_963]) ).
cnf(refute_0_965,plain,
least_upper_bound(X_296,least_upper_bound(X_295,X_297)) = least_upper_bound(X_296,least_upper_bound(X_297,X_295)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_295,X_297)),least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) )],[refute_0_961,refute_0_964]) ).
cnf(refute_0_966,plain,
( least_upper_bound(X_296,least_upper_bound(X_295,X_297)) != least_upper_bound(X_296,least_upper_bound(X_297,X_295))
| least_upper_bound(X_296,least_upper_bound(X_297,X_295)) = least_upper_bound(X_296,least_upper_bound(X_295,X_297)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_296,least_upper_bound(X_295,X_297)))),bind(Y0,$fot(least_upper_bound(X_296,least_upper_bound(X_297,X_295))))]]) ).
cnf(refute_0_967,plain,
least_upper_bound(X_296,least_upper_bound(X_297,X_295)) = least_upper_bound(X_296,least_upper_bound(X_295,X_297)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_295,X_297)),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) )],[refute_0_965,refute_0_966]) ).
cnf(refute_0_968,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)) = least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),
inference(subst,[],[refute_0_967:[bind(X_295,$fot(X_312)),bind(X_296,$fot(X_20)),bind(X_297,$fot(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))]]) ).
cnf(refute_0_969,plain,
( least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) != least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)) != least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)) = least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))))]]) ).
cnf(refute_0_970,plain,
( least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) != least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)) = least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)),least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)) = least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_312,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) )],[refute_0_954,refute_0_970]) ).
cnf(refute_0_972,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))))]]) ).
cnf(refute_0_973,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)) != least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)))) ),[1,1],$fot(least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))))]]) ).
cnf(refute_0_974,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)) != least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)))) )],[refute_0_972,refute_0_973]) ).
cnf(refute_0_975,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)),least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) )],[refute_0_971,refute_0_974]) ).
cnf(refute_0_976,plain,
least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X)))),
inference(subst,[],[refute_0_729:[bind(Y,$fot(least_upper_bound(X_21,X))),bind(X_20,$fot(X_296)),bind(X_21,$fot(X_297))]]) ).
cnf(refute_0_977,plain,
least_upper_bound(X,least_upper_bound(X_297,X_21)) = least_upper_bound(X_297,least_upper_bound(X_21,X)),
inference(subst,[],[refute_0_680:[bind(X_20,$fot(X_297))]]) ).
cnf(refute_0_978,plain,
( least_upper_bound(X,least_upper_bound(X_297,X_21)) != least_upper_bound(X_297,least_upper_bound(X_21,X))
| least_upper_bound(X_297,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(X_297,X_21)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_297,X_21)))),bind(Y0,$fot(least_upper_bound(X_297,least_upper_bound(X_21,X))))]]) ).
cnf(refute_0_979,plain,
least_upper_bound(X_297,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(X_297,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_297,X_21)),least_upper_bound(X_297,least_upper_bound(X_21,X))) )],[refute_0_977,refute_0_978]) ).
cnf(refute_0_980,plain,
( least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))))
| least_upper_bound(X_297,least_upper_bound(X_21,X)) != least_upper_bound(X,least_upper_bound(X_297,X_21))
| least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))),least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))))) ),[1,1,1],$fot(least_upper_bound(X,least_upper_bound(X_297,X_21)))]]) ).
cnf(refute_0_981,plain,
( least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))))
| least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,least_upper_bound(X_21,X)),least_upper_bound(X,least_upper_bound(X_297,X_21))) )],[refute_0_979,refute_0_980]) ).
cnf(refute_0_982,plain,
least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) = least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))),least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))))) )],[refute_0_976,refute_0_981]) ).
cnf(refute_0_983,plain,
least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20)))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)),
inference(subst,[],[refute_0_680:[bind(X_21,$fot(least_upper_bound(X_139,least_upper_bound(X_140,X_20))))]]) ).
cnf(refute_0_984,plain,
least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20))) = least_upper_bound(X_20,least_upper_bound(X_139,X_140)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(X_20)),bind(X_20,$fot(X_139)),bind(X_21,$fot(X_140))]]) ).
cnf(refute_0_985,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20)))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))
| least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20))) != least_upper_bound(X_20,least_upper_bound(X_139,X_140))
| least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20)))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))) ),[0,1],$fot(least_upper_bound(X_20,least_upper_bound(X_139,X_140)))]]) ).
cnf(refute_0_986,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20)))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))
| least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20))),least_upper_bound(X_20,least_upper_bound(X_139,X_140))) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,X_20)))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))) )],[refute_0_983,refute_0_986]) ).
cnf(refute_0_988,plain,
least_upper_bound(least_upper_bound(X_140,X_20),X) = least_upper_bound(X_140,least_upper_bound(X_20,X)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_140)),bind(Y,$fot(X_20)),bind(Z,$fot(X))]]) ).
cnf(refute_0_989,plain,
least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)) = least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)))]]) ).
cnf(refute_0_990,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)) != least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X))
| least_upper_bound(least_upper_bound(X_140,X_20),X) != least_upper_bound(X_140,least_upper_bound(X_20,X))
| least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)),least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X))) ),[1,1],$fot(least_upper_bound(X_140,least_upper_bound(X_20,X)))]]) ).
cnf(refute_0_991,plain,
( least_upper_bound(least_upper_bound(X_140,X_20),X) != least_upper_bound(X_140,least_upper_bound(X_20,X))
| least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)),least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X))) )],[refute_0_989,refute_0_990]) ).
cnf(refute_0_992,plain,
least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_140,X_20),X),least_upper_bound(X_140,least_upper_bound(X_20,X))) )],[refute_0_988,refute_0_991]) ).
cnf(refute_0_993,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X) = least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_139)),bind(Y,$fot(least_upper_bound(X_140,X_20))),bind(Z,$fot(X))]]) ).
cnf(refute_0_994,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X) != least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))),bind(Y0,$fot(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)))),bind(Z0,$fot(least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))))]]) ).
cnf(refute_0_995,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X),least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X_20),X)),least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) )],[refute_0_992,refute_0_995]) ).
cnf(refute_0_997,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)))]]) ).
cnf(refute_0_998,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) = least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))) ),[1,1],$fot(least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))))]]) ).
cnf(refute_0_999,plain,
( least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) = least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))) )],[refute_0_997,refute_0_998]) ).
cnf(refute_0_1000,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) = least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X),least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) )],[refute_0_996,refute_0_999]) ).
cnf(refute_0_1001,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)) != least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))))
| least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) = least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))),least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)))]]) ).
cnf(refute_0_1002,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))
| least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) = least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X)),least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))))) )],[refute_0_1000,refute_0_1001]) ).
cnf(refute_0_1003,plain,
least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) = least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X_20)),X))) )],[refute_0_987,refute_0_1002]) ).
cnf(refute_0_1004,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) != least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))))
| least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) = least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))))))]]) ).
cnf(refute_0_1005,plain,
least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X)))) = least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_139,X_140))),least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X_20,X))))) )],[refute_0_1003,refute_0_1004]) ).
cnf(refute_0_1006,plain,
least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21)))) = least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X))),
inference(subst,[],[refute_0_1005:[bind(X,$fot(X_21)),bind(X_139,$fot(X_296)),bind(X_140,$fot(X)),bind(X_20,$fot(X_297))]]) ).
cnf(refute_0_1007,plain,
( least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21))))
| least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21)))) != least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X)))
| least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) = least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))),least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X)))) ),[0],$fot(least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21)))))]]) ).
cnf(refute_0_1008,plain,
( least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) != least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21))))
| least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) = least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21)))),least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X)))) )],[refute_0_1006,refute_0_1007]) ).
cnf(refute_0_1009,plain,
least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) = least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))),least_upper_bound(X_297,least_upper_bound(X_296,least_upper_bound(X,least_upper_bound(X_297,X_21))))) )],[refute_0_982,refute_0_1008]) ).
cnf(refute_0_1010,plain,
( least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) != least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X)))
| least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X))) = least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X)))))]]) ).
cnf(refute_0_1011,plain,
least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X))) = least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_297,least_upper_bound(X_21,X))),least_upper_bound(X_21,least_upper_bound(X_297,least_upper_bound(X_296,X)))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))),
inference(subst,[],[refute_0_1011:[bind(X,$fot(X_312)),bind(X_21,$fot(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),bind(X_296,$fot(X_21)),bind(X_297,$fot(X_20))]]) ).
cnf(refute_0_1013,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))))),bind(Z0,$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))))))]]) ).
cnf(refute_0_1014,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312)))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),X_312))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))))) )],[refute_0_975,refute_0_1014]) ).
cnf(refute_0_1016,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))) ),[0],$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))))]]) ).
cnf(refute_0_1017,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310))))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295))),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(least_upper_bound(X_296,least_upper_bound(X_19,X_295))))]]) ).
cnf(refute_0_1019,plain,
least_upper_bound(X_296,least_upper_bound(X_19,X_295)) = least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295))),
inference(subst,[],[refute_0_729:[bind(Y,$fot(X_295)),bind(X_20,$fot(X_296)),bind(X_21,$fot(X_19))]]) ).
cnf(refute_0_1020,plain,
( least_upper_bound(X_296,least_upper_bound(X_19,X_295)) != least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))
| least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295))) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_296,least_upper_bound(X_19,X_295)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))))]]) ).
cnf(refute_0_1021,plain,
least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295))) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_296,least_upper_bound(X_19,X_295)),least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) )],[refute_0_1019,refute_0_1020]) ).
cnf(refute_0_1022,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) != least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))
| least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295))) != least_upper_bound(X_296,least_upper_bound(X_19,X_295))
| least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))),least_upper_bound(X_296,least_upper_bound(X_19,X_295))) ),[0],$fot(least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295))))]]) ).
cnf(refute_0_1023,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) != least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))
| least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295))),least_upper_bound(X_296,least_upper_bound(X_19,X_295))) )],[refute_0_1021,refute_0_1022]) ).
cnf(refute_0_1024,plain,
least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))),least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) )],[refute_0_1018,refute_0_1023]) ).
cnf(refute_0_1025,plain,
least_upper_bound(X_19,least_upper_bound(X_19,X_296)) = least_upper_bound(X_19,X_296),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(X_296))]]) ).
cnf(refute_0_1026,plain,
least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))) = least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))))]]) ).
cnf(refute_0_1027,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,X_296)) != least_upper_bound(X_19,X_296)
| least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))) != least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296)))
| least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))),least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296)))) ),[1,1],$fot(least_upper_bound(X_19,X_296))]]) ).
cnf(refute_0_1028,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,X_296)) != least_upper_bound(X_19,X_296)
| least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))),least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296)))) )],[refute_0_1026,refute_0_1027]) ).
cnf(refute_0_1029,plain,
least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,X_296)),least_upper_bound(X_19,X_296)) )],[refute_0_1025,refute_0_1028]) ).
cnf(refute_0_1030,plain,
least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))),
inference(subst,[],[refute_0_1005:[bind(X,$fot(X_295)),bind(X_139,$fot(X_19)),bind(X_140,$fot(X_296)),bind(X_20,$fot(X_19))]]) ).
cnf(refute_0_1031,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) != least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296)))
| least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))) != least_upper_bound(X_295,least_upper_bound(X_19,X_296))
| least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))))),bind(Y0,$fot(least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))))),bind(Z0,$fot(least_upper_bound(X_295,least_upper_bound(X_19,X_296))))]]) ).
cnf(refute_0_1032,plain,
( least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))) != least_upper_bound(X_295,least_upper_bound(X_19,X_296))
| least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))),least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296)))) )],[refute_0_1030,refute_0_1031]) ).
cnf(refute_0_1033,plain,
least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_295,least_upper_bound(X_19,least_upper_bound(X_19,X_296))),least_upper_bound(X_295,least_upper_bound(X_19,X_296))) )],[refute_0_1029,refute_0_1032]) ).
cnf(refute_0_1034,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) != least_upper_bound(X_295,least_upper_bound(X_19,X_296))
| least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) != least_upper_bound(X_296,least_upper_bound(X_19,X_295))
| least_upper_bound(X_295,least_upper_bound(X_19,X_296)) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))),least_upper_bound(X_296,least_upper_bound(X_19,X_295))) ),[0],$fot(least_upper_bound(X_295,least_upper_bound(X_19,X_296)))]]) ).
cnf(refute_0_1035,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))) != least_upper_bound(X_296,least_upper_bound(X_19,X_295))
| least_upper_bound(X_295,least_upper_bound(X_19,X_296)) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))),least_upper_bound(X_295,least_upper_bound(X_19,X_296))) )],[refute_0_1033,refute_0_1034]) ).
cnf(refute_0_1036,plain,
least_upper_bound(X_295,least_upper_bound(X_19,X_296)) = least_upper_bound(X_296,least_upper_bound(X_19,X_295)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,least_upper_bound(X_296,least_upper_bound(X_19,X_295)))),least_upper_bound(X_296,least_upper_bound(X_19,X_295))) )],[refute_0_1024,refute_0_1035]) ).
cnf(refute_0_1037,plain,
( least_upper_bound(X_295,least_upper_bound(X_19,X_296)) != least_upper_bound(X_296,least_upper_bound(X_19,X_295))
| least_upper_bound(X_296,least_upper_bound(X_19,X_295)) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_295,least_upper_bound(X_19,X_296)))),bind(Y0,$fot(least_upper_bound(X_296,least_upper_bound(X_19,X_295))))]]) ).
cnf(refute_0_1038,plain,
least_upper_bound(X_296,least_upper_bound(X_19,X_295)) = least_upper_bound(X_295,least_upper_bound(X_19,X_296)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_295,least_upper_bound(X_19,X_296)),least_upper_bound(X_296,least_upper_bound(X_19,X_295))) )],[refute_0_1036,refute_0_1037]) ).
cnf(refute_0_1039,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),
inference(subst,[],[refute_0_1038:[bind(X_19,$fot(X_20)),bind(X_295,$fot(X_21)),bind(X_296,$fot(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))]]) ).
cnf(refute_0_1040,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))
| least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1041,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21)),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) )],[refute_0_1039,refute_0_1040]) ).
cnf(refute_0_1042,plain,
( least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))) )],[refute_0_1017,refute_0_1041]) ).
cnf(refute_0_1043,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,least_upper_bound(X_21,X_312))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_21,X_310),X_312),least_upper_bound(X_20,X_21))) )],[refute_0_949,refute_0_1042]) ).
cnf(refute_0_1044,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))),
inference(subst,[],[refute_0_549:[bind(Y,$fot(X_310)),bind(X_20,$fot(X_311)),bind(X_22,$fot(least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))))]]) ).
cnf(refute_0_1045,plain,
least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) = least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(greatest_lower_bound(X_311,X_310)))]]) ).
cnf(refute_0_1046,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))
| least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) != least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1047,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))),least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) )],[refute_0_1045,refute_0_1046]) ).
cnf(refute_0_1048,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) )],[refute_0_1044,refute_0_1047]) ).
cnf(refute_0_1049,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) = least_upper_bound(X_311,least_upper_bound(X_20,X_21)),
inference(subst,[],[refute_0_549:[bind(Y,$fot(X_310)),bind(X_20,$fot(X_311)),bind(X_22,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1050,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) != least_upper_bound(X_311,least_upper_bound(X_20,X_21))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))
| least_upper_bound(X_311,least_upper_bound(X_20,X_21)) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) ),[0],$fot(least_upper_bound(X_311,least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1051,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))
| least_upper_bound(X_311,least_upper_bound(X_20,X_21)) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))),least_upper_bound(X_311,least_upper_bound(X_20,X_21))) )],[refute_0_1049,refute_0_1050]) ).
cnf(refute_0_1052,plain,
least_upper_bound(X_311,least_upper_bound(X_20,X_21)) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,X_21))),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) )],[refute_0_1048,refute_0_1051]) ).
cnf(refute_0_1053,plain,
( least_upper_bound(X_311,least_upper_bound(X_20,X_21)) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))
| least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) = least_upper_bound(X_311,least_upper_bound(X_20,X_21)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_311,least_upper_bound(X_20,X_21)))),bind(Y0,$fot(least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))))]]) ).
cnf(refute_0_1054,plain,
least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310)))) = least_upper_bound(X_311,least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(X_20,X_21)),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_311,X_310))))) )],[refute_0_1052,refute_0_1053]) ).
cnf(refute_0_1055,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) = least_upper_bound(X_21,least_upper_bound(X_20,X_312)),
inference(subst,[],[refute_0_1054:[bind(X_21,$fot(X_312)),bind(X_311,$fot(X_21))]]) ).
cnf(refute_0_1056,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) != least_upper_bound(X_21,least_upper_bound(X_20,X_312))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_21,least_upper_bound(X_20,X_312)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) ),[0],$fot(least_upper_bound(X_21,least_upper_bound(X_20,X_312)))]]) ).
cnf(refute_0_1057,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_21,least_upper_bound(X_20,X_312)) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))),least_upper_bound(X_21,least_upper_bound(X_20,X_312))) )],[refute_0_1055,refute_0_1056]) ).
cnf(refute_0_1058,plain,
least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))),
inference(subst,[],[refute_0_747:[bind(X_22,$fot(least_upper_bound(greatest_lower_bound(Y,X_310),X_312)))]]) ).
cnf(refute_0_1059,plain,
least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312)) = least_upper_bound(Y,X_312),
inference(subst,[],[refute_0_549:[bind(Y,$fot(X_310)),bind(X_20,$fot(Y)),bind(X_22,$fot(X_312))]]) ).
cnf(refute_0_1060,plain,
( least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))) != least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312)))
| least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312)) != least_upper_bound(Y,X_312)
| least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(Y,X_312)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))),least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312)))) ),[1,1],$fot(least_upper_bound(Y,X_312))]]) ).
cnf(refute_0_1061,plain,
( least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))) != least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312)))
| least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(Y,X_312)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312)),least_upper_bound(Y,X_312)) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(Y,X_312)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(Y,X_310),X_312))),least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(greatest_lower_bound(Y,X_310),X_312)))) )],[refute_0_1058,refute_0_1061]) ).
cnf(refute_0_1063,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) = least_upper_bound(X_20,least_upper_bound(X_21,X_312)),
inference(subst,[],[refute_0_1062:[bind(Y,$fot(X_21))]]) ).
cnf(refute_0_1064,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,X_312)) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))) != least_upper_bound(X_20,least_upper_bound(X_21,X_312))
| least_upper_bound(X_21,least_upper_bound(X_20,X_312)) = least_upper_bound(X_20,least_upper_bound(X_21,X_312)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_21,least_upper_bound(X_20,X_312)),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) ),[0],$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))))]]) ).
cnf(refute_0_1065,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,X_312)) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_21,least_upper_bound(X_20,X_312)) = least_upper_bound(X_20,least_upper_bound(X_21,X_312)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312))),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) )],[refute_0_1063,refute_0_1064]) ).
cnf(refute_0_1066,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))
| least_upper_bound(X_21,least_upper_bound(X_20,X_312)) = least_upper_bound(X_20,least_upper_bound(X_21,X_312)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,X_312)),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) )],[refute_0_1057,refute_0_1065]) ).
cnf(refute_0_1067,plain,
least_upper_bound(X_21,least_upper_bound(X_20,X_312)) = least_upper_bound(X_20,least_upper_bound(X_21,X_312)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_312,greatest_lower_bound(X_21,X_310)))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_21,X_310),X_312)))) )],[refute_0_1043,refute_0_1066]) ).
cnf(refute_0_1068,plain,
( least_upper_bound(X_21,least_upper_bound(X_20,X_312)) != least_upper_bound(X_20,least_upper_bound(X_21,X_312))
| least_upper_bound(X_20,least_upper_bound(X_21,X_312)) = least_upper_bound(X_21,least_upper_bound(X_20,X_312)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_21,least_upper_bound(X_20,X_312)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,X_312))))]]) ).
cnf(refute_0_1069,plain,
least_upper_bound(X_20,least_upper_bound(X_21,X_312)) = least_upper_bound(X_21,least_upper_bound(X_20,X_312)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,X_312)),least_upper_bound(X_20,least_upper_bound(X_21,X_312))) )],[refute_0_1067,refute_0_1068]) ).
cnf(refute_0_1070,plain,
least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))),
inference(subst,[],[refute_0_1069:[bind(X_20,$fot(greatest_lower_bound(X_157,identity))),bind(X_21,$fot(identity)),bind(X_312,$fot(greatest_lower_bound(identity,inverse(X_157))))]]) ).
cnf(refute_0_1071,plain,
( least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))) != identity
| least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) = identity ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1072,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))) != identity
| least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157))))) )],[refute_0_1070,refute_0_1071]) ).
cnf(refute_0_1073,plain,
least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_157,identity),greatest_lower_bound(identity,inverse(X_157)))),identity) )],[refute_0_937,refute_0_1072]) ).
cnf(refute_0_1074,plain,
( least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))) != identity
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) != least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))),least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157))))) ),[1],$fot(identity)]]) ).
cnf(refute_0_1075,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) != least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157)))),identity) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_157)),greatest_lower_bound(X_157,identity))),least_upper_bound(greatest_lower_bound(X_157,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_157))))) )],[refute_0_797,refute_0_1075]) ).
cnf(refute_0_1077,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) = identity,
inference(subst,[],[refute_0_1076:[bind(X_157,$fot(X_363))]]) ).
cnf(refute_0_1078,plain,
( greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))) != multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) != identity
| greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))),multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_1079,plain,
( greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))) != multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))
| greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))),identity) )],[refute_0_1077,refute_0_1078]) ).
cnf(refute_0_1080,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))),multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) )],[refute_0_611,refute_0_1079]) ).
cnf(refute_0_1081,plain,
greatest_lower_bound(identity,least_upper_bound(X_363,identity)) = identity,
inference(subst,[],[refute_0_262:[bind(X,$fot(identity)),bind(Y,$fot(X_363))]]) ).
cnf(refute_0_1082,plain,
multiply(identity,least_upper_bound(X_363,identity)) = least_upper_bound(X_363,identity),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_363,identity)))]]) ).
cnf(refute_0_1083,plain,
least_upper_bound(identity,multiply(identity,X_363)) = multiply(identity,least_upper_bound(X_363,identity)),
inference(subst,[],[refute_0_337:[bind(X_82,$fot(identity)),bind(X_83,$fot(X_363))]]) ).
cnf(refute_0_1084,plain,
( multiply(identity,least_upper_bound(X_363,identity)) != least_upper_bound(X_363,identity)
| least_upper_bound(identity,multiply(identity,X_363)) != multiply(identity,least_upper_bound(X_363,identity))
| least_upper_bound(identity,multiply(identity,X_363)) = least_upper_bound(X_363,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,X_363)))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_363,identity)))),bind(Z0,$fot(least_upper_bound(X_363,identity)))]]) ).
cnf(refute_0_1085,plain,
( multiply(identity,least_upper_bound(X_363,identity)) != least_upper_bound(X_363,identity)
| least_upper_bound(identity,multiply(identity,X_363)) = least_upper_bound(X_363,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_363)),multiply(identity,least_upper_bound(X_363,identity))) )],[refute_0_1083,refute_0_1084]) ).
cnf(refute_0_1086,plain,
least_upper_bound(identity,multiply(identity,X_363)) = least_upper_bound(X_363,identity),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_363,identity)),least_upper_bound(X_363,identity)) )],[refute_0_1082,refute_0_1085]) ).
cnf(refute_0_1087,plain,
multiply(least_upper_bound(identity,inverse(X_363)),X_363) = least_upper_bound(identity,multiply(identity,X_363)),
inference(subst,[],[refute_0_413:[bind(X_89,$fot(X_363)),bind(X_90,$fot(identity))]]) ).
cnf(refute_0_1088,plain,
( multiply(least_upper_bound(identity,inverse(X_363)),X_363) != least_upper_bound(identity,multiply(identity,X_363))
| least_upper_bound(identity,multiply(identity,X_363)) != least_upper_bound(X_363,identity)
| multiply(least_upper_bound(identity,inverse(X_363)),X_363) = least_upper_bound(X_363,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_363)),X_363))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,X_363)))),bind(Z0,$fot(least_upper_bound(X_363,identity)))]]) ).
cnf(refute_0_1089,plain,
( least_upper_bound(identity,multiply(identity,X_363)) != least_upper_bound(X_363,identity)
| multiply(least_upper_bound(identity,inverse(X_363)),X_363) = least_upper_bound(X_363,identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_363)),X_363),least_upper_bound(identity,multiply(identity,X_363))) )],[refute_0_1087,refute_0_1088]) ).
cnf(refute_0_1090,plain,
multiply(least_upper_bound(identity,inverse(X_363)),X_363) = least_upper_bound(X_363,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_363)),least_upper_bound(X_363,identity)) )],[refute_0_1086,refute_0_1089]) ).
cnf(refute_0_1091,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)))]]) ).
cnf(refute_0_1092,plain,
( multiply(least_upper_bound(identity,inverse(X_363)),X_363) != least_upper_bound(X_363,identity)
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) = greatest_lower_bound(identity,least_upper_bound(X_363,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))) ),[1,1],$fot(least_upper_bound(X_363,identity))]]) ).
cnf(refute_0_1093,plain,
( multiply(least_upper_bound(identity,inverse(X_363)),X_363) != least_upper_bound(X_363,identity)
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) = greatest_lower_bound(identity,least_upper_bound(X_363,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) = greatest_lower_bound(identity,least_upper_bound(X_363,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_363)),X_363),least_upper_bound(X_363,identity)) )],[refute_0_1090,refute_0_1093]) ).
cnf(refute_0_1095,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) != greatest_lower_bound(identity,least_upper_bound(X_363,identity))
| greatest_lower_bound(identity,least_upper_bound(X_363,identity)) != identity
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) = identity ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_363,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1096,plain,
( greatest_lower_bound(identity,least_upper_bound(X_363,identity)) != identity
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)),greatest_lower_bound(identity,least_upper_bound(X_363,identity))) )],[refute_0_1094,refute_0_1095]) ).
cnf(refute_0_1097,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_363,identity)),identity) )],[refute_0_1081,refute_0_1096]) ).
cnf(refute_0_1098,plain,
greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(X_56,Y)),X_58),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(least_upper_bound(X_56,Y))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1099,plain,
greatest_lower_bound(X_56,least_upper_bound(X_56,Y)) = X_56,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_56))]]) ).
cnf(refute_0_1100,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(X_56,Y)),X_58)
| greatest_lower_bound(X_56,least_upper_bound(X_56,Y)) != X_56
| greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)) = greatest_lower_bound(X_56,X_58) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(X_56,Y)),X_58)) ),[1,0],$fot(X_56)]]) ).
cnf(refute_0_1101,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(X_56,Y)),X_58)
| greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)) = greatest_lower_bound(X_56,X_58) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,least_upper_bound(X_56,Y)),X_56) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)) = greatest_lower_bound(X_56,X_58),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_56,Y),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(X_56,Y)),X_58)) )],[refute_0_1098,refute_0_1101]) ).
cnf(refute_0_1103,plain,
greatest_lower_bound(X_214,greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))) = greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154)),
inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_213)),bind(X_56,$fot(X_214)),bind(X_58,$fot(multiply(least_upper_bound(X_214,X_213),X_154)))]]) ).
cnf(refute_0_1104,plain,
multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity)) = greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154)),
inference(subst,[],[refute_0_785:[bind(X_153,$fot(least_upper_bound(X_214,X_213)))]]) ).
cnf(refute_0_1105,plain,
( multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity)) != greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))
| greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154)) = multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))))]]) ).
cnf(refute_0_1106,plain,
greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154)) = multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity)),greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))) )],[refute_0_1104,refute_0_1105]) ).
cnf(refute_0_1107,plain,
( greatest_lower_bound(X_214,greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))) != greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154))
| greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154)) != multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity))
| greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity))) = greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_214,greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))),greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154))) ),[0,1],$fot(multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity)))]]) ).
cnf(refute_0_1108,plain,
( greatest_lower_bound(X_214,greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))) != greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154))
| greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity))) = greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154)),multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity))) )],[refute_0_1106,refute_0_1107]) ).
cnf(refute_0_1109,plain,
greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),greatest_lower_bound(X_154,identity))) = greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_214,greatest_lower_bound(least_upper_bound(X_214,X_213),multiply(least_upper_bound(X_214,X_213),X_154))),greatest_lower_bound(X_214,multiply(least_upper_bound(X_214,X_213),X_154))) )],[refute_0_1103,refute_0_1108]) ).
cnf(refute_0_1110,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)),
inference(subst,[],[refute_0_1109:[bind(X_154,$fot(X_363)),bind(X_213,$fot(inverse(X_363))),bind(X_214,$fot(identity))]]) ).
cnf(refute_0_1111,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))))]]) ).
cnf(refute_0_1112,plain,
( greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))
| greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))))]]) ).
cnf(refute_0_1113,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))
| greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)))) )],[refute_0_1111,refute_0_1112]) ).
cnf(refute_0_1114,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))) )],[refute_0_1110,refute_0_1113]) ).
cnf(refute_0_1115,plain,
( greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) != identity
| greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = identity ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1116,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)) != identity
| greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363))) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X_363)),X_363)),identity) )],[refute_0_1097,refute_0_1116]) ).
cnf(refute_0_1118,plain,
( greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) != multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))
| greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) != identity
| identity = multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity),multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1119,plain,
( greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity) != multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))
| identity = multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity),identity) )],[refute_0_1117,refute_0_1118]) ).
cnf(refute_0_1120,plain,
identity = multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity)),identity),multiply(least_upper_bound(identity,inverse(X_363)),greatest_lower_bound(X_363,identity))) )],[refute_0_1080,refute_0_1119]) ).
cnf(refute_0_1121,plain,
identity = multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity)),
inference(subst,[],[refute_0_1120:[bind(X_363,$fot(X_364))]]) ).
cnf(refute_0_1122,plain,
( identity != multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))
| multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity)) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))))]]) ).
cnf(refute_0_1123,plain,
multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity)) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))) )],[refute_0_1121,refute_0_1122]) ).
cnf(refute_0_1124,plain,
( multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity)) != identity
| inverse(greatest_lower_bound(X_364,identity)) != multiply(inverse(multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))),least_upper_bound(identity,inverse(X_364)))
| inverse(greatest_lower_bound(X_364,identity)) = multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_364,identity)),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))),least_upper_bound(identity,inverse(X_364)))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_1125,plain,
( inverse(greatest_lower_bound(X_364,identity)) != multiply(inverse(multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))),least_upper_bound(identity,inverse(X_364)))
| inverse(greatest_lower_bound(X_364,identity)) = multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity)),identity) )],[refute_0_1123,refute_0_1124]) ).
cnf(refute_0_1126,plain,
inverse(greatest_lower_bound(X_364,identity)) = multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_364,identity)),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_364)),greatest_lower_bound(X_364,identity))),least_upper_bound(identity,inverse(X_364)))) )],[refute_0_610,refute_0_1125]) ).
cnf(refute_0_1127,plain,
multiply(identity,least_upper_bound(identity,inverse(X_364))) = least_upper_bound(identity,inverse(X_364)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(X_364))))]]) ).
cnf(refute_0_1128,plain,
multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) = multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))))]]) ).
cnf(refute_0_1129,plain,
( multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) != multiply(inverse(identity),least_upper_bound(identity,inverse(X_364)))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) = multiply(identity,least_upper_bound(identity,inverse(X_364))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))),multiply(inverse(identity),least_upper_bound(identity,inverse(X_364)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1130,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) = multiply(identity,least_upper_bound(identity,inverse(X_364))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))),multiply(inverse(identity),least_upper_bound(identity,inverse(X_364)))) )],[refute_0_1128,refute_0_1129]) ).
cnf(refute_0_1131,plain,
multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) = multiply(identity,least_upper_bound(identity,inverse(X_364))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_1130]) ).
cnf(refute_0_1132,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_364))) != least_upper_bound(identity,inverse(X_364))
| multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) != multiply(identity,least_upper_bound(identity,inverse(X_364)))
| multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) = least_upper_bound(identity,inverse(X_364)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(X_364))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_364))))]]) ).
cnf(refute_0_1133,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_364))) != least_upper_bound(identity,inverse(X_364))
| multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) = least_upper_bound(identity,inverse(X_364)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))),multiply(identity,least_upper_bound(identity,inverse(X_364)))) )],[refute_0_1131,refute_0_1132]) ).
cnf(refute_0_1134,plain,
multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) = least_upper_bound(identity,inverse(X_364)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(X_364))),least_upper_bound(identity,inverse(X_364))) )],[refute_0_1127,refute_0_1133]) ).
cnf(refute_0_1135,plain,
( multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))) != least_upper_bound(identity,inverse(X_364))
| inverse(greatest_lower_bound(X_364,identity)) != multiply(inverse(identity),least_upper_bound(identity,inverse(X_364)))
| inverse(greatest_lower_bound(X_364,identity)) = least_upper_bound(identity,inverse(X_364)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_364,identity)),multiply(inverse(identity),least_upper_bound(identity,inverse(X_364)))) ),[1],$fot(least_upper_bound(identity,inverse(X_364)))]]) ).
cnf(refute_0_1136,plain,
( inverse(greatest_lower_bound(X_364,identity)) != multiply(inverse(identity),least_upper_bound(identity,inverse(X_364)))
| inverse(greatest_lower_bound(X_364,identity)) = least_upper_bound(identity,inverse(X_364)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,inverse(X_364))),least_upper_bound(identity,inverse(X_364))) )],[refute_0_1134,refute_0_1135]) ).
cnf(refute_0_1137,plain,
inverse(greatest_lower_bound(X_364,identity)) = least_upper_bound(identity,inverse(X_364)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_364,identity)),multiply(inverse(identity),least_upper_bound(identity,inverse(X_364)))) )],[refute_0_1126,refute_0_1136]) ).
cnf(refute_0_1138,plain,
( inverse(greatest_lower_bound(X_364,identity)) != least_upper_bound(identity,inverse(X_364))
| least_upper_bound(identity,inverse(X_364)) = inverse(greatest_lower_bound(X_364,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(X_364,identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_364))))]]) ).
cnf(refute_0_1139,plain,
least_upper_bound(identity,inverse(X_364)) = inverse(greatest_lower_bound(X_364,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_364,identity)),least_upper_bound(identity,inverse(X_364))) )],[refute_0_1137,refute_0_1138]) ).
cnf(refute_0_1140,plain,
least_upper_bound(identity,inverse(multiply(X_45,X_86))) = inverse(greatest_lower_bound(multiply(X_45,X_86),identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(multiply(X_45,X_86)))]]) ).
cnf(refute_0_1141,plain,
( inverse(greatest_lower_bound(multiply(X_45,X_86),identity)) != inverse(greatest_lower_bound(identity,multiply(X_45,X_86)))
| least_upper_bound(identity,inverse(multiply(X_45,X_86))) != inverse(greatest_lower_bound(multiply(X_45,X_86),identity))
| least_upper_bound(identity,inverse(multiply(X_45,X_86))) = inverse(greatest_lower_bound(identity,multiply(X_45,X_86))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(multiply(X_45,X_86))))),bind(Y0,$fot(inverse(greatest_lower_bound(multiply(X_45,X_86),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_45,X_86)))))]]) ).
cnf(refute_0_1142,plain,
( inverse(greatest_lower_bound(multiply(X_45,X_86),identity)) != inverse(greatest_lower_bound(identity,multiply(X_45,X_86)))
| least_upper_bound(identity,inverse(multiply(X_45,X_86))) = inverse(greatest_lower_bound(identity,multiply(X_45,X_86))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_45,X_86))),inverse(greatest_lower_bound(multiply(X_45,X_86),identity))) )],[refute_0_1140,refute_0_1141]) ).
cnf(refute_0_1143,plain,
least_upper_bound(identity,inverse(multiply(X_45,X_86))) = inverse(greatest_lower_bound(identity,multiply(X_45,X_86))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_45,X_86),identity)),inverse(greatest_lower_bound(identity,multiply(X_45,X_86)))) )],[refute_0_609,refute_0_1142]) ).
cnf(refute_0_1144,plain,
( multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) != least_upper_bound(identity,inverse(multiply(X_45,X_86)))
| least_upper_bound(identity,inverse(multiply(X_45,X_86))) != inverse(greatest_lower_bound(identity,multiply(X_45,X_86)))
| multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) = inverse(greatest_lower_bound(identity,multiply(X_45,X_86))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)),inverse(greatest_lower_bound(identity,multiply(X_45,X_86)))) ),[0],$fot(least_upper_bound(identity,inverse(multiply(X_45,X_86))))]]) ).
cnf(refute_0_1145,plain,
( multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) != least_upper_bound(identity,inverse(multiply(X_45,X_86)))
| multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) = inverse(greatest_lower_bound(identity,multiply(X_45,X_86))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_45,X_86))),inverse(greatest_lower_bound(identity,multiply(X_45,X_86)))) )],[refute_0_1143,refute_0_1144]) ).
cnf(refute_0_1146,plain,
multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)) = inverse(greatest_lower_bound(identity,multiply(X_45,X_86))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(inverse(X_45),X_86)),least_upper_bound(identity,inverse(multiply(X_45,X_86)))) )],[refute_0_557,refute_0_1145]) ).
cnf(refute_0_1147,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))),
inference(subst,[],[refute_0_1146:[bind(X_45,$fot(least_upper_bound(a,b))),bind(X_86,$fot(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))]]) ).
cnf(refute_0_1148,plain,
multiply(least_upper_bound(X_83,X_84),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) = inverse(inverse(X_84)),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(inverse(X_84))),bind(X_55,$fot(least_upper_bound(X_83,X_84)))]]) ).
cnf(refute_0_1149,plain,
( multiply(inverse(X_84),least_upper_bound(X_83,X_84)) != least_upper_bound(identity,multiply(inverse(X_84),X_83))
| multiply(least_upper_bound(X_83,X_84),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) != inverse(inverse(X_84))
| multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = inverse(inverse(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_83,X_84),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),inverse(inverse(X_84))) ),[0,1,0],$fot(least_upper_bound(identity,multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_1150,plain,
( multiply(least_upper_bound(X_83,X_84),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) != inverse(inverse(X_84))
| multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = inverse(inverse(X_84)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_83,X_84)),least_upper_bound(identity,multiply(inverse(X_84),X_83))) )],[refute_0_67,refute_0_1149]) ).
cnf(refute_0_1151,plain,
multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = inverse(inverse(X_84)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_83,X_84),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),inverse(inverse(X_84))) )],[refute_0_1148,refute_0_1150]) ).
cnf(refute_0_1152,plain,
( multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(inverse(X_84))
| inverse(inverse(X_84)) != X_84
| multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = X_84 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))),X_84) ),[0],$fot(inverse(inverse(X_84)))]]) ).
cnf(refute_0_1153,plain,
( multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(inverse(X_84))
| multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = X_84 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_84)),X_84) )],[refute_0_834,refute_0_1152]) ).
cnf(refute_0_1154,plain,
multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = X_84,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_83,X_84),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))),inverse(inverse(X_84))) )],[refute_0_1151,refute_0_1153]) ).
cnf(refute_0_1155,plain,
multiply(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),
inference(subst,[],[refute_0_1154:[bind(X_83,$fot(identity)),bind(X_84,$fot(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_1156,plain,
multiply(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(c)),bind(X_91,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1157,plain,
least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_21,X))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X))),
inference(subst,[],[refute_0_135:[bind(X_22,$fot(least_upper_bound(X_21,X)))]]) ).
cnf(refute_0_1158,plain,
least_upper_bound(X,least_upper_bound(c,X_21)) = least_upper_bound(c,least_upper_bound(X_21,X)),
inference(subst,[],[refute_0_680:[bind(X_20,$fot(c))]]) ).
cnf(refute_0_1159,plain,
( least_upper_bound(X,least_upper_bound(c,X_21)) != least_upper_bound(c,least_upper_bound(X_21,X))
| least_upper_bound(c,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(c,X_21)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(c,X_21)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_21,X))))]]) ).
cnf(refute_0_1160,plain,
least_upper_bound(c,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(c,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(c,X_21)),least_upper_bound(c,least_upper_bound(X_21,X))) )],[refute_0_1158,refute_0_1159]) ).
cnf(refute_0_1161,plain,
( least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_21,X))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X)))
| least_upper_bound(c,least_upper_bound(X_21,X)) != least_upper_bound(X,least_upper_bound(c,X_21))
| least_upper_bound(b,least_upper_bound(X,least_upper_bound(c,X_21))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_21,X))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X)))) ),[0,1],$fot(least_upper_bound(X,least_upper_bound(c,X_21)))]]) ).
cnf(refute_0_1162,plain,
( least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_21,X))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X)))
| least_upper_bound(b,least_upper_bound(X,least_upper_bound(c,X_21))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_21,X)),least_upper_bound(X,least_upper_bound(c,X_21))) )],[refute_0_1160,refute_0_1161]) ).
cnf(refute_0_1163,plain,
least_upper_bound(b,least_upper_bound(X,least_upper_bound(c,X_21))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_21,X))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_21,X)))) )],[refute_0_1157,refute_0_1162]) ).
cnf(refute_0_1164,plain,
least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))),
inference(subst,[],[refute_0_1163:[bind(X,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),bind(X_21,$fot(b))]]) ).
cnf(refute_0_1165,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))) = greatest_lower_bound(least_upper_bound(a,c),X_59),
inference(subst,[],[refute_0_270:[bind(X_10,$fot(greatest_lower_bound(least_upper_bound(a,c),X_59))),bind(X_11,$fot(b))]]) ).
cnf(refute_0_1166,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)) = greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_58),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(a,c))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1167,plain,
greatest_lower_bound(b,least_upper_bound(b,c)) = b,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_1168,plain,
( greatest_lower_bound(b,least_upper_bound(b,c)) != b
| least_upper_bound(b,c) != least_upper_bound(a,c)
| greatest_lower_bound(b,least_upper_bound(a,c)) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) ),[0,1],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_1169,plain,
( greatest_lower_bound(b,least_upper_bound(b,c)) != b
| greatest_lower_bound(b,least_upper_bound(a,c)) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_126,refute_0_1168]) ).
cnf(refute_0_1170,plain,
greatest_lower_bound(b,least_upper_bound(a,c)) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) )],[refute_0_1167,refute_0_1169]) ).
cnf(refute_0_1171,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_58)
| greatest_lower_bound(b,least_upper_bound(a,c)) != b
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)) = greatest_lower_bound(b,X_58) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_58)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_1172,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_58)
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)) = greatest_lower_bound(b,X_58) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),b) )],[refute_0_1170,refute_0_1171]) ).
cnf(refute_0_1173,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)) = greatest_lower_bound(b,X_58),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_58)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_58)) )],[refute_0_1166,refute_0_1172]) ).
cnf(refute_0_1174,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)) = greatest_lower_bound(b,X_59),
inference(subst,[],[refute_0_1173:[bind(X_58,$fot(X_59))]]) ).
cnf(refute_0_1175,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)) != greatest_lower_bound(b,X_59)
| least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))) != greatest_lower_bound(least_upper_bound(a,c),X_59)
| least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(least_upper_bound(a,c),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))),greatest_lower_bound(least_upper_bound(a,c),X_59)) ),[0,1],$fot(greatest_lower_bound(b,X_59))]]) ).
cnf(refute_0_1176,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))) != greatest_lower_bound(least_upper_bound(a,c),X_59)
| least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(least_upper_bound(a,c),X_59) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)) )],[refute_0_1174,refute_0_1175]) ).
cnf(refute_0_1177,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(least_upper_bound(a,c),X_59),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))),greatest_lower_bound(least_upper_bound(a,c),X_59)) )],[refute_0_1165,refute_0_1176]) ).
cnf(refute_0_1178,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59)),
inference(subst,[],[refute_0_63:[bind(X,$fot(greatest_lower_bound(b,X_59))),bind(Y,$fot(greatest_lower_bound(least_upper_bound(a,c),X_59)))]]) ).
cnf(refute_0_1179,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(least_upper_bound(a,c),X_59)
| least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59))
| least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59)) = greatest_lower_bound(least_upper_bound(a,c),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) ),[0],$fot(least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59)))]]) ).
cnf(refute_0_1180,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(least_upper_bound(a,c),X_59)
| least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59)) = greatest_lower_bound(least_upper_bound(a,c),X_59) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59))) )],[refute_0_1178,refute_0_1179]) ).
cnf(refute_0_1181,plain,
least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59)) = greatest_lower_bound(least_upper_bound(a,c),X_59),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) )],[refute_0_1177,refute_0_1180]) ).
cnf(refute_0_1182,plain,
least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),
inference(subst,[],[refute_0_1181:[bind(X_59,$fot(least_upper_bound(b,Y)))]]) ).
cnf(refute_0_1183,plain,
greatest_lower_bound(b,least_upper_bound(b,Y)) = b,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(b))]]) ).
cnf(refute_0_1184,plain,
( greatest_lower_bound(b,least_upper_bound(b,Y)) != b
| least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_1185,plain,
( least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,Y)),b) )],[refute_0_1183,refute_0_1184]) ).
cnf(refute_0_1186,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(b,Y)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) )],[refute_0_1182,refute_0_1185]) ).
cnf(refute_0_1187,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))) ),[1,1,1],$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))]]) ).
cnf(refute_0_1188,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) )],[refute_0_1186,refute_0_1187]) ).
cnf(refute_0_1189,plain,
least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))) )],[refute_0_1164,refute_0_1188]) ).
cnf(refute_0_1190,plain,
least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))) = least_upper_bound(X_20,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))),
inference(subst,[],[refute_0_747:[bind(Y,$fot(b)),bind(X_22,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))))]]) ).
cnf(refute_0_1191,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)),
inference(subst,[],[refute_0_1186:[bind(Y,$fot(X_123))]]) ).
cnf(refute_0_1192,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))
| least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))) != least_upper_bound(X_20,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))))
| least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))) = least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))),least_upper_bound(X_20,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))))) ),[1,1],$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))]]) ).
cnf(refute_0_1193,plain,
( least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))) != least_upper_bound(X_20,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))))
| least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))) = least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) )],[refute_0_1191,refute_0_1192]) ).
cnf(refute_0_1194,plain,
least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))) = least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_20,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)))),least_upper_bound(X_20,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))))) )],[refute_0_1190,refute_0_1193]) ).
cnf(refute_0_1195,plain,
least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),
inference(subst,[],[refute_0_1194:[bind(X_123,$fot(Y)),bind(X_20,$fot(c))]]) ).
cnf(refute_0_1196,plain,
least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,least_upper_bound(Y,X_32))),
inference(subst,[],[refute_0_680:[bind(X,$fot(least_upper_bound(Y,X_32))),bind(X_20,$fot(X_31)),bind(X_21,$fot(X_32))]]) ).
cnf(refute_0_1197,plain,
least_upper_bound(X_32,least_upper_bound(Y,X_32)) = least_upper_bound(X_32,Y),
inference(subst,[],[refute_0_279:[bind(X_13,$fot(X_32))]]) ).
cnf(refute_0_1198,plain,
( least_upper_bound(X_32,least_upper_bound(Y,X_32)) != least_upper_bound(X_32,Y)
| least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,least_upper_bound(Y,X_32)))
| least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,least_upper_bound(Y,X_32)))) ),[1,1],$fot(least_upper_bound(X_32,Y))]]) ).
cnf(refute_0_1199,plain,
( least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,least_upper_bound(Y,X_32)))
| least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(Y,X_32)),least_upper_bound(X_32,Y)) )],[refute_0_1197,refute_0_1198]) ).
cnf(refute_0_1200,plain,
least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_31,least_upper_bound(X_32,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,least_upper_bound(Y,X_32)))) )],[refute_0_1196,refute_0_1199]) ).
cnf(refute_0_1201,plain,
least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32))) = least_upper_bound(X_32,least_upper_bound(X_31,Y)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(X_32)),bind(X_20,$fot(X_31)),bind(X_21,$fot(Y))]]) ).
cnf(refute_0_1202,plain,
least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32))),
inference(subst,[],[refute_0_929:[bind(Y,$fot(least_upper_bound(Y,X_32))),bind(X_30,$fot(X_32))]]) ).
cnf(refute_0_1203,plain,
( least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32))) != least_upper_bound(X_32,least_upper_bound(X_31,Y))
| least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32)))
| least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,Y)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)))),bind(Y0,$fot(least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32))))),bind(Z0,$fot(least_upper_bound(X_32,least_upper_bound(X_31,Y))))]]) ).
cnf(refute_0_1204,plain,
( least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32))) != least_upper_bound(X_32,least_upper_bound(X_31,Y))
| least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)),least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32)))) )],[refute_0_1202,refute_0_1203]) ).
cnf(refute_0_1205,plain,
least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,least_upper_bound(X_31,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_31,least_upper_bound(Y,X_32))),least_upper_bound(X_32,least_upper_bound(X_31,Y))) )],[refute_0_1201,refute_0_1204]) ).
cnf(refute_0_1206,plain,
( least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,Y))
| least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,least_upper_bound(X_31,Y))
| least_upper_bound(X_32,least_upper_bound(X_31,Y)) = least_upper_bound(X_31,least_upper_bound(X_32,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,Y))) ),[0],$fot(least_upper_bound(X_32,least_upper_bound(X_31,Y)))]]) ).
cnf(refute_0_1207,plain,
( least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)) != least_upper_bound(X_31,least_upper_bound(X_32,Y))
| least_upper_bound(X_32,least_upper_bound(X_31,Y)) = least_upper_bound(X_31,least_upper_bound(X_32,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)),least_upper_bound(X_32,least_upper_bound(X_31,Y))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
least_upper_bound(X_32,least_upper_bound(X_31,Y)) = least_upper_bound(X_31,least_upper_bound(X_32,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_32),least_upper_bound(X_31,X_32)),least_upper_bound(X_31,least_upper_bound(X_32,Y))) )],[refute_0_1200,refute_0_1207]) ).
cnf(refute_0_1209,plain,
( least_upper_bound(X_32,least_upper_bound(X_31,Y)) != least_upper_bound(X_31,least_upper_bound(X_32,Y))
| least_upper_bound(X_31,least_upper_bound(X_32,Y)) = least_upper_bound(X_32,least_upper_bound(X_31,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_32,least_upper_bound(X_31,Y)))),bind(Y0,$fot(least_upper_bound(X_31,least_upper_bound(X_32,Y))))]]) ).
cnf(refute_0_1210,plain,
least_upper_bound(X_31,least_upper_bound(X_32,Y)) = least_upper_bound(X_32,least_upper_bound(X_31,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_31,Y)),least_upper_bound(X_31,least_upper_bound(X_32,Y))) )],[refute_0_1208,refute_0_1209]) ).
cnf(refute_0_1211,plain,
least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),
inference(subst,[],[refute_0_1210:[bind(Y,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),bind(X_31,$fot(c)),bind(X_32,$fot(b))]]) ).
cnf(refute_0_1212,plain,
( least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))),bind(Z0,$fot(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))]]) ).
cnf(refute_0_1213,plain,
( least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))) )],[refute_0_1211,refute_0_1212]) ).
cnf(refute_0_1214,plain,
least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) )],[refute_0_1195,refute_0_1213]) ).
cnf(refute_0_1215,plain,
least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),
inference(subst,[],[refute_0_131:[bind(X,$fot(c)),bind(Y,$fot(b)),bind(Z,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))]]) ).
cnf(refute_0_1216,plain,
( least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))),bind(Z0,$fot(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))]]) ).
cnf(refute_0_1217,plain,
( least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))) )],[refute_0_1215,refute_0_1216]) ).
cnf(refute_0_1218,plain,
least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) )],[refute_0_1214,refute_0_1217]) ).
cnf(refute_0_1219,plain,
least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),
inference(subst,[],[refute_0_1194:[bind(X_123,$fot(Y)),bind(X_20,$fot(least_upper_bound(c,b)))]]) ).
cnf(refute_0_1220,plain,
( least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))),bind(Z0,$fot(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))]]) ).
cnf(refute_0_1221,plain,
( least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) )],[refute_0_1219,refute_0_1220]) ).
cnf(refute_0_1222,plain,
least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) )],[refute_0_1218,refute_0_1221]) ).
cnf(refute_0_1223,plain,
least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))) = least_upper_bound(X_20,X_21),
inference(subst,[],[refute_0_270:[bind(X_10,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1224,plain,
least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))) = least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))))]]) ).
cnf(refute_0_1225,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))) != least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))
| least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))) = least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))))]]) ).
cnf(refute_0_1226,plain,
least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))) = least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))),least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))) )],[refute_0_1224,refute_0_1225]) ).
cnf(refute_0_1227,plain,
( least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))) != least_upper_bound(X_20,X_21)
| least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))) != least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))))
| least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))) = least_upper_bound(X_20,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))),least_upper_bound(X_20,X_21)) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))))]]) ).
cnf(refute_0_1228,plain,
( least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))) != least_upper_bound(X_20,X_21)
| least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))) = least_upper_bound(X_20,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))))) )],[refute_0_1226,refute_0_1227]) ).
cnf(refute_0_1229,plain,
least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(X_11,least_upper_bound(X_20,X_21)))) = least_upper_bound(X_20,X_21),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(X_11,least_upper_bound(X_20,X_21))),least_upper_bound(X_20,X_21)) )],[refute_0_1223,refute_0_1228]) ).
cnf(refute_0_1230,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))))) = least_upper_bound(X_20,least_upper_bound(X_248,X_11)),
inference(subst,[],[refute_0_1229:[bind(X_21,$fot(least_upper_bound(X_248,X_11)))]]) ).
cnf(refute_0_1231,plain,
greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_20,X_21),X)) = X,
inference(subst,[],[refute_0_262:[bind(Y,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1232,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_20,X_21),X)) != X
| least_upper_bound(least_upper_bound(X_20,X_21),X) != least_upper_bound(X_20,least_upper_bound(X_21,X))
| greatest_lower_bound(X,least_upper_bound(X_20,least_upper_bound(X_21,X))) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_20,X_21),X)),X) ),[0,1],$fot(least_upper_bound(X_20,least_upper_bound(X_21,X)))]]) ).
cnf(refute_0_1233,plain,
( greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_20,X_21),X)) != X
| greatest_lower_bound(X,least_upper_bound(X_20,least_upper_bound(X_21,X))) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),X),least_upper_bound(X_20,least_upper_bound(X_21,X))) )],[refute_0_677,refute_0_1232]) ).
cnf(refute_0_1234,plain,
greatest_lower_bound(X,least_upper_bound(X_20,least_upper_bound(X_21,X))) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(least_upper_bound(X_20,X_21),X)),X) )],[refute_0_1231,refute_0_1233]) ).
cnf(refute_0_1235,plain,
greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))) = X_11,
inference(subst,[],[refute_0_1234:[bind(X,$fot(X_11)),bind(X_21,$fot(X_248))]]) ).
cnf(refute_0_1236,plain,
( greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))) != X_11
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))))) != least_upper_bound(X_20,least_upper_bound(X_248,X_11))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) = least_upper_bound(X_20,least_upper_bound(X_248,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))))),least_upper_bound(X_20,least_upper_bound(X_248,X_11))) ),[0,1,1],$fot(X_11)]]) ).
cnf(refute_0_1237,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))))) != least_upper_bound(X_20,least_upper_bound(X_248,X_11))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) = least_upper_bound(X_20,least_upper_bound(X_248,X_11)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))),X_11) )],[refute_0_1235,refute_0_1236]) ).
cnf(refute_0_1238,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) = least_upper_bound(X_20,least_upper_bound(X_248,X_11)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_248,X_11))))),least_upper_bound(X_20,least_upper_bound(X_248,X_11))) )],[refute_0_1230,refute_0_1237]) ).
cnf(refute_0_1239,plain,
least_upper_bound(X_11,least_upper_bound(X_248,X_11)) = least_upper_bound(X_11,X_248),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_248)),bind(X_13,$fot(X_11))]]) ).
cnf(refute_0_1240,plain,
least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))) = least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))))]]) ).
cnf(refute_0_1241,plain,
( least_upper_bound(X_11,least_upper_bound(X_248,X_11)) != least_upper_bound(X_11,X_248)
| least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))) != least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11)))
| least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))),least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11)))) ),[1,1],$fot(least_upper_bound(X_11,X_248))]]) ).
cnf(refute_0_1242,plain,
( least_upper_bound(X_11,least_upper_bound(X_248,X_11)) != least_upper_bound(X_11,X_248)
| least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))),least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11)))) )],[refute_0_1240,refute_0_1241]) ).
cnf(refute_0_1243,plain,
least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_248,X_11)),least_upper_bound(X_11,X_248)) )],[refute_0_1239,refute_0_1242]) ).
cnf(refute_0_1244,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) = least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y),
inference(subst,[],[refute_0_279:[bind(X_13,$fot(least_upper_bound(X_139,least_upper_bound(X_140,Y))))]]) ).
cnf(refute_0_1245,plain,
least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))) = least_upper_bound(Y,least_upper_bound(X_139,X_140)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(Y)),bind(X_20,$fot(X_139)),bind(X_21,$fot(X_140))]]) ).
cnf(refute_0_1246,plain,
( least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))) != least_upper_bound(Y,least_upper_bound(X_139,X_140))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) != least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))),least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)) ),[0,1],$fot(least_upper_bound(Y,least_upper_bound(X_139,X_140)))]]) ).
cnf(refute_0_1247,plain,
( least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) != least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))),least_upper_bound(Y,least_upper_bound(X_139,X_140))) )],[refute_0_1245,refute_0_1246]) ).
cnf(refute_0_1248,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))),least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)) )],[refute_0_1244,refute_0_1247]) ).
cnf(refute_0_1249,plain,
least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))) = least_upper_bound(Y,least_upper_bound(X_140,X_139)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(Y)),bind(X_20,$fot(X_140)),bind(X_21,$fot(X_139))]]) ).
cnf(refute_0_1250,plain,
least_upper_bound(X_139,least_upper_bound(Y,X_139)) = least_upper_bound(X_139,Y),
inference(subst,[],[refute_0_279:[bind(X_13,$fot(X_139))]]) ).
cnf(refute_0_1251,plain,
least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))) = least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))))]]) ).
cnf(refute_0_1252,plain,
( least_upper_bound(X_139,least_upper_bound(Y,X_139)) != least_upper_bound(X_139,Y)
| least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))) != least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139)))
| least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))) = least_upper_bound(X_140,least_upper_bound(X_139,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))),least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139)))) ),[1,1],$fot(least_upper_bound(X_139,Y))]]) ).
cnf(refute_0_1253,plain,
( least_upper_bound(X_139,least_upper_bound(Y,X_139)) != least_upper_bound(X_139,Y)
| least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))) = least_upper_bound(X_140,least_upper_bound(X_139,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))),least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139)))) )],[refute_0_1251,refute_0_1252]) ).
cnf(refute_0_1254,plain,
least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))) = least_upper_bound(X_140,least_upper_bound(X_139,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(Y,X_139)),least_upper_bound(X_139,Y)) )],[refute_0_1250,refute_0_1253]) ).
cnf(refute_0_1255,plain,
least_upper_bound(least_upper_bound(X_40,X_41),Y) = least_upper_bound(Y,least_upper_bound(X_40,X_41)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(X_40,X_41)))]]) ).
cnf(refute_0_1256,plain,
least_upper_bound(Y,least_upper_bound(X_40,X_41)) = least_upper_bound(X_40,least_upper_bound(Y,X_41)),
inference(subst,[],[refute_0_747:[bind(X_20,$fot(X_40)),bind(X_22,$fot(X_41))]]) ).
cnf(refute_0_1257,plain,
( least_upper_bound(Y,least_upper_bound(X_40,X_41)) != least_upper_bound(X_40,least_upper_bound(Y,X_41))
| least_upper_bound(least_upper_bound(X_40,X_41),Y) != least_upper_bound(Y,least_upper_bound(X_40,X_41))
| least_upper_bound(least_upper_bound(X_40,X_41),Y) = least_upper_bound(X_40,least_upper_bound(Y,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_40,X_41),Y),least_upper_bound(Y,least_upper_bound(X_40,X_41))) ),[1],$fot(least_upper_bound(X_40,least_upper_bound(Y,X_41)))]]) ).
cnf(refute_0_1258,plain,
( least_upper_bound(least_upper_bound(X_40,X_41),Y) != least_upper_bound(Y,least_upper_bound(X_40,X_41))
| least_upper_bound(least_upper_bound(X_40,X_41),Y) = least_upper_bound(X_40,least_upper_bound(Y,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_40,X_41)),least_upper_bound(X_40,least_upper_bound(Y,X_41))) )],[refute_0_1256,refute_0_1257]) ).
cnf(refute_0_1259,plain,
least_upper_bound(least_upper_bound(X_40,X_41),Y) = least_upper_bound(X_40,least_upper_bound(Y,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_40,X_41),Y),least_upper_bound(Y,least_upper_bound(X_40,X_41))) )],[refute_0_1255,refute_0_1258]) ).
cnf(refute_0_1260,plain,
least_upper_bound(least_upper_bound(X_40,X_41),Y) = least_upper_bound(X_40,least_upper_bound(X_41,Y)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_40)),bind(Y,$fot(X_41)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1261,plain,
( least_upper_bound(least_upper_bound(X_40,X_41),Y) != least_upper_bound(X_40,least_upper_bound(Y,X_41))
| least_upper_bound(least_upper_bound(X_40,X_41),Y) != least_upper_bound(X_40,least_upper_bound(X_41,Y))
| least_upper_bound(X_40,least_upper_bound(X_41,Y)) = least_upper_bound(X_40,least_upper_bound(Y,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_40,X_41),Y),least_upper_bound(X_40,least_upper_bound(Y,X_41))) ),[0],$fot(least_upper_bound(X_40,least_upper_bound(X_41,Y)))]]) ).
cnf(refute_0_1262,plain,
( least_upper_bound(least_upper_bound(X_40,X_41),Y) != least_upper_bound(X_40,least_upper_bound(Y,X_41))
| least_upper_bound(X_40,least_upper_bound(X_41,Y)) = least_upper_bound(X_40,least_upper_bound(Y,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_40,X_41),Y),least_upper_bound(X_40,least_upper_bound(X_41,Y))) )],[refute_0_1260,refute_0_1261]) ).
cnf(refute_0_1263,plain,
least_upper_bound(X_40,least_upper_bound(X_41,Y)) = least_upper_bound(X_40,least_upper_bound(Y,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_40,X_41),Y),least_upper_bound(X_40,least_upper_bound(Y,X_41))) )],[refute_0_1259,refute_0_1262]) ).
cnf(refute_0_1264,plain,
( least_upper_bound(X_40,least_upper_bound(X_41,Y)) != least_upper_bound(X_40,least_upper_bound(Y,X_41))
| least_upper_bound(X_40,least_upper_bound(Y,X_41)) = least_upper_bound(X_40,least_upper_bound(X_41,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_40,least_upper_bound(X_41,Y)))),bind(Y0,$fot(least_upper_bound(X_40,least_upper_bound(Y,X_41))))]]) ).
cnf(refute_0_1265,plain,
least_upper_bound(X_40,least_upper_bound(Y,X_41)) = least_upper_bound(X_40,least_upper_bound(X_41,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(X_41,Y)),least_upper_bound(X_40,least_upper_bound(Y,X_41))) )],[refute_0_1263,refute_0_1264]) ).
cnf(refute_0_1266,plain,
least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)) = least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))),
inference(subst,[],[refute_0_1265:[bind(Y,$fot(least_upper_bound(Y,X_139))),bind(X_40,$fot(X_140)),bind(X_41,$fot(X_139))]]) ).
cnf(refute_0_1267,plain,
( least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))) != least_upper_bound(X_140,least_upper_bound(X_139,Y))
| least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)) != least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139)))
| least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)) = least_upper_bound(X_140,least_upper_bound(X_139,Y)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))),bind(Y0,$fot(least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))))),bind(Z0,$fot(least_upper_bound(X_140,least_upper_bound(X_139,Y))))]]) ).
cnf(refute_0_1268,plain,
( least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))) != least_upper_bound(X_140,least_upper_bound(X_139,Y))
| least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)) = least_upper_bound(X_140,least_upper_bound(X_139,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)),least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139)))) )],[refute_0_1266,refute_0_1267]) ).
cnf(refute_0_1269,plain,
least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)) = least_upper_bound(X_140,least_upper_bound(X_139,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(X_139,least_upper_bound(Y,X_139))),least_upper_bound(X_140,least_upper_bound(X_139,Y))) )],[refute_0_1254,refute_0_1268]) ).
cnf(refute_0_1270,plain,
least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))))]]) ).
cnf(refute_0_1271,plain,
( least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) != least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))
| least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)) != least_upper_bound(X_140,least_upper_bound(X_139,Y))
| least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))) ),[1,1],$fot(least_upper_bound(X_140,least_upper_bound(X_139,Y)))]]) ).
cnf(refute_0_1272,plain,
( least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)) != least_upper_bound(X_140,least_upper_bound(X_139,Y))
| least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))) )],[refute_0_1270,refute_0_1271]) ).
cnf(refute_0_1273,plain,
least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)),least_upper_bound(X_140,least_upper_bound(X_139,Y))) )],[refute_0_1269,refute_0_1272]) ).
cnf(refute_0_1274,plain,
( least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))) != least_upper_bound(Y,least_upper_bound(X_140,X_139))
| least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) != least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y)))
| least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) = least_upper_bound(Y,least_upper_bound(X_140,X_139)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_140,X_139))))]]) ).
cnf(refute_0_1275,plain,
( least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))) != least_upper_bound(Y,least_upper_bound(X_140,X_139))
| least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) = least_upper_bound(Y,least_upper_bound(X_140,X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y)))) )],[refute_0_1273,refute_0_1274]) ).
cnf(refute_0_1276,plain,
least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) = least_upper_bound(Y,least_upper_bound(X_140,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(X_139,Y))),least_upper_bound(Y,least_upper_bound(X_140,X_139))) )],[refute_0_1249,refute_0_1275]) ).
cnf(refute_0_1277,plain,
least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y)))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),
inference(subst,[],[refute_0_1005:[bind(X,$fot(Y)),bind(X_139,$fot(least_upper_bound(Y,X_139))),bind(X_140,$fot(X_139)),bind(X_20,$fot(X_140))]]) ).
cnf(refute_0_1278,plain,
least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))) = least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y)))),
inference(subst,[],[refute_0_1265:[bind(Y,$fot(least_upper_bound(X_139,least_upper_bound(X_140,Y)))),bind(X_40,$fot(X_140)),bind(X_41,$fot(least_upper_bound(Y,X_139)))]]) ).
cnf(refute_0_1279,plain,
( least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y)))) != least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))
| least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))) != least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y))))
| least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))))),bind(Y0,$fot(least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y)))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))))]]) ).
cnf(refute_0_1280,plain,
( least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y)))) != least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))
| least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))),least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y))))) )],[refute_0_1278,refute_0_1279]) ).
cnf(refute_0_1281,plain,
least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),least_upper_bound(X_139,least_upper_bound(X_140,Y)))),least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))) )],[refute_0_1277,refute_0_1280]) ).
cnf(refute_0_1282,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))),Z),
inference(subst,[],[associativity_of_lub:[bind(Y,$fot(least_upper_bound(X_139,least_upper_bound(X_140,X))))]]) ).
cnf(refute_0_1283,plain,
least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))) = least_upper_bound(X,least_upper_bound(X_139,X_140)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(X)),bind(X_20,$fot(X_139)),bind(X_21,$fot(X_140))]]) ).
cnf(refute_0_1284,plain,
( least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))) != least_upper_bound(X,least_upper_bound(X_139,X_140))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))),Z)
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))),Z)) ),[1,0],$fot(least_upper_bound(X,least_upper_bound(X_139,X_140)))]]) ).
cnf(refute_0_1285,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))),Z)
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))),least_upper_bound(X,least_upper_bound(X_139,X_140))) )],[refute_0_1283,refute_0_1284]) ).
cnf(refute_0_1286,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,X))),Z)) )],[refute_0_1282,refute_0_1285]) ).
cnf(refute_0_1287,plain,
least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))) = least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))),
inference(subst,[],[refute_0_1005:[bind(X,$fot(Z)),bind(X_20,$fot(X))]]) ).
cnf(refute_0_1288,plain,
least_upper_bound(least_upper_bound(X_140,X),Z) = least_upper_bound(X_140,least_upper_bound(X,Z)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_140)),bind(Y,$fot(X))]]) ).
cnf(refute_0_1289,plain,
least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)) = least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)))]]) ).
cnf(refute_0_1290,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)) != least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z))
| least_upper_bound(least_upper_bound(X_140,X),Z) != least_upper_bound(X_140,least_upper_bound(X,Z))
| least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)),least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z))) ),[1,1],$fot(least_upper_bound(X_140,least_upper_bound(X,Z)))]]) ).
cnf(refute_0_1291,plain,
( least_upper_bound(least_upper_bound(X_140,X),Z) != least_upper_bound(X_140,least_upper_bound(X,Z))
| least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)),least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z))) )],[refute_0_1289,refute_0_1290]) ).
cnf(refute_0_1292,plain,
least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_140,X),Z),least_upper_bound(X_140,least_upper_bound(X,Z))) )],[refute_0_1288,refute_0_1291]) ).
cnf(refute_0_1293,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z) = least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_139)),bind(Y,$fot(least_upper_bound(X_140,X)))]]) ).
cnf(refute_0_1294,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z) != least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z))),bind(Y0,$fot(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)))),bind(Z0,$fot(least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))))]]) ).
cnf(refute_0_1295,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z),least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z))) )],[refute_0_1293,refute_0_1294]) ).
cnf(refute_0_1296,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z) = least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(X_140,X),Z)),least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))) )],[refute_0_1292,refute_0_1295]) ).
cnf(refute_0_1297,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),
introduced(tautology,[refl,[$fot(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)))]]) ).
cnf(refute_0_1298,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z))) ),[1,1],$fot(least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))))]]) ).
cnf(refute_0_1299,plain,
( least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z) != least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z))) )],[refute_0_1297,refute_0_1298]) ).
cnf(refute_0_1300,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z),least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))) )],[refute_0_1296,refute_0_1299]) ).
cnf(refute_0_1301,plain,
( least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))) != least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140)))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))))),bind(Z0,$fot(least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140)))))]]) ).
cnf(refute_0_1302,plain,
( least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))) != least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140)))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z))))) )],[refute_0_1300,refute_0_1301]) ).
cnf(refute_0_1303,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) = least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,least_upper_bound(X,Z)))),least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140)))) )],[refute_0_1287,refute_0_1302]) ).
cnf(refute_0_1304,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140)))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)
| least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)) ),[0],$fot(least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))))]]) ).
cnf(refute_0_1305,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)
| least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140)))) )],[refute_0_1303,refute_0_1304]) ).
cnf(refute_0_1306,plain,
least_upper_bound(least_upper_bound(X_139,X_140),Z) = least_upper_bound(X_139,least_upper_bound(X_140,Z)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_139)),bind(Y,$fot(X_140))]]) ).
cnf(refute_0_1307,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)) = least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)),
introduced(tautology,[refl,[$fot(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)))]]) ).
cnf(refute_0_1308,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)) != least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z))
| least_upper_bound(least_upper_bound(X_139,X_140),Z) != least_upper_bound(X_139,least_upper_bound(X_140,Z))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z))) ),[1,1],$fot(least_upper_bound(X_139,least_upper_bound(X_140,Z)))]]) ).
cnf(refute_0_1309,plain,
( least_upper_bound(least_upper_bound(X_139,X_140),Z) != least_upper_bound(X_139,least_upper_bound(X_140,Z))
| least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z))) )],[refute_0_1307,refute_0_1308]) ).
cnf(refute_0_1310,plain,
least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,X_140),Z),least_upper_bound(X_139,least_upper_bound(X_140,Z))) )],[refute_0_1306,refute_0_1309]) ).
cnf(refute_0_1311,plain,
least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) = least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)),
inference(subst,[],[refute_0_131:[bind(Y,$fot(least_upper_bound(X_139,X_140)))]]) ).
cnf(refute_0_1312,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)) != least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))
| least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) != least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z))
| least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)))),bind(Z0,$fot(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))))]]) ).
cnf(refute_0_1313,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)) != least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))
| least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z),least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z))) )],[refute_0_1311,refute_0_1312]) ).
cnf(refute_0_1314,plain,
least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,X_140),Z)),least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))) )],[refute_0_1310,refute_0_1313]) ).
cnf(refute_0_1315,plain,
( least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)
| least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z) != least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))
| least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))),least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))) ),[0],$fot(least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z))]]) ).
cnf(refute_0_1316,plain,
( least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)
| least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z),least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))) )],[refute_0_1314,refute_0_1315]) ).
cnf(refute_0_1317,plain,
( least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)
| least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))),least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)) )],[refute_0_1305,refute_0_1316]) ).
cnf(refute_0_1318,plain,
least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) = least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,X)),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_139,X_140)),Z)) )],[refute_0_1286,refute_0_1317]) ).
cnf(refute_0_1319,plain,
( least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) != least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))
| least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) = least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))))]]) ).
cnf(refute_0_1320,plain,
least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z))) = least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))),
inference(resolve,[$cnf( $equal(least_upper_bound(Z,least_upper_bound(X,least_upper_bound(X_139,X_140))),least_upper_bound(X,least_upper_bound(X_139,least_upper_bound(X_140,Z)))) )],[refute_0_1318,refute_0_1319]) ).
cnf(refute_0_1321,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))),
inference(subst,[],[refute_0_1320:[bind(X,$fot(least_upper_bound(X_139,least_upper_bound(X_140,Y)))),bind(Z,$fot(X_140)),bind(X_139,$fot(Y)),bind(X_140,$fot(X_139))]]) ).
cnf(refute_0_1322,plain,
( least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))) != least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) != least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))))),bind(Y0,$fot(least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))))]]) ).
cnf(refute_0_1323,plain,
( least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))) != least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))),least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139)))) )],[refute_0_1321,refute_0_1322]) ).
cnf(refute_0_1324,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,X_139))),least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))) )],[refute_0_1281,refute_0_1323]) ).
cnf(refute_0_1325,plain,
( least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) != least_upper_bound(Y,least_upper_bound(X_140,X_139))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) != least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(Y,least_upper_bound(X_140,X_139)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_140,X_139))))]]) ).
cnf(refute_0_1326,plain,
( least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))) != least_upper_bound(Y,least_upper_bound(X_140,X_139))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(Y,least_upper_bound(X_140,X_139)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))),least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139)))) )],[refute_0_1324,refute_0_1325]) ).
cnf(refute_0_1327,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) = least_upper_bound(Y,least_upper_bound(X_140,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_140,least_upper_bound(least_upper_bound(Y,X_139),X_139))),least_upper_bound(Y,least_upper_bound(X_140,X_139))) )],[refute_0_1276,refute_0_1326]) ).
cnf(refute_0_1328,plain,
( least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) != least_upper_bound(Y,least_upper_bound(X_140,X_139))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) != least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)
| least_upper_bound(Y,least_upper_bound(X_140,X_139)) = least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))),least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_140,X_139)))]]) ).
cnf(refute_0_1329,plain,
( least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) != least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)
| least_upper_bound(Y,least_upper_bound(X_140,X_139)) = least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))),least_upper_bound(Y,least_upper_bound(X_140,X_139))) )],[refute_0_1327,refute_0_1328]) ).
cnf(refute_0_1330,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))))) = least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))),
inference(subst,[],[refute_0_1229:[bind(X_21,$fot(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))))]]) ).
cnf(refute_0_1331,plain,
least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,X_137),
inference(subst,[],[refute_0_1229:[bind(X_11,$fot(X_135)),bind(X_21,$fot(X_137))]]) ).
cnf(refute_0_1332,plain,
( least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,X_137)
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))))) != least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))))),least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) ),[0,1,1,1],$fot(least_upper_bound(X_20,X_137))]]) ).
cnf(refute_0_1333,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))))) != least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,X_137)) )],[refute_0_1331,refute_0_1332]) ).
cnf(refute_0_1334,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))))),least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) )],[refute_0_1330,refute_0_1333]) ).
cnf(refute_0_1335,plain,
least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))) = least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_137)),bind(Y,$fot(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))),bind(Z,$fot(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))]]) ).
cnf(refute_0_1336,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))))]]) ).
cnf(refute_0_1337,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))
| least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))) != least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) ),[1,1],$fot(least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))))]]) ).
cnf(refute_0_1338,plain,
( least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))) != least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) )],[refute_0_1336,refute_0_1337]) ).
cnf(refute_0_1339,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))),least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) )],[refute_0_1335,refute_0_1338]) ).
cnf(refute_0_1340,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))))
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))))]]) ).
cnf(refute_0_1341,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))))) )],[refute_0_1339,refute_0_1340]) ).
cnf(refute_0_1342,plain,
( least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,X_137)
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) != least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_20,X_137) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))),least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) ),[1],$fot(least_upper_bound(X_20,X_137))]]) ).
cnf(refute_0_1343,plain,
( least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) != least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_20,X_137) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,X_137)) )],[refute_0_1331,refute_0_1342]) ).
cnf(refute_0_1344,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_20,X_137) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))),least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) )],[refute_0_1341,refute_0_1343]) ).
cnf(refute_0_1345,plain,
least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_20,X_137),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) )],[refute_0_1334,refute_0_1344]) ).
cnf(refute_0_1346,plain,
least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)) = X_10,
inference(subst,[],[refute_0_270:[bind(X_11,$fot(greatest_lower_bound(X_56,X_57)))]]) ).
cnf(refute_0_1347,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_1348,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)))]]) ).
cnf(refute_0_1349,plain,
greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)) )],[refute_0_1347,refute_0_1348]) ).
cnf(refute_0_1350,plain,
( greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10))
| least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)),X_10) ),[0,1],$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10)))]]) ).
cnf(refute_0_1351,plain,
( least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10))) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10))) )],[refute_0_1349,refute_0_1350]) ).
cnf(refute_0_1352,plain,
least_upper_bound(X_10,greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_10))) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_10)),X_10) )],[refute_0_1346,refute_0_1351]) ).
cnf(refute_0_1353,plain,
least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)))) = least_upper_bound(X_116,X_117),
inference(subst,[],[refute_0_1352:[bind(X_10,$fot(least_upper_bound(X_116,X_117))),bind(X_57,$fot(least_upper_bound(X_117,X_116)))]]) ).
cnf(refute_0_1354,plain,
greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)) = least_upper_bound(X_117,X_116),
inference(subst,[],[refute_0_283:[bind(Y,$fot(X_116)),bind(X_18,$fot(X_117))]]) ).
cnf(refute_0_1355,plain,
( greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)) != least_upper_bound(X_117,X_116)
| least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)))) != least_upper_bound(X_116,X_117)
| least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))) = least_upper_bound(X_116,X_117) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)))),least_upper_bound(X_116,X_117)) ),[0,1,1],$fot(least_upper_bound(X_117,X_116))]]) ).
cnf(refute_0_1356,plain,
( least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)))) != least_upper_bound(X_116,X_117)
| least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))) = least_upper_bound(X_116,X_117) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)),least_upper_bound(X_117,X_116)) )],[refute_0_1354,refute_0_1355]) ).
cnf(refute_0_1357,plain,
least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))) = least_upper_bound(X_116,X_117),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_117,X_116),least_upper_bound(X_116,X_117)))),least_upper_bound(X_116,X_117)) )],[refute_0_1353,refute_0_1356]) ).
cnf(refute_0_1358,plain,
least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))) = least_upper_bound(X_116,least_upper_bound(X_117,greatest_lower_bound(X_56,least_upper_bound(X_117,X_116)))),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_116)),bind(Y,$fot(X_117)),bind(Z,$fot(greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))))]]) ).
cnf(refute_0_1359,plain,
( least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))) != least_upper_bound(X_116,X_117)
| least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))) != least_upper_bound(X_116,least_upper_bound(X_117,greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))))
| least_upper_bound(X_116,least_upper_bound(X_117,greatest_lower_bound(X_56,least_upper_bound(X_117,X_116)))) = least_upper_bound(X_116,X_117) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))),least_upper_bound(X_116,X_117)) ),[0],$fot(least_upper_bound(X_116,least_upper_bound(X_117,greatest_lower_bound(X_56,least_upper_bound(X_117,X_116)))))]]) ).
cnf(refute_0_1360,plain,
( least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))) != least_upper_bound(X_116,X_117)
| least_upper_bound(X_116,least_upper_bound(X_117,greatest_lower_bound(X_56,least_upper_bound(X_117,X_116)))) = least_upper_bound(X_116,X_117) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))),least_upper_bound(X_116,least_upper_bound(X_117,greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))))) )],[refute_0_1358,refute_0_1359]) ).
cnf(refute_0_1361,plain,
least_upper_bound(X_116,least_upper_bound(X_117,greatest_lower_bound(X_56,least_upper_bound(X_117,X_116)))) = least_upper_bound(X_116,X_117),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_116,X_117),greatest_lower_bound(X_56,least_upper_bound(X_117,X_116))),least_upper_bound(X_116,X_117)) )],[refute_0_1357,refute_0_1360]) ).
cnf(refute_0_1362,plain,
least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) = least_upper_bound(X_137,X_20),
inference(subst,[],[refute_0_1361:[bind(X_116,$fot(X_137)),bind(X_117,$fot(X_20)),bind(X_56,$fot(X_11))]]) ).
cnf(refute_0_1363,plain,
least_upper_bound(X_20,least_upper_bound(X_21,X)) = least_upper_bound(X_21,least_upper_bound(X_20,X)),
inference(subst,[],[refute_0_747:[bind(Y,$fot(X_20)),bind(X_20,$fot(X_21)),bind(X_22,$fot(X))]]) ).
cnf(refute_0_1364,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_21)) != least_upper_bound(X_20,least_upper_bound(X_21,X))
| least_upper_bound(X_20,least_upper_bound(X_21,X)) != least_upper_bound(X_21,least_upper_bound(X_20,X))
| least_upper_bound(X,least_upper_bound(X_20,X_21)) = least_upper_bound(X_21,least_upper_bound(X_20,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_20,X_21)),least_upper_bound(X_21,least_upper_bound(X_20,X))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(X_21,X)))]]) ).
cnf(refute_0_1365,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_21)) != least_upper_bound(X_20,least_upper_bound(X_21,X))
| least_upper_bound(X,least_upper_bound(X_20,X_21)) = least_upper_bound(X_21,least_upper_bound(X_20,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,X)),least_upper_bound(X_21,least_upper_bound(X_20,X))) )],[refute_0_1363,refute_0_1364]) ).
cnf(refute_0_1366,plain,
least_upper_bound(X,least_upper_bound(X_20,X_21)) = least_upper_bound(X_21,least_upper_bound(X_20,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,X_21)),least_upper_bound(X_20,least_upper_bound(X_21,X))) )],[refute_0_680,refute_0_1365]) ).
cnf(refute_0_1367,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_21)) != least_upper_bound(X_21,least_upper_bound(X_20,X))
| least_upper_bound(X_21,least_upper_bound(X_20,X)) = least_upper_bound(X,least_upper_bound(X_20,X_21)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_20,X_21)))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(X_20,X))))]]) ).
cnf(refute_0_1368,plain,
least_upper_bound(X_21,least_upper_bound(X_20,X)) = least_upper_bound(X,least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,X_21)),least_upper_bound(X_21,least_upper_bound(X_20,X))) )],[refute_0_1366,refute_0_1367]) ).
cnf(refute_0_1369,plain,
least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)) = least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),
inference(subst,[],[refute_0_1368:[bind(X,$fot(X_137)),bind(X_21,$fot(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))]]) ).
cnf(refute_0_1370,plain,
( least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_137,X_20)
| least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)) != least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))
| least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)) = least_upper_bound(X_137,X_20) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)))),bind(Y0,$fot(least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))))),bind(Z0,$fot(least_upper_bound(X_137,X_20)))]]) ).
cnf(refute_0_1371,plain,
( least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_137,X_20)
| least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)) = least_upper_bound(X_137,X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)),least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) )],[refute_0_1369,refute_0_1370]) ).
cnf(refute_0_1372,plain,
least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)) = least_upper_bound(X_137,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_137,least_upper_bound(X_20,greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)))),least_upper_bound(X_137,X_20)) )],[refute_0_1362,refute_0_1371]) ).
cnf(refute_0_1373,plain,
least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)),
inference(subst,[],[refute_0_680:[bind(X_21,$fot(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))))]]) ).
cnf(refute_0_1374,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))
| least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))) != least_upper_bound(X_20,X_137)
| least_upper_bound(X,least_upper_bound(X_20,X_137)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))) ),[0,1],$fot(least_upper_bound(X_20,X_137))]]) ).
cnf(refute_0_1375,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))
| least_upper_bound(X,least_upper_bound(X_20,X_137)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))),least_upper_bound(X_20,X_137)) )],[refute_0_1331,refute_0_1374]) ).
cnf(refute_0_1376,plain,
least_upper_bound(X,least_upper_bound(X_20,X_137)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))) )],[refute_0_1373,refute_0_1375]) ).
cnf(refute_0_1377,plain,
least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X) = least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_137)),bind(Y,$fot(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_1378,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)))]]) ).
cnf(refute_0_1379,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))
| least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X) != least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))) ),[1,1],$fot(least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)))]]) ).
cnf(refute_0_1380,plain,
( least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X) != least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))) )],[refute_0_1378,refute_0_1379]) ).
cnf(refute_0_1381,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X),least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))) )],[refute_0_1377,refute_0_1380]) ).
cnf(refute_0_1382,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_137)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)) != least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)))
| least_upper_bound(X,least_upper_bound(X_20,X_137)) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)))]]) ).
cnf(refute_0_1383,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_137)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))
| least_upper_bound(X,least_upper_bound(X_20,X_137)) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X)),least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)))) )],[refute_0_1381,refute_0_1382]) ).
cnf(refute_0_1384,plain,
least_upper_bound(X,least_upper_bound(X_20,X_137)) = least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_137,greatest_lower_bound(X_135,least_upper_bound(X_20,X_137))),X))) )],[refute_0_1376,refute_0_1383]) ).
cnf(refute_0_1385,plain,
( least_upper_bound(X,least_upper_bound(X_20,X_137)) != least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)))
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))) = least_upper_bound(X,least_upper_bound(X_20,X_137)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_20,X_137)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)))))]]) ).
cnf(refute_0_1386,plain,
least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X))) = least_upper_bound(X,least_upper_bound(X_20,X_137)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),X)))) )],[refute_0_1384,refute_0_1385]) ).
cnf(refute_0_1387,plain,
least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)),
inference(subst,[],[refute_0_1386:[bind(X,$fot(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))]]) ).
cnf(refute_0_1388,plain,
( least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) != least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137))
| least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)) != least_upper_bound(X_137,X_20)
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_137,X_20) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)))),bind(Z0,$fot(least_upper_bound(X_137,X_20)))]]) ).
cnf(refute_0_1389,plain,
( least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)) != least_upper_bound(X_137,X_20)
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_137,X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))),least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137))) )],[refute_0_1387,refute_0_1388]) ).
cnf(refute_0_1390,plain,
least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) = least_upper_bound(X_137,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_11,least_upper_bound(X_20,X_137)),least_upper_bound(X_20,X_137)),least_upper_bound(X_137,X_20)) )],[refute_0_1372,refute_0_1389]) ).
cnf(refute_0_1391,plain,
( least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) != least_upper_bound(X_137,X_20)
| least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) != least_upper_bound(X_20,X_137)
| least_upper_bound(X_137,X_20) = least_upper_bound(X_20,X_137) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))),least_upper_bound(X_20,X_137)) ),[0],$fot(least_upper_bound(X_137,X_20))]]) ).
cnf(refute_0_1392,plain,
( least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))) != least_upper_bound(X_20,X_137)
| least_upper_bound(X_137,X_20) = least_upper_bound(X_20,X_137) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))),least_upper_bound(X_137,X_20)) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
least_upper_bound(X_137,X_20) = least_upper_bound(X_20,X_137),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_137,least_upper_bound(greatest_lower_bound(X_135,least_upper_bound(X_20,X_137)),greatest_lower_bound(X_11,least_upper_bound(X_20,X_137))))),least_upper_bound(X_20,X_137)) )],[refute_0_1345,refute_0_1392]) ).
cnf(refute_0_1394,plain,
( least_upper_bound(X_137,X_20) != least_upper_bound(X_20,X_137)
| least_upper_bound(X_20,X_137) = least_upper_bound(X_137,X_20) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_137,X_20))),bind(Y0,$fot(least_upper_bound(X_20,X_137)))]]) ).
cnf(refute_0_1395,plain,
least_upper_bound(X_20,X_137) = least_upper_bound(X_137,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_137,X_20),least_upper_bound(X_20,X_137)) )],[refute_0_1393,refute_0_1394]) ).
cnf(refute_0_1396,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) = least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))),
inference(subst,[],[refute_0_1395:[bind(X_137,$fot(Y)),bind(X_20,$fot(least_upper_bound(X_139,least_upper_bound(X_140,Y))))]]) ).
cnf(refute_0_1397,plain,
( least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))) != least_upper_bound(Y,least_upper_bound(X_139,X_140))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) != least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) = least_upper_bound(Y,least_upper_bound(X_139,X_140)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_139,X_140))))]]) ).
cnf(refute_0_1398,plain,
( least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))) != least_upper_bound(Y,least_upper_bound(X_139,X_140))
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) = least_upper_bound(Y,least_upper_bound(X_139,X_140)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y),least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) )],[refute_0_1396,refute_0_1397]) ).
cnf(refute_0_1399,plain,
least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) = least_upper_bound(Y,least_upper_bound(X_139,X_140)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))),least_upper_bound(Y,least_upper_bound(X_139,X_140))) )],[refute_0_1245,refute_0_1398]) ).
cnf(refute_0_1400,plain,
( least_upper_bound(Y,least_upper_bound(X_140,X_139)) != least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)
| least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y) != least_upper_bound(Y,least_upper_bound(X_139,X_140))
| least_upper_bound(Y,least_upper_bound(X_140,X_139)) = least_upper_bound(Y,least_upper_bound(X_139,X_140)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_140,X_139)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) ),[0],$fot(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y))]]) ).
cnf(refute_0_1401,plain,
( least_upper_bound(Y,least_upper_bound(X_140,X_139)) != least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)
| least_upper_bound(Y,least_upper_bound(X_140,X_139)) = least_upper_bound(Y,least_upper_bound(X_139,X_140)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y),least_upper_bound(Y,least_upper_bound(X_139,X_140))) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
( least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) != least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)
| least_upper_bound(Y,least_upper_bound(X_140,X_139)) = least_upper_bound(Y,least_upper_bound(X_139,X_140)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_140,X_139)),least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)) )],[refute_0_1329,refute_0_1401]) ).
cnf(refute_0_1403,plain,
least_upper_bound(Y,least_upper_bound(X_140,X_139)) = least_upper_bound(Y,least_upper_bound(X_139,X_140)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),least_upper_bound(Y,least_upper_bound(X_139,X_140))),least_upper_bound(least_upper_bound(X_139,least_upper_bound(X_140,Y)),Y)) )],[refute_0_1248,refute_0_1402]) ).
cnf(refute_0_1404,plain,
( least_upper_bound(Y,least_upper_bound(X_140,X_139)) != least_upper_bound(Y,least_upper_bound(X_139,X_140))
| least_upper_bound(Y,least_upper_bound(X_139,X_140)) = least_upper_bound(Y,least_upper_bound(X_140,X_139)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_140,X_139)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_139,X_140))))]]) ).
cnf(refute_0_1405,plain,
least_upper_bound(Y,least_upper_bound(X_139,X_140)) = least_upper_bound(Y,least_upper_bound(X_140,X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_140,X_139)),least_upper_bound(Y,least_upper_bound(X_139,X_140))) )],[refute_0_1403,refute_0_1404]) ).
cnf(refute_0_1406,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) = least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))),
inference(subst,[],[refute_0_1405:[bind(Y,$fot(X_20)),bind(X_139,$fot(least_upper_bound(X_248,X_11))),bind(X_140,$fot(X_11))]]) ).
cnf(refute_0_1407,plain,
( least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))) != least_upper_bound(X_20,least_upper_bound(X_11,X_248))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) != least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_11,X_248))))]]) ).
cnf(refute_0_1408,plain,
( least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))) != least_upper_bound(X_20,least_upper_bound(X_11,X_248))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)),least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11)))) )],[refute_0_1406,refute_0_1407]) ).
cnf(refute_0_1409,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_11,least_upper_bound(X_248,X_11))),least_upper_bound(X_20,least_upper_bound(X_11,X_248))) )],[refute_0_1243,refute_0_1408]) ).
cnf(refute_0_1410,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) != least_upper_bound(X_20,least_upper_bound(X_11,X_248))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) != least_upper_bound(X_20,least_upper_bound(X_248,X_11))
| least_upper_bound(X_20,least_upper_bound(X_11,X_248)) = least_upper_bound(X_20,least_upper_bound(X_248,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)),least_upper_bound(X_20,least_upper_bound(X_248,X_11))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(X_11,X_248)))]]) ).
cnf(refute_0_1411,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)) != least_upper_bound(X_20,least_upper_bound(X_248,X_11))
| least_upper_bound(X_20,least_upper_bound(X_11,X_248)) = least_upper_bound(X_20,least_upper_bound(X_248,X_11)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)),least_upper_bound(X_20,least_upper_bound(X_11,X_248))) )],[refute_0_1409,refute_0_1410]) ).
cnf(refute_0_1412,plain,
least_upper_bound(X_20,least_upper_bound(X_11,X_248)) = least_upper_bound(X_20,least_upper_bound(X_248,X_11)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_248,X_11),X_11)),least_upper_bound(X_20,least_upper_bound(X_248,X_11))) )],[refute_0_1238,refute_0_1411]) ).
cnf(refute_0_1413,plain,
( least_upper_bound(X_20,least_upper_bound(X_11,X_248)) != least_upper_bound(X_20,least_upper_bound(X_248,X_11))
| least_upper_bound(X_20,least_upper_bound(X_248,X_11)) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_11,X_248)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_248,X_11))))]]) ).
cnf(refute_0_1414,plain,
least_upper_bound(X_20,least_upper_bound(X_248,X_11)) = least_upper_bound(X_20,least_upper_bound(X_11,X_248)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_11,X_248)),least_upper_bound(X_20,least_upper_bound(X_248,X_11))) )],[refute_0_1412,refute_0_1413]) ).
cnf(refute_0_1415,plain,
least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),
inference(subst,[],[refute_0_1414:[bind(X_11,$fot(least_upper_bound(c,b))),bind(X_20,$fot(b)),bind(X_248,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))]]) ).
cnf(refute_0_1416,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) != least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))),bind(Z0,$fot(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))))]]) ).
cnf(refute_0_1417,plain,
( least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))),least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(c,b),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) )],[refute_0_1222,refute_0_1417]) ).
cnf(refute_0_1419,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))) ),[0],$fot(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))]]) ).
cnf(refute_0_1420,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))),least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) )],[refute_0_1418,refute_0_1419]) ).
cnf(refute_0_1421,plain,
least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_20,X_21),
inference(subst,[],[lub_absorbtion:[bind(X,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1422,plain,
least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))) = least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(greatest_lower_bound(least_upper_bound(X_20,X_21),Y)))]]) ).
cnf(refute_0_1423,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))) != least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y))
| least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y))))]]) ).
cnf(refute_0_1424,plain,
least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))),least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y))) )],[refute_0_1422,refute_0_1423]) ).
cnf(refute_0_1425,plain,
( least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_20,X_21)
| least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y)))
| least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))) = least_upper_bound(X_20,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_20,X_21)) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))))]]) ).
cnf(refute_0_1426,plain,
( least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_20,X_21)
| least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))) = least_upper_bound(X_20,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y)))) )],[refute_0_1424,refute_0_1425]) ).
cnf(refute_0_1427,plain,
least_upper_bound(X_20,least_upper_bound(X_21,greatest_lower_bound(least_upper_bound(X_20,X_21),Y))) = least_upper_bound(X_20,X_21),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),greatest_lower_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_20,X_21)) )],[refute_0_1421,refute_0_1426]) ).
cnf(refute_0_1428,plain,
least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) = least_upper_bound(a,c),
inference(subst,[],[refute_0_1427:[bind(Y,$fot(least_upper_bound(b,Y))),bind(X_20,$fot(a)),bind(X_21,$fot(c))]]) ).
cnf(refute_0_1429,plain,
( least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))) != least_upper_bound(a,c)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))) ),[1],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_1430,plain,
( least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) != least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)))),least_upper_bound(a,c)) )],[refute_0_1428,refute_0_1429]) ).
cnf(refute_0_1431,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))),least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))) )],[refute_0_1420,refute_0_1430]) ).
cnf(refute_0_1432,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y)),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,Y))))) )],[refute_0_1189,refute_0_1431]) ).
cnf(refute_0_1433,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,multiply(b,X_413)))) = least_upper_bound(a,c),
inference(subst,[],[refute_0_1432:[bind(Y,$fot(multiply(b,X_413)))]]) ).
cnf(refute_0_1434,plain,
multiply(b,least_upper_bound(X_413,identity)) = least_upper_bound(b,multiply(b,X_413)),
inference(subst,[],[refute_0_335:[bind(X_82,$fot(b)),bind(X_83,$fot(X_413))]]) ).
cnf(refute_0_1435,plain,
( multiply(b,least_upper_bound(X_413,identity)) != least_upper_bound(b,multiply(b,X_413))
| least_upper_bound(b,multiply(b,X_413)) = multiply(b,least_upper_bound(X_413,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(b,least_upper_bound(X_413,identity)))),bind(Y0,$fot(least_upper_bound(b,multiply(b,X_413))))]]) ).
cnf(refute_0_1436,plain,
least_upper_bound(b,multiply(b,X_413)) = multiply(b,least_upper_bound(X_413,identity)),
inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(X_413,identity)),least_upper_bound(b,multiply(b,X_413))) )],[refute_0_1434,refute_0_1435]) ).
cnf(refute_0_1437,plain,
( least_upper_bound(b,multiply(b,X_413)) != multiply(b,least_upper_bound(X_413,identity))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,multiply(b,X_413)))) != least_upper_bound(a,c)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_413,identity)))) = least_upper_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,multiply(b,X_413)))),least_upper_bound(a,c)) ),[0,1,1],$fot(multiply(b,least_upper_bound(X_413,identity)))]]) ).
cnf(refute_0_1438,plain,
( least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,multiply(b,X_413)))) != least_upper_bound(a,c)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_413,identity)))) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,multiply(b,X_413)),multiply(b,least_upper_bound(X_413,identity))) )],[refute_0_1436,refute_0_1437]) ).
cnf(refute_0_1439,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_413,identity)))) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,multiply(b,X_413)))),least_upper_bound(a,c)) )],[refute_0_1433,refute_0_1438]) ).
cnf(refute_0_1440,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_415,identity)))) = least_upper_bound(a,c),
inference(subst,[],[refute_0_1439:[bind(X_413,$fot(X_415))]]) ).
cnf(refute_0_1441,plain,
least_upper_bound(identity,X_415) = least_upper_bound(X_415,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_415))]]) ).
cnf(refute_0_1442,plain,
( least_upper_bound(identity,X_415) != least_upper_bound(X_415,identity)
| least_upper_bound(X_415,identity) = least_upper_bound(identity,X_415) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(identity,X_415))),bind(Y0,$fot(least_upper_bound(X_415,identity)))]]) ).
cnf(refute_0_1443,plain,
least_upper_bound(X_415,identity) = least_upper_bound(identity,X_415),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_415),least_upper_bound(X_415,identity)) )],[refute_0_1441,refute_0_1442]) ).
cnf(refute_0_1444,plain,
( least_upper_bound(X_415,identity) != least_upper_bound(identity,X_415)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_415,identity)))) != least_upper_bound(a,c)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,X_415)))) = least_upper_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_415,identity)))),least_upper_bound(a,c)) ),[0,1,1,1],$fot(least_upper_bound(identity,X_415))]]) ).
cnf(refute_0_1445,plain,
( least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_415,identity)))) != least_upper_bound(a,c)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,X_415)))) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_415,identity),least_upper_bound(identity,X_415)) )],[refute_0_1443,refute_0_1444]) ).
cnf(refute_0_1446,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,X_415)))) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(X_415,identity)))),least_upper_bound(a,c)) )],[refute_0_1440,refute_0_1445]) ).
cnf(refute_0_1447,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = least_upper_bound(a,c),
inference(subst,[],[refute_0_1446:[bind(X_415,$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))]]) ).
cnf(refute_0_1448,plain,
multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(identity)),bind(X_91,$fot(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))]]) ).
cnf(refute_0_1449,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)))) = identity,
inference(subst,[],[refute_0_121:[bind(X_162,$fot(least_upper_bound(a,b))),bind(X_163,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_1450,plain,
greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(least_upper_bound(X_20,X_21),Y)) = least_upper_bound(X_20,X_21),
inference(subst,[],[glb_absorbtion:[bind(X,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_1451,plain,
( greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_20,X_21)
| least_upper_bound(least_upper_bound(X_20,X_21),Y) != least_upper_bound(X_20,least_upper_bound(X_21,Y))
| greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(X_20,least_upper_bound(X_21,Y))) = least_upper_bound(X_20,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_20,X_21)) ),[0,1],$fot(least_upper_bound(X_20,least_upper_bound(X_21,Y)))]]) ).
cnf(refute_0_1452,plain,
( greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(least_upper_bound(X_20,X_21),Y)) != least_upper_bound(X_20,X_21)
| greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(X_20,least_upper_bound(X_21,Y))) = least_upper_bound(X_20,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,X_21),Y),least_upper_bound(X_20,least_upper_bound(X_21,Y))) )],[refute_0_716,refute_0_1451]) ).
cnf(refute_0_1453,plain,
greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(X_20,least_upper_bound(X_21,Y))) = least_upper_bound(X_20,X_21),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_20,X_21),least_upper_bound(least_upper_bound(X_20,X_21),Y)),least_upper_bound(X_20,X_21)) )],[refute_0_1450,refute_0_1452]) ).
cnf(refute_0_1454,plain,
greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(b,least_upper_bound(X_292,c))) = least_upper_bound(b,X_292),
inference(subst,[],[refute_0_1453:[bind(Y,$fot(c)),bind(X_20,$fot(b)),bind(X_21,$fot(X_292))]]) ).
cnf(refute_0_1455,plain,
least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(b,least_upper_bound(c,X_33)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(c,X_33))),bind(Y,$fot(b))]]) ).
cnf(refute_0_1456,plain,
( least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(c,X_33))
| least_upper_bound(least_upper_bound(c,X_33),b) != least_upper_bound(b,least_upper_bound(c,X_33))
| least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(a,least_upper_bound(c,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_33),b),least_upper_bound(b,least_upper_bound(c,X_33))) ),[1],$fot(least_upper_bound(a,least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_1457,plain,
( least_upper_bound(least_upper_bound(c,X_33),b) != least_upper_bound(b,least_upper_bound(c,X_33))
| least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(a,least_upper_bound(c,X_33)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(c,X_33))) )],[refute_0_136,refute_0_1456]) ).
cnf(refute_0_1458,plain,
least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(a,least_upper_bound(c,X_33)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_33),b),least_upper_bound(b,least_upper_bound(c,X_33))) )],[refute_0_1455,refute_0_1457]) ).
cnf(refute_0_1459,plain,
least_upper_bound(c,least_upper_bound(X_33,b)) = least_upper_bound(b,least_upper_bound(X_33,c)),
inference(subst,[],[refute_0_929:[bind(Y,$fot(c)),bind(X_30,$fot(b)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_1460,plain,
least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(c,least_upper_bound(X_33,b)),
inference(subst,[],[refute_0_131:[bind(X,$fot(c)),bind(Y,$fot(X_33)),bind(Z,$fot(b))]]) ).
cnf(refute_0_1461,plain,
( least_upper_bound(c,least_upper_bound(X_33,b)) != least_upper_bound(b,least_upper_bound(X_33,c))
| least_upper_bound(least_upper_bound(c,X_33),b) != least_upper_bound(c,least_upper_bound(X_33,b))
| least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(b,least_upper_bound(X_33,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,X_33),b))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_33,b)))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(X_33,c))))]]) ).
cnf(refute_0_1462,plain,
( least_upper_bound(c,least_upper_bound(X_33,b)) != least_upper_bound(b,least_upper_bound(X_33,c))
| least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(b,least_upper_bound(X_33,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_33),b),least_upper_bound(c,least_upper_bound(X_33,b))) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
least_upper_bound(least_upper_bound(c,X_33),b) = least_upper_bound(b,least_upper_bound(X_33,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_33,b)),least_upper_bound(b,least_upper_bound(X_33,c))) )],[refute_0_1459,refute_0_1462]) ).
cnf(refute_0_1464,plain,
( least_upper_bound(least_upper_bound(c,X_33),b) != least_upper_bound(a,least_upper_bound(c,X_33))
| least_upper_bound(least_upper_bound(c,X_33),b) != least_upper_bound(b,least_upper_bound(X_33,c))
| least_upper_bound(b,least_upper_bound(X_33,c)) = least_upper_bound(a,least_upper_bound(c,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_33),b),least_upper_bound(a,least_upper_bound(c,X_33))) ),[0],$fot(least_upper_bound(b,least_upper_bound(X_33,c)))]]) ).
cnf(refute_0_1465,plain,
( least_upper_bound(least_upper_bound(c,X_33),b) != least_upper_bound(a,least_upper_bound(c,X_33))
| least_upper_bound(b,least_upper_bound(X_33,c)) = least_upper_bound(a,least_upper_bound(c,X_33)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_33),b),least_upper_bound(b,least_upper_bound(X_33,c))) )],[refute_0_1463,refute_0_1464]) ).
cnf(refute_0_1466,plain,
least_upper_bound(b,least_upper_bound(X_33,c)) = least_upper_bound(a,least_upper_bound(c,X_33)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_33),b),least_upper_bound(a,least_upper_bound(c,X_33))) )],[refute_0_1458,refute_0_1465]) ).
cnf(refute_0_1467,plain,
least_upper_bound(b,least_upper_bound(X_292,c)) = least_upper_bound(a,least_upper_bound(c,X_292)),
inference(subst,[],[refute_0_1466:[bind(X_33,$fot(X_292))]]) ).
cnf(refute_0_1468,plain,
( greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(b,least_upper_bound(X_292,c))) != least_upper_bound(b,X_292)
| least_upper_bound(b,least_upper_bound(X_292,c)) != least_upper_bound(a,least_upper_bound(c,X_292))
| greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(a,least_upper_bound(c,X_292))) = least_upper_bound(b,X_292) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(b,least_upper_bound(X_292,c))),least_upper_bound(b,X_292)) ),[0,1],$fot(least_upper_bound(a,least_upper_bound(c,X_292)))]]) ).
cnf(refute_0_1469,plain,
( greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(b,least_upper_bound(X_292,c))) != least_upper_bound(b,X_292)
| greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(a,least_upper_bound(c,X_292))) = least_upper_bound(b,X_292) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_292,c)),least_upper_bound(a,least_upper_bound(c,X_292))) )],[refute_0_1467,refute_0_1468]) ).
cnf(refute_0_1470,plain,
greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(a,least_upper_bound(c,X_292))) = least_upper_bound(b,X_292),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,X_292),least_upper_bound(b,least_upper_bound(X_292,c))),least_upper_bound(b,X_292)) )],[refute_0_1454,refute_0_1469]) ).
cnf(refute_0_1471,plain,
greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,least_upper_bound(c,a))) = least_upper_bound(b,a),
inference(subst,[],[refute_0_1470:[bind(X_292,$fot(a))]]) ).
cnf(refute_0_1472,plain,
least_upper_bound(a,least_upper_bound(c,a)) = least_upper_bound(a,c),
inference(subst,[],[refute_0_279:[bind(Y,$fot(c)),bind(X_13,$fot(a))]]) ).
cnf(refute_0_1473,plain,
( greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,least_upper_bound(c,a))) != least_upper_bound(b,a)
| least_upper_bound(a,least_upper_bound(c,a)) != least_upper_bound(a,c)
| greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) = least_upper_bound(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,least_upper_bound(c,a))),least_upper_bound(b,a)) ),[0,1],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_1474,plain,
( greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,least_upper_bound(c,a))) != least_upper_bound(b,a)
| greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) = least_upper_bound(b,a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,a)),least_upper_bound(a,c)) )],[refute_0_1472,refute_0_1473]) ).
cnf(refute_0_1475,plain,
greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) = least_upper_bound(b,a),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,least_upper_bound(c,a))),least_upper_bound(b,a)) )],[refute_0_1471,refute_0_1474]) ).
cnf(refute_0_1476,plain,
least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c)))) = greatest_lower_bound(X_64,least_upper_bound(a,c)),
inference(subst,[],[refute_0_270:[bind(X_10,$fot(greatest_lower_bound(X_64,least_upper_bound(a,c)))),bind(X_11,$fot(b))]]) ).
cnf(refute_0_1477,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b),
inference(subst,[],[refute_0_570:[bind(Y,$fot(b)),bind(X_15,$fot(greatest_lower_bound(least_upper_bound(a,c),X_59)))]]) ).
cnf(refute_0_1478,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)) != greatest_lower_bound(b,X_59)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)) ),[0,1],$fot(greatest_lower_bound(b,X_59))]]) ).
cnf(refute_0_1479,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)) )],[refute_0_1174,refute_0_1478]) ).
cnf(refute_0_1480,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)) )],[refute_0_1477,refute_0_1479]) ).
cnf(refute_0_1481,plain,
greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)) = greatest_lower_bound(X_59,least_upper_bound(a,c)),
inference(subst,[],[refute_0_570:[bind(Y,$fot(least_upper_bound(a,c))),bind(X_15,$fot(X_59))]]) ).
cnf(refute_0_1482,plain,
greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) = greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))))]]) ).
cnf(refute_0_1483,plain,
( greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)) != greatest_lower_bound(X_59,least_upper_bound(a,c))
| greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) != greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))
| greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) = greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))),greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))) ),[1,1],$fot(greatest_lower_bound(X_59,least_upper_bound(a,c)))]]) ).
cnf(refute_0_1484,plain,
( greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)) != greatest_lower_bound(X_59,least_upper_bound(a,c))
| greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) = greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))),greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))) )],[refute_0_1482,refute_0_1483]) ).
cnf(refute_0_1485,plain,
greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) = greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(X_59,least_upper_bound(a,c))) )],[refute_0_1481,refute_0_1484]) ).
cnf(refute_0_1486,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1487,plain,
greatest_lower_bound(X_58,X_57) = greatest_lower_bound(X_57,X_58),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_58)),bind(Y,$fot(X_57))]]) ).
cnf(refute_0_1488,plain,
( greatest_lower_bound(X_58,X_57) != greatest_lower_bound(X_57,X_58)
| greatest_lower_bound(X_57,X_58) = greatest_lower_bound(X_58,X_57) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_58,X_57))),bind(Y0,$fot(greatest_lower_bound(X_57,X_58)))]]) ).
cnf(refute_0_1489,plain,
greatest_lower_bound(X_57,X_58) = greatest_lower_bound(X_58,X_57),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_58,X_57),greatest_lower_bound(X_57,X_58)) )],[refute_0_1487,refute_0_1488]) ).
cnf(refute_0_1490,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58)
| greatest_lower_bound(X_57,X_58) != greatest_lower_bound(X_58,X_57)
| greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58)) ),[0,1],$fot(greatest_lower_bound(X_58,X_57))]]) ).
cnf(refute_0_1491,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58)
| greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_57,X_58),greatest_lower_bound(X_58,X_57)) )],[refute_0_1489,refute_0_1490]) ).
cnf(refute_0_1492,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58)) )],[refute_0_1486,refute_0_1491]) ).
cnf(refute_0_1493,plain,
greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1494,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58)
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58))]]) ).
cnf(refute_0_1495,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58)
| greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58))) )],[refute_0_1493,refute_0_1494]) ).
cnf(refute_0_1496,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_58)) )],[refute_0_1492,refute_0_1495]) ).
cnf(refute_0_1497,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)))),bind(Y0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58))))]]) ).
cnf(refute_0_1498,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_58,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_58))) )],[refute_0_1496,refute_0_1497]) ).
cnf(refute_0_1499,plain,
greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59)) = greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))),
inference(subst,[],[refute_0_1498:[bind(X_56,$fot(b)),bind(X_57,$fot(greatest_lower_bound(least_upper_bound(a,c),X_59))),bind(X_58,$fot(X_59))]]) ).
cnf(refute_0_1500,plain,
greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)),X_58),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(greatest_lower_bound(Y,X_56))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1501,plain,
greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)) = greatest_lower_bound(X_56,Y),
inference(subst,[],[refute_0_570:[bind(X_15,$fot(X_56))]]) ).
cnf(refute_0_1502,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)) != greatest_lower_bound(X_56,Y)
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)),X_58)
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)),X_58)) ),[1,0],$fot(greatest_lower_bound(X_56,Y))]]) ).
cnf(refute_0_1503,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)),X_58)
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)),greatest_lower_bound(X_56,Y)) )],[refute_0_1501,refute_0_1502]) ).
cnf(refute_0_1504,plain,
greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,greatest_lower_bound(Y,X_56)),X_58)) )],[refute_0_1500,refute_0_1503]) ).
cnf(refute_0_1505,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57))) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(greatest_lower_bound(Y,X_57)))]]) ).
cnf(refute_0_1506,plain,
greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57)) = greatest_lower_bound(X_57,Y),
inference(subst,[],[refute_0_570:[bind(X_15,$fot(X_57))]]) ).
cnf(refute_0_1507,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57))) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57))
| greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57)) != greatest_lower_bound(X_57,Y)
| greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57))),greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57))) ),[0,1],$fot(greatest_lower_bound(X_57,Y))]]) ).
cnf(refute_0_1508,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57))) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57))
| greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57)),greatest_lower_bound(X_57,Y)) )],[refute_0_1506,refute_0_1507]) ).
cnf(refute_0_1509,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(Y,X_57))),greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57))) )],[refute_0_1505,refute_0_1508]) ).
cnf(refute_0_1510,plain,
greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1511,plain,
greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) = greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)))]]) ).
cnf(refute_0_1512,plain,
( greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) != greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y))
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))
| greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)),greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y))) ),[1,1],$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))]]) ).
cnf(refute_0_1513,plain,
( greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))
| greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)),greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y))) )],[refute_0_1511,refute_0_1512]) ).
cnf(refute_0_1514,plain,
greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y),greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) )],[refute_0_1510,refute_0_1513]) ).
cnf(refute_0_1515,plain,
greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_56,X_57)))]]) ).
cnf(refute_0_1516,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(X))]]) ).
cnf(refute_0_1517,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X)
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),X) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X)))]]) ).
cnf(refute_0_1518,plain,
greatest_lower_bound(greatest_lower_bound(X_56,X_57),X) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),X)) )],[refute_0_1516,refute_0_1517]) ).
cnf(refute_0_1519,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X)
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),X) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))
| greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X))]]) ).
cnf(refute_0_1520,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X)
| greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))) )],[refute_0_1518,refute_0_1519]) ).
cnf(refute_0_1521,plain,
greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),X)) )],[refute_0_1515,refute_0_1520]) ).
cnf(refute_0_1522,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))
| greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) = greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)))),bind(Y0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))))]]) ).
cnf(refute_0_1523,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) = greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))) )],[refute_0_1521,refute_0_1522]) ).
cnf(refute_0_1524,plain,
greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)),
inference(subst,[],[refute_0_1523:[bind(X,$fot(X_57)),bind(X_56,$fot(greatest_lower_bound(X_56,X_57))),bind(X_57,$fot(Y))]]) ).
cnf(refute_0_1525,plain,
( greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) != greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y))
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)))),bind(Y0,$fot(greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)))),bind(Z0,$fot(greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))))]]) ).
cnf(refute_0_1526,plain,
( greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)),greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y))) )],[refute_0_1524,refute_0_1525]) ).
cnf(refute_0_1527,plain,
greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_57,greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))) )],[refute_0_1514,refute_0_1526]) ).
cnf(refute_0_1528,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57))
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))
| greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)))]]) ).
cnf(refute_0_1529,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57))
| greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))) )],[refute_0_1527,refute_0_1528]) ).
cnf(refute_0_1530,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(Y,X_57))) )],[refute_0_1509,refute_0_1529]) ).
cnf(refute_0_1531,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))
| greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))),bind(Y0,$fot(greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))))]]) ).
cnf(refute_0_1532,plain,
greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))) )],[refute_0_1530,refute_0_1531]) ).
cnf(refute_0_1533,plain,
greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) = greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)),
inference(subst,[],[refute_0_1532:[bind(Y,$fot(X_58)),bind(X_56,$fot(Y)),bind(X_57,$fot(X_56))]]) ).
cnf(refute_0_1534,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58) = greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)),
inference(subst,[],[refute_0_566:[bind(X,$fot(Y)),bind(Y,$fot(X_56)),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1535,plain,
greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)))]]) ).
cnf(refute_0_1536,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58))
| greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58) != greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)))]]) ).
cnf(refute_0_1537,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58) != greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58))) )],[refute_0_1535,refute_0_1536]) ).
cnf(refute_0_1538,plain,
greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58),greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) )],[refute_0_1534,refute_0_1537]) ).
cnf(refute_0_1539,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) != greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)))),bind(Y0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))))]]) ).
cnf(refute_0_1540,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) != greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)))) )],[refute_0_1538,refute_0_1539]) ).
cnf(refute_0_1541,plain,
greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) = greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))),greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) )],[refute_0_1533,refute_0_1540]) ).
cnf(refute_0_1542,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)
| greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)))]]) ).
cnf(refute_0_1543,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)
| greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58))) )],[refute_0_1541,refute_0_1542]) ).
cnf(refute_0_1544,plain,
greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_56)),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1545,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)
| greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58) != greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58))
| greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)),greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58))]]) ).
cnf(refute_0_1546,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)
| greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58),greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58))) )],[refute_0_1544,refute_0_1545]) ).
cnf(refute_0_1547,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)
| greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)),greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)) )],[refute_0_1543,refute_0_1546]) ).
cnf(refute_0_1548,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(Y,X_56),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,Y),X_58)) )],[refute_0_1504,refute_0_1547]) ).
cnf(refute_0_1549,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) != greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58))
| greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58)) = greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)))),bind(Y0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58))))]]) ).
cnf(refute_0_1550,plain,
greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58)) = greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_56,X_58)),greatest_lower_bound(X_56,greatest_lower_bound(Y,X_58))) )],[refute_0_1548,refute_0_1549]) ).
cnf(refute_0_1551,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59)),
inference(subst,[],[refute_0_1550:[bind(Y,$fot(b)),bind(X_56,$fot(greatest_lower_bound(least_upper_bound(a,c),X_59))),bind(X_58,$fot(X_59))]]) ).
cnf(refute_0_1552,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59)) != greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59)))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))))]]) ).
cnf(refute_0_1553,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59)) != greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59))) )],[refute_0_1551,refute_0_1552]) ).
cnf(refute_0_1554,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),X_59)),greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))) )],[refute_0_1499,refute_0_1553]) ).
cnf(refute_0_1555,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) != greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1556,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))) != greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59)))) )],[refute_0_1554,refute_0_1555]) ).
cnf(refute_0_1557,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) = greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_59,greatest_lower_bound(least_upper_bound(a,c),X_59))),greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c)))) )],[refute_0_1485,refute_0_1556]) ).
cnf(refute_0_1558,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)
| greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1559,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)
| greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c)))) )],[refute_0_1557,refute_0_1558]) ).
cnf(refute_0_1560,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)),
inference(subst,[],[refute_0_1523:[bind(X,$fot(b)),bind(X_56,$fot(least_upper_bound(a,c))),bind(X_57,$fot(X_59))]]) ).
cnf(refute_0_1561,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)) != greatest_lower_bound(b,X_59)
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)) = greatest_lower_bound(b,X_59) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)))),bind(Z0,$fot(greatest_lower_bound(b,X_59)))]]) ).
cnf(refute_0_1562,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)) != greatest_lower_bound(b,X_59)
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)) = greatest_lower_bound(b,X_59) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59))) )],[refute_0_1560,refute_0_1561]) ).
cnf(refute_0_1563,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)) = greatest_lower_bound(b,X_59),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)) )],[refute_0_1174,refute_0_1562]) ).
cnf(refute_0_1564,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)),
inference(subst,[],[refute_0_566:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(X_59)),bind(Z,$fot(b))]]) ).
cnf(refute_0_1565,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)) != greatest_lower_bound(b,X_59)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) = greatest_lower_bound(b,X_59) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)))),bind(Z0,$fot(greatest_lower_bound(b,X_59)))]]) ).
cnf(refute_0_1566,plain,
( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)) != greatest_lower_bound(b,X_59)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) = greatest_lower_bound(b,X_59) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b))) )],[refute_0_1564,refute_0_1565]) ).
cnf(refute_0_1567,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) = greatest_lower_bound(b,X_59),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_59,b)),greatest_lower_bound(b,X_59)) )],[refute_0_1563,refute_0_1566]) ).
cnf(refute_0_1568,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b) != greatest_lower_bound(b,X_59)
| greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) = greatest_lower_bound(b,X_59) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))),greatest_lower_bound(b,X_59)) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b))]]) ).
cnf(refute_0_1569,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)
| greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) = greatest_lower_bound(b,X_59) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b),greatest_lower_bound(b,X_59)) )],[refute_0_1567,refute_0_1568]) ).
cnf(refute_0_1570,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)
| greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) = greatest_lower_bound(b,X_59) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)) )],[refute_0_1559,refute_0_1569]) ).
cnf(refute_0_1571,plain,
greatest_lower_bound(b,greatest_lower_bound(X_59,least_upper_bound(a,c))) = greatest_lower_bound(b,X_59),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),greatest_lower_bound(b,X_59)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_59),b)) )],[refute_0_1480,refute_0_1570]) ).
cnf(refute_0_1572,plain,
greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))) = greatest_lower_bound(b,X_64),
inference(subst,[],[refute_0_1571:[bind(X_59,$fot(X_64))]]) ).
cnf(refute_0_1573,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))) != greatest_lower_bound(b,X_64)
| least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c)))) != greatest_lower_bound(X_64,least_upper_bound(a,c))
| least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)) = greatest_lower_bound(X_64,least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c)))),greatest_lower_bound(X_64,least_upper_bound(a,c))) ),[0,1],$fot(greatest_lower_bound(b,X_64))]]) ).
cnf(refute_0_1574,plain,
( least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c)))) != greatest_lower_bound(X_64,least_upper_bound(a,c))
| least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)) = greatest_lower_bound(X_64,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))),greatest_lower_bound(b,X_64)) )],[refute_0_1572,refute_0_1573]) ).
cnf(refute_0_1575,plain,
least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)) = greatest_lower_bound(X_64,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c)))),greatest_lower_bound(X_64,least_upper_bound(a,c))) )],[refute_0_1476,refute_0_1574]) ).
cnf(refute_0_1576,plain,
least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)) = least_upper_bound(greatest_lower_bound(b,X_64),greatest_lower_bound(X_64,least_upper_bound(a,c))),
inference(subst,[],[refute_0_63:[bind(X,$fot(greatest_lower_bound(b,X_64))),bind(Y,$fot(greatest_lower_bound(X_64,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1577,plain,
( least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)) != greatest_lower_bound(X_64,least_upper_bound(a,c))
| least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)) != least_upper_bound(greatest_lower_bound(b,X_64),greatest_lower_bound(X_64,least_upper_bound(a,c)))
| least_upper_bound(greatest_lower_bound(b,X_64),greatest_lower_bound(X_64,least_upper_bound(a,c))) = greatest_lower_bound(X_64,least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)),greatest_lower_bound(X_64,least_upper_bound(a,c))) ),[0],$fot(least_upper_bound(greatest_lower_bound(b,X_64),greatest_lower_bound(X_64,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1578,plain,
( least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)) != greatest_lower_bound(X_64,least_upper_bound(a,c))
| least_upper_bound(greatest_lower_bound(b,X_64),greatest_lower_bound(X_64,least_upper_bound(a,c))) = greatest_lower_bound(X_64,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)),least_upper_bound(greatest_lower_bound(b,X_64),greatest_lower_bound(X_64,least_upper_bound(a,c)))) )],[refute_0_1576,refute_0_1577]) ).
cnf(refute_0_1579,plain,
least_upper_bound(greatest_lower_bound(b,X_64),greatest_lower_bound(X_64,least_upper_bound(a,c))) = greatest_lower_bound(X_64,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),greatest_lower_bound(b,X_64)),greatest_lower_bound(X_64,least_upper_bound(a,c))) )],[refute_0_1575,refute_0_1578]) ).
cnf(refute_0_1580,plain,
least_upper_bound(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)),
inference(subst,[],[refute_0_1579:[bind(X_64,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)))]]) ).
cnf(refute_0_1581,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) = greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))),X_58),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(a,least_upper_bound(c,X_33)))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_1582,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))),X_58)
| greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))) != b
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) = greatest_lower_bound(b,X_58) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))),X_58)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_1583,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))),X_58)
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) = greatest_lower_bound(b,X_58) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))),b) )],[refute_0_139,refute_0_1582]) ).
cnf(refute_0_1584,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) = greatest_lower_bound(b,X_58),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))),X_58)) )],[refute_0_1581,refute_0_1583]) ).
cnf(refute_0_1585,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) != greatest_lower_bound(b,X_58)
| least_upper_bound(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) ),[0,0],$fot(greatest_lower_bound(b,X_58))]]) ).
cnf(refute_0_1586,plain,
( least_upper_bound(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(b,X_58)) )],[refute_0_1584,refute_0_1585]) ).
cnf(refute_0_1587,plain,
least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) )],[refute_0_1580,refute_0_1586]) ).
cnf(refute_0_1588,plain,
least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)) = greatest_lower_bound(least_upper_bound(a,c),X_58),
inference(subst,[],[refute_0_1181:[bind(X_59,$fot(X_58))]]) ).
cnf(refute_0_1589,plain,
greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_213),X_215)) = greatest_lower_bound(least_upper_bound(X,Y),X_215),
inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_213)),bind(X_56,$fot(least_upper_bound(X,Y))),bind(X_58,$fot(X_215))]]) ).
cnf(refute_0_1590,plain,
least_upper_bound(X,least_upper_bound(Y,X_213)) = least_upper_bound(least_upper_bound(X,Y),X_213),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(X_213))]]) ).
cnf(refute_0_1591,plain,
( least_upper_bound(X,least_upper_bound(Y,X_213)) != least_upper_bound(least_upper_bound(X,Y),X_213)
| least_upper_bound(least_upper_bound(X,Y),X_213) = least_upper_bound(X,least_upper_bound(Y,X_213)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_213)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),X_213)))]]) ).
cnf(refute_0_1592,plain,
least_upper_bound(least_upper_bound(X,Y),X_213) = least_upper_bound(X,least_upper_bound(Y,X_213)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_213)),least_upper_bound(least_upper_bound(X,Y),X_213)) )],[refute_0_1590,refute_0_1591]) ).
cnf(refute_0_1593,plain,
( greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_213),X_215)) != greatest_lower_bound(least_upper_bound(X,Y),X_215)
| least_upper_bound(least_upper_bound(X,Y),X_213) != least_upper_bound(X,least_upper_bound(Y,X_213))
| greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_213)),X_215)) = greatest_lower_bound(least_upper_bound(X,Y),X_215) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_213),X_215)),greatest_lower_bound(least_upper_bound(X,Y),X_215)) ),[0,1,0],$fot(least_upper_bound(X,least_upper_bound(Y,X_213)))]]) ).
cnf(refute_0_1594,plain,
( greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_213),X_215)) != greatest_lower_bound(least_upper_bound(X,Y),X_215)
| greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_213)),X_215)) = greatest_lower_bound(least_upper_bound(X,Y),X_215) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_213),least_upper_bound(X,least_upper_bound(Y,X_213))) )],[refute_0_1592,refute_0_1593]) ).
cnf(refute_0_1595,plain,
greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,X_213)),X_215)) = greatest_lower_bound(least_upper_bound(X,Y),X_215),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(least_upper_bound(least_upper_bound(X,Y),X_213),X_215)),greatest_lower_bound(least_upper_bound(X,Y),X_215)) )],[refute_0_1589,refute_0_1594]) ).
cnf(refute_0_1596,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) = greatest_lower_bound(least_upper_bound(a,c),X_58),
inference(subst,[],[refute_0_1595:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(X_213,$fot(X_33)),bind(X_215,$fot(X_58))]]) ).
cnf(refute_0_1597,plain,
least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) = least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))))]]) ).
cnf(refute_0_1598,plain,
( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) != greatest_lower_bound(least_upper_bound(a,c),X_58)
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) != least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)))
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) = least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))),least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)))) ),[1,1],$fot(greatest_lower_bound(least_upper_bound(a,c),X_58))]]) ).
cnf(refute_0_1599,plain,
( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)) != greatest_lower_bound(least_upper_bound(a,c),X_58)
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) = least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))),least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)))) )],[refute_0_1597,refute_0_1598]) ).
cnf(refute_0_1600,plain,
least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) = least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)),greatest_lower_bound(least_upper_bound(a,c),X_58)) )],[refute_0_1596,refute_0_1599]) ).
cnf(refute_0_1601,plain,
( least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)) != greatest_lower_bound(least_upper_bound(a,c),X_58)
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) != least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58))
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) = greatest_lower_bound(least_upper_bound(a,c),X_58) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,c),X_58)))]]) ).
cnf(refute_0_1602,plain,
( least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)) != greatest_lower_bound(least_upper_bound(a,c),X_58)
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) = greatest_lower_bound(least_upper_bound(a,c),X_58) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))),least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58))) )],[refute_0_1600,refute_0_1601]) ).
cnf(refute_0_1603,plain,
least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) = greatest_lower_bound(least_upper_bound(a,c),X_58),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),X_58)),greatest_lower_bound(least_upper_bound(a,c),X_58)) )],[refute_0_1588,refute_0_1602]) ).
cnf(refute_0_1604,plain,
least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) = least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192))),
inference(subst,[],[refute_0_680:[bind(X,$fot(greatest_lower_bound(X_191,X_192))),bind(X_21,$fot(greatest_lower_bound(X_192,X_191)))]]) ).
cnf(refute_0_1605,plain,
least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))) = greatest_lower_bound(X_16,X_11),
inference(subst,[],[refute_0_270:[bind(X_10,$fot(greatest_lower_bound(X_16,X_11)))]]) ).
cnf(refute_0_1606,plain,
greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)) = greatest_lower_bound(X_11,X_16),
inference(subst,[],[refute_0_570:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_11))]]) ).
cnf(refute_0_1607,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_1608,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( $equal(greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11)),greatest_lower_bound(X_11,X_16)) )],[refute_0_1606,refute_0_1607]) ).
cnf(refute_0_1609,plain,
least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) = greatest_lower_bound(X_16,X_11),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_16,X_11))),greatest_lower_bound(X_16,X_11)) )],[refute_0_1605,refute_0_1608]) ).
cnf(refute_0_1610,plain,
least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)) = greatest_lower_bound(X_192,X_191),
inference(subst,[],[refute_0_1609:[bind(X_11,$fot(X_191)),bind(X_16,$fot(X_192))]]) ).
cnf(refute_0_1611,plain,
( least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) != least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))
| least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)) != greatest_lower_bound(X_192,X_191)
| least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))),least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))) ),[1,1],$fot(greatest_lower_bound(X_192,X_191))]]) ).
cnf(refute_0_1612,plain,
( least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) != least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))
| least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)),greatest_lower_bound(X_192,X_191)) )],[refute_0_1610,refute_0_1611]) ).
cnf(refute_0_1613,plain,
least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))),least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))) )],[refute_0_1604,refute_0_1612]) ).
cnf(refute_0_1614,plain,
least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))) = least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192))),
inference(subst,[],[refute_0_747:[bind(Y,$fot(greatest_lower_bound(X_192,X_191))),bind(X_22,$fot(greatest_lower_bound(X_191,X_192)))]]) ).
cnf(refute_0_1615,plain,
( least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)) != greatest_lower_bound(X_192,X_191)
| least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))) != least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))
| least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))),least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))) ),[1,1],$fot(greatest_lower_bound(X_192,X_191))]]) ).
cnf(refute_0_1616,plain,
( least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))) != least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))
| least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)),greatest_lower_bound(X_192,X_191)) )],[refute_0_1610,refute_0_1615]) ).
cnf(refute_0_1617,plain,
least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))),least_upper_bound(X_20,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)))) )],[refute_0_1614,refute_0_1616]) ).
cnf(refute_0_1618,plain,
least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) = least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)),
inference(subst,[],[refute_0_1617:[bind(X_191,$fot(X_192)),bind(X_192,$fot(X_191))]]) ).
cnf(refute_0_1619,plain,
( least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) != least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))
| least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) != least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))
| least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) ),[0],$fot(least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)))]]) ).
cnf(refute_0_1620,plain,
( least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) != least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))
| least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))),least_upper_bound(X_20,greatest_lower_bound(X_191,X_192))) )],[refute_0_1618,refute_0_1619]) ).
cnf(refute_0_1621,plain,
least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)) = least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_191,X_192),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) )],[refute_0_1613,refute_0_1620]) ).
cnf(refute_0_1622,plain,
( least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)) != least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))
| least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) = least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)))),bind(Y0,$fot(least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))))]]) ).
cnf(refute_0_1623,plain,
least_upper_bound(X_20,greatest_lower_bound(X_192,X_191)) = least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,greatest_lower_bound(X_191,X_192)),least_upper_bound(X_20,greatest_lower_bound(X_192,X_191))) )],[refute_0_1621,refute_0_1622]) ).
cnf(refute_0_1624,plain,
least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))),
inference(subst,[],[refute_0_1623:[bind(X_191,$fot(least_upper_bound(a,c))),bind(X_192,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))),bind(X_20,$fot(greatest_lower_bound(b,X_58)))]]) ).
cnf(refute_0_1625,plain,
( least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)))
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) != greatest_lower_bound(least_upper_bound(a,c),X_58)
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),X_58) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,c),X_58)))]]) ).
cnf(refute_0_1626,plain,
( least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))) != greatest_lower_bound(least_upper_bound(a,c),X_58)
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),X_58) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))),least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58)))) )],[refute_0_1624,refute_0_1625]) ).
cnf(refute_0_1627,plain,
least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),X_58),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58))),greatest_lower_bound(least_upper_bound(a,c),X_58)) )],[refute_0_1603,refute_0_1626]) ).
cnf(refute_0_1628,plain,
( least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))
| least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),X_58)
| greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) ),[0],$fot(greatest_lower_bound(least_upper_bound(a,c),X_58))]]) ).
cnf(refute_0_1629,plain,
( least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),X_58)) )],[refute_0_1627,refute_0_1628]) ).
cnf(refute_0_1630,plain,
greatest_lower_bound(X_77,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78))) = greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)),
inference(subst,[],[refute_0_1521:[bind(X,$fot(X_77)),bind(X_56,$fot(X_78)),bind(X_57,$fot(greatest_lower_bound(Y,X_78)))]]) ).
cnf(refute_0_1631,plain,
greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78)) = greatest_lower_bound(X_78,Y),
inference(subst,[],[refute_0_570:[bind(X_15,$fot(X_78))]]) ).
cnf(refute_0_1632,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78))) != greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))
| greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78)) != greatest_lower_bound(X_78,Y)
| greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78))),greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))) ),[0,1],$fot(greatest_lower_bound(X_78,Y))]]) ).
cnf(refute_0_1633,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78))) != greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))
| greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78)),greatest_lower_bound(X_78,Y)) )],[refute_0_1631,refute_0_1632]) ).
cnf(refute_0_1634,plain,
greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_78))),greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))) )],[refute_0_1630,refute_0_1633]) ).
cnf(refute_0_1635,plain,
greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)),
inference(subst,[],[refute_0_1532:[bind(Y,$fot(X_77)),bind(X_56,$fot(Y)),bind(X_57,$fot(X_78))]]) ).
cnf(refute_0_1636,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)),
inference(subst,[],[refute_0_566:[bind(X,$fot(Y)),bind(Y,$fot(X_78)),bind(Z,$fot(X_77))]]) ).
cnf(refute_0_1637,plain,
greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) = greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)))]]) ).
cnf(refute_0_1638,plain,
( greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) != greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))
| greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77) != greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))
| greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) = greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)),greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)))]]) ).
cnf(refute_0_1639,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77) != greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))
| greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) = greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)),greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))) )],[refute_0_1637,refute_0_1638]) ).
cnf(refute_0_1640,plain,
greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) = greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77),greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) )],[refute_0_1636,refute_0_1639]) ).
cnf(refute_0_1641,plain,
( greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) != greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))
| greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) != greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)))
| greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)))),bind(Y0,$fot(greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))))]]) ).
cnf(refute_0_1642,plain,
( greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) != greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))
| greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)),greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)))) )],[refute_0_1640,refute_0_1641]) ).
cnf(refute_0_1643,plain,
greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_78,greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))),greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) )],[refute_0_1635,refute_0_1642]) ).
cnf(refute_0_1644,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) != greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))
| greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)) != greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))
| greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) ),[0],$fot(greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)))]]) ).
cnf(refute_0_1645,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) != greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))
| greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77)),greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) )],[refute_0_1643,refute_0_1644]) ).
cnf(refute_0_1646,plain,
greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)),greatest_lower_bound(X_78,greatest_lower_bound(greatest_lower_bound(Y,X_78),X_77))) )],[refute_0_1634,refute_0_1645]) ).
cnf(refute_0_1647,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))
| greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)) = greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))))]]) ).
cnf(refute_0_1648,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77)) = greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(X_78,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_78,X_77))) )],[refute_0_1646,refute_0_1647]) ).
cnf(refute_0_1649,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(least_upper_bound(a,least_upper_bound(c,X_33)))),bind(X_77,$fot(least_upper_bound(a,c))),bind(X_78,$fot(X_58))]]) ).
cnf(refute_0_1650,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c))),
inference(subst,[],[refute_0_566:[bind(X,$fot(least_upper_bound(a,least_upper_bound(c,X_33)))),bind(Y,$fot(X_58)),bind(Z,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_1651,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) != greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))))]]) ).
cnf(refute_0_1652,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c)))) )],[refute_0_1650,refute_0_1651]) ).
cnf(refute_0_1653,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_58,least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))) )],[refute_0_1649,refute_0_1652]) ).
cnf(refute_0_1654,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(least_upper_bound(a,c),X_58) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) ),[1],$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))))]]) ).
cnf(refute_0_1655,plain,
( greatest_lower_bound(least_upper_bound(a,c),X_58) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))) )],[refute_0_1653,refute_0_1654]) ).
cnf(refute_0_1656,plain,
( least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) )],[refute_0_1629,refute_0_1655]) ).
cnf(refute_0_1657,plain,
greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_58),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),X_58),least_upper_bound(a,c))) )],[refute_0_1587,refute_0_1656]) ).
cnf(refute_0_1658,plain,
greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) = greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290)))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(least_upper_bound(X_291,least_upper_bound(X_292,X_290)))),bind(X_57,$fot(least_upper_bound(X_291,X_292)))]]) ).
cnf(refute_0_1659,plain,
greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290))) = least_upper_bound(X_291,X_292),
inference(subst,[],[refute_0_1453:[bind(Y,$fot(X_290)),bind(X_20,$fot(X_291)),bind(X_21,$fot(X_292))]]) ).
cnf(refute_0_1660,plain,
( greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290))) != least_upper_bound(X_291,X_292)
| greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) != greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290))))
| greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) = greatest_lower_bound(X_56,least_upper_bound(X_291,X_292)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290))))) ),[1,1],$fot(least_upper_bound(X_291,X_292))]]) ).
cnf(refute_0_1661,plain,
( greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) != greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290))))
| greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) = greatest_lower_bound(X_56,least_upper_bound(X_291,X_292)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290))),least_upper_bound(X_291,X_292)) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) = greatest_lower_bound(X_56,least_upper_bound(X_291,X_292)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_291,X_292),least_upper_bound(X_291,least_upper_bound(X_292,X_290))))) )],[refute_0_1658,refute_0_1661]) ).
cnf(refute_0_1663,plain,
greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) = greatest_lower_bound(least_upper_bound(X_291,X_292),greatest_lower_bound(X_56,least_upper_bound(X_291,least_upper_bound(X_292,X_290)))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(least_upper_bound(X_291,least_upper_bound(X_292,X_290)))),bind(X_77,$fot(least_upper_bound(X_291,X_292))),bind(X_78,$fot(X_56))]]) ).
cnf(refute_0_1664,plain,
( greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) != greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))
| greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) != greatest_lower_bound(least_upper_bound(X_291,X_292),greatest_lower_bound(X_56,least_upper_bound(X_291,least_upper_bound(X_292,X_290))))
| greatest_lower_bound(least_upper_bound(X_291,X_292),greatest_lower_bound(X_56,least_upper_bound(X_291,least_upper_bound(X_292,X_290)))) = greatest_lower_bound(X_56,least_upper_bound(X_291,X_292)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_291,X_292),greatest_lower_bound(X_56,least_upper_bound(X_291,least_upper_bound(X_292,X_290)))))]]) ).
cnf(refute_0_1665,plain,
( greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) != greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))
| greatest_lower_bound(least_upper_bound(X_291,X_292),greatest_lower_bound(X_56,least_upper_bound(X_291,least_upper_bound(X_292,X_290)))) = greatest_lower_bound(X_56,least_upper_bound(X_291,X_292)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))),greatest_lower_bound(least_upper_bound(X_291,X_292),greatest_lower_bound(X_56,least_upper_bound(X_291,least_upper_bound(X_292,X_290))))) )],[refute_0_1663,refute_0_1664]) ).
cnf(refute_0_1666,plain,
greatest_lower_bound(least_upper_bound(X_291,X_292),greatest_lower_bound(X_56,least_upper_bound(X_291,least_upper_bound(X_292,X_290)))) = greatest_lower_bound(X_56,least_upper_bound(X_291,X_292)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,least_upper_bound(X_292,X_290)),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))),greatest_lower_bound(X_56,least_upper_bound(X_291,X_292))) )],[refute_0_1662,refute_0_1665]) ).
cnf(refute_0_1667,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))) = greatest_lower_bound(X_58,least_upper_bound(a,c)),
inference(subst,[],[refute_0_1666:[bind(X_290,$fot(X_33)),bind(X_291,$fot(a)),bind(X_292,$fot(c)),bind(X_56,$fot(X_58))]]) ).
cnf(refute_0_1668,plain,
( greatest_lower_bound(least_upper_bound(a,c),X_58) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))) != greatest_lower_bound(X_58,least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(X_58,least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(a,c),X_58),greatest_lower_bound(X_58,least_upper_bound(a,c))) ),[0],$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))))]]) ).
cnf(refute_0_1669,plain,
( greatest_lower_bound(least_upper_bound(a,c),X_58) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(X_58,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33)))),greatest_lower_bound(X_58,least_upper_bound(a,c))) )],[refute_0_1667,refute_0_1668]) ).
cnf(refute_0_1670,plain,
greatest_lower_bound(least_upper_bound(a,c),X_58) = greatest_lower_bound(X_58,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),X_58),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_58,least_upper_bound(a,least_upper_bound(c,X_33))))) )],[refute_0_1657,refute_0_1669]) ).
cnf(refute_0_1671,plain,
greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b)) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),
inference(subst,[],[refute_0_1670:[bind(X_58,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_1672,plain,
least_upper_bound(greatest_lower_bound(b,least_upper_bound(Y,b)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b)),
inference(subst,[],[refute_0_1181:[bind(X_59,$fot(least_upper_bound(Y,b)))]]) ).
cnf(refute_0_1673,plain,
greatest_lower_bound(b,least_upper_bound(Y,b)) = b,
inference(subst,[],[refute_0_262:[bind(X,$fot(b))]]) ).
cnf(refute_0_1674,plain,
( greatest_lower_bound(b,least_upper_bound(Y,b)) != b
| least_upper_bound(greatest_lower_bound(b,least_upper_bound(Y,b)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(Y,b)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_1675,plain,
( least_upper_bound(greatest_lower_bound(b,least_upper_bound(Y,b)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(Y,b)),b) )],[refute_0_1673,refute_0_1674]) ).
cnf(refute_0_1676,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,least_upper_bound(Y,b)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(Y,b))) )],[refute_0_1672,refute_0_1675]) ).
cnf(refute_0_1677,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)),
inference(subst,[],[refute_0_1676:[bind(Y,$fot(X_122))]]) ).
cnf(refute_0_1678,plain,
greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(least_upper_bound(X_122,b))),bind(Y,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_1679,plain,
( greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c)) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)) = greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))))]]) ).
cnf(refute_0_1680,plain,
greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)) = greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))) )],[refute_0_1678,refute_0_1679]) ).
cnf(refute_0_1681,plain,
( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)) != greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))) ),[0,1],$fot(greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c)))]]) ).
cnf(refute_0_1682,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)),greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c))) )],[refute_0_1680,refute_0_1681]) ).
cnf(refute_0_1683,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_122,b),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_122,b))) )],[refute_0_1677,refute_0_1682]) ).
cnf(refute_0_1684,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_251,b),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b)),
inference(subst,[],[refute_0_1683:[bind(X_122,$fot(X_251))]]) ).
cnf(refute_0_1685,plain,
least_upper_bound(b,X_251) = least_upper_bound(X_251,b),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(b)),bind(Y,$fot(X_251))]]) ).
cnf(refute_0_1686,plain,
( least_upper_bound(b,X_251) != least_upper_bound(X_251,b)
| least_upper_bound(X_251,b) = least_upper_bound(b,X_251) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(b,X_251))),bind(Y0,$fot(least_upper_bound(X_251,b)))]]) ).
cnf(refute_0_1687,plain,
least_upper_bound(X_251,b) = least_upper_bound(b,X_251),
inference(resolve,[$cnf( $equal(least_upper_bound(b,X_251),least_upper_bound(X_251,b)) )],[refute_0_1685,refute_0_1686]) ).
cnf(refute_0_1688,plain,
( least_upper_bound(X_251,b) != least_upper_bound(b,X_251)
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_251,b),least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_251,b),least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))) ),[0,1,0],$fot(least_upper_bound(b,X_251))]]) ).
cnf(refute_0_1689,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_251,b),least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_251,b),least_upper_bound(b,X_251)) )],[refute_0_1687,refute_0_1688]) ).
cnf(refute_0_1690,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(X_251,b),least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))) )],[refute_0_1684,refute_0_1689]) ).
cnf(refute_0_1691,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)),
inference(subst,[],[refute_0_1186:[bind(Y,$fot(X_251))]]) ).
cnf(refute_0_1692,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) = least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))),
inference(subst,[],[refute_0_1623:[bind(X_191,$fot(least_upper_bound(a,c))),bind(X_192,$fot(least_upper_bound(b,X_251))),bind(X_20,$fot(b))]]) ).
cnf(refute_0_1693,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) != least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))))),bind(Y0,$fot(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))))]]) ).
cnf(refute_0_1694,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))),least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)))) )],[refute_0_1692,refute_0_1693]) ).
cnf(refute_0_1695,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))) )],[refute_0_1691,refute_0_1694]) ).
cnf(refute_0_1696,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))) ),[0],$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)))]]) ).
cnf(refute_0_1697,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251))) )],[refute_0_1695,refute_0_1696]) ).
cnf(refute_0_1698,plain,
greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_251)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(b,X_251),least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_251,b))) )],[refute_0_1690,refute_0_1697]) ).
cnf(refute_0_1699,plain,
greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b)),
inference(subst,[],[refute_0_1698:[bind(X_251,$fot(a))]]) ).
cnf(refute_0_1700,plain,
( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b)) != greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))))]]) ).
cnf(refute_0_1701,plain,
( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b)) != greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b))) )],[refute_0_1699,refute_0_1700]) ).
cnf(refute_0_1702,plain,
greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))) )],[refute_0_1671,refute_0_1701]) ).
cnf(refute_0_1703,plain,
( greatest_lower_bound(least_upper_bound(a,c),X_58) != greatest_lower_bound(X_58,least_upper_bound(a,c))
| greatest_lower_bound(X_58,least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),X_58) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),X_58))),bind(Y0,$fot(greatest_lower_bound(X_58,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1704,plain,
greatest_lower_bound(X_58,least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),X_58),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),X_58),greatest_lower_bound(X_58,least_upper_bound(a,c))) )],[refute_0_1670,refute_0_1703]) ).
cnf(refute_0_1705,plain,
greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)),
inference(subst,[],[refute_0_1704:[bind(X_58,$fot(least_upper_bound(b,a)))]]) ).
cnf(refute_0_1706,plain,
( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)) != greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a))
| greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))))]]) ).
cnf(refute_0_1707,plain,
( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)) != greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a))) )],[refute_0_1705,refute_0_1706]) ).
cnf(refute_0_1708,plain,
greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,a)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))) )],[refute_0_1702,refute_0_1707]) ).
cnf(refute_0_1709,plain,
( greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) != greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) != least_upper_bound(b,a)
| greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) = least_upper_bound(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)),least_upper_bound(b,a)) ),[0],$fot(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)))]]) ).
cnf(refute_0_1710,plain,
( greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) != least_upper_bound(b,a)
| greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) = least_upper_bound(b,a) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c))) )],[refute_0_1708,refute_0_1709]) ).
cnf(refute_0_1711,plain,
least_upper_bound(b,a) = least_upper_bound(a,b),
inference(subst,[],[refute_0_1395:[bind(X_137,$fot(a)),bind(X_20,$fot(b))]]) ).
cnf(refute_0_1712,plain,
( greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) != least_upper_bound(b,a)
| least_upper_bound(b,a) != least_upper_bound(a,b)
| greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),least_upper_bound(a,b)) ),[0],$fot(least_upper_bound(b,a))]]) ).
cnf(refute_0_1713,plain,
( greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) != least_upper_bound(b,a)
| greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,a),least_upper_bound(a,b)) )],[refute_0_1711,refute_0_1712]) ).
cnf(refute_0_1714,plain,
( greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)) != least_upper_bound(b,a)
| greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),least_upper_bound(b,a)) )],[refute_0_1710,refute_0_1713]) ).
cnf(refute_0_1715,plain,
greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) = least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,a),least_upper_bound(a,c)),least_upper_bound(b,a)) )],[refute_0_1475,refute_0_1714]) ).
cnf(refute_0_1716,plain,
( greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) != least_upper_bound(a,b)
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)))) != identity
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)))),identity) ),[0,1,1],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_1717,plain,
( least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)))) != identity
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),least_upper_bound(a,b)) )],[refute_0_1715,refute_0_1716]) ).
cnf(refute_0_1718,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)))),identity) )],[refute_0_1449,refute_0_1717]) ).
cnf(refute_0_1719,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) != identity
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_1720,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity) )],[refute_0_1718,refute_0_1719]) ).
cnf(refute_0_1721,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))) )],[refute_0_1448,refute_0_1720]) ).
cnf(refute_0_1722,plain,
inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) = multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(least_upper_bound(a,c))),bind(X_74,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_1723,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))]]) ).
cnf(refute_0_1724,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))
| inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) != multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))),bind(Y0,$fot(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))]]) ).
cnf(refute_0_1725,plain,
( inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) != multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) )],[refute_0_1723,refute_0_1724]) ).
cnf(refute_0_1726,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) )],[refute_0_1722,refute_0_1725]) ).
cnf(refute_0_1727,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))) ),[0],$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))]]) ).
cnf(refute_0_1728,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) )],[refute_0_1726,refute_0_1727]) ).
cnf(refute_0_1729,plain,
least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))]]) ).
cnf(refute_0_1730,plain,
( inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) != multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) ),[1,1],$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))]]) ).
cnf(refute_0_1731,plain,
( inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))) != multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) )],[refute_0_1729,refute_0_1730]) ).
cnf(refute_0_1732,plain,
least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) )],[refute_0_1722,refute_0_1731]) ).
cnf(refute_0_1733,plain,
multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))))]]) ).
cnf(refute_0_1734,plain,
multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)) = multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),
inference(subst,[],[refute_0_320:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))]]) ).
cnf(refute_0_1735,plain,
( multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)) != multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))))]]) ).
cnf(refute_0_1736,plain,
( multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)),multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))) )],[refute_0_1734,refute_0_1735]) ).
cnf(refute_0_1737,plain,
multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) )],[refute_0_1733,refute_0_1736]) ).
cnf(refute_0_1738,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)),
inference(subst,[],[refute_0_337:[bind(X_82,$fot(identity)),bind(X_83,$fot(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))]]) ).
cnf(refute_0_1739,plain,
( multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) != multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))))]]) ).
cnf(refute_0_1740,plain,
( multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity))) )],[refute_0_1738,refute_0_1739]) ).
cnf(refute_0_1741,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))),identity)),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) )],[refute_0_1737,refute_0_1740]) ).
cnf(refute_0_1742,plain,
( least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1743,plain,
( least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) )],[refute_0_1741,refute_0_1742]) ).
cnf(refute_0_1744,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) )],[refute_0_1732,refute_0_1743]) ).
cnf(refute_0_1745,plain,
( multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))))]]) ).
cnf(refute_0_1746,plain,
( multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b))))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) )],[refute_0_1744,refute_0_1745]) ).
cnf(refute_0_1747,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))
| multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))) )],[refute_0_1728,refute_0_1746]) ).
cnf(refute_0_1748,plain,
multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,b)))))) )],[refute_0_1721,refute_0_1747]) ).
cnf(refute_0_1749,plain,
( multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1750,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) )],[refute_0_1748,refute_0_1749]) ).
cnf(refute_0_1751,plain,
( least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != least_upper_bound(a,c)
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),least_upper_bound(a,c)) ),[0,1,1,1],$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))]]) ).
cnf(refute_0_1752,plain,
( least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != least_upper_bound(a,c)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) )],[refute_0_1750,refute_0_1751]) ).
cnf(refute_0_1753,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),least_upper_bound(a,c)) )],[refute_0_1447,refute_0_1752]) ).
cnf(refute_0_1754,plain,
multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)) = multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),
inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(inverse(least_upper_bound(a,b)))),bind(Z,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_1755,plain,
least_upper_bound(b,b) = b,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(b))]]) ).
cnf(refute_0_1756,plain,
least_upper_bound(a,least_upper_bound(b,b)) = least_upper_bound(a,least_upper_bound(b,b)),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(b,b)))]]) ).
cnf(refute_0_1757,plain,
( least_upper_bound(a,least_upper_bound(b,b)) != least_upper_bound(a,least_upper_bound(b,b))
| least_upper_bound(b,b) != b
| least_upper_bound(a,least_upper_bound(b,b)) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,b)),least_upper_bound(a,least_upper_bound(b,b))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_1758,plain,
( least_upper_bound(b,b) != b
| least_upper_bound(a,least_upper_bound(b,b)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,b)),least_upper_bound(a,least_upper_bound(b,b))) )],[refute_0_1756,refute_0_1757]) ).
cnf(refute_0_1759,plain,
least_upper_bound(a,least_upper_bound(b,b)) = least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(b,b),b) )],[refute_0_1755,refute_0_1758]) ).
cnf(refute_0_1760,plain,
inverse(least_upper_bound(a,least_upper_bound(b,b))) = inverse(least_upper_bound(a,least_upper_bound(b,b))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(a,least_upper_bound(b,b))))]]) ).
cnf(refute_0_1761,plain,
( inverse(least_upper_bound(a,least_upper_bound(b,b))) != inverse(least_upper_bound(a,least_upper_bound(b,b)))
| least_upper_bound(a,least_upper_bound(b,b)) != least_upper_bound(a,b)
| inverse(least_upper_bound(a,least_upper_bound(b,b))) = inverse(least_upper_bound(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(b,b))),inverse(least_upper_bound(a,least_upper_bound(b,b)))) ),[1,0],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_1762,plain,
( least_upper_bound(a,least_upper_bound(b,b)) != least_upper_bound(a,b)
| inverse(least_upper_bound(a,least_upper_bound(b,b))) = inverse(least_upper_bound(a,b)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(b,b))),inverse(least_upper_bound(a,least_upper_bound(b,b)))) )],[refute_0_1760,refute_0_1761]) ).
cnf(refute_0_1763,plain,
inverse(least_upper_bound(a,least_upper_bound(b,b))) = inverse(least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,b)),least_upper_bound(a,b)) )],[refute_0_1759,refute_0_1762]) ).
cnf(refute_0_1764,plain,
inverse(least_upper_bound(X_85,X_86)) = multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),inverse(X_86)),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(X_86))),bind(X_69,$fot(least_upper_bound(X_85,X_86)))]]) ).
cnf(refute_0_1765,plain,
( multiply(inverse(X_86),least_upper_bound(X_85,X_86)) != least_upper_bound(identity,multiply(inverse(X_86),X_85))
| inverse(least_upper_bound(X_85,X_86)) != multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),inverse(X_86))
| inverse(least_upper_bound(X_85,X_86)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_85,X_86)),multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),inverse(X_86))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(inverse(X_86),X_85)))]]) ).
cnf(refute_0_1766,plain,
( inverse(least_upper_bound(X_85,X_86)) != multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),inverse(X_86))
| inverse(least_upper_bound(X_85,X_86)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(X_85,X_86)),least_upper_bound(identity,multiply(inverse(X_86),X_85))) )],[refute_0_576,refute_0_1765]) ).
cnf(refute_0_1767,plain,
inverse(least_upper_bound(X_85,X_86)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_85,X_86)),multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),inverse(X_86))) )],[refute_0_1764,refute_0_1766]) ).
cnf(refute_0_1768,plain,
multiply(X_86,identity) = X_86,
inference(subst,[],[refute_0_51:[bind(X_48,$fot(X_86))]]) ).
cnf(refute_0_1769,plain,
least_upper_bound(multiply(X_86,identity),X_85) = least_upper_bound(multiply(X_86,identity),X_85),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_86,identity),X_85))]]) ).
cnf(refute_0_1770,plain,
( multiply(X_86,identity) != X_86
| least_upper_bound(multiply(X_86,identity),X_85) != least_upper_bound(multiply(X_86,identity),X_85)
| least_upper_bound(multiply(X_86,identity),X_85) = least_upper_bound(X_86,X_85) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_86,identity),X_85),least_upper_bound(multiply(X_86,identity),X_85)) ),[1,0],$fot(X_86)]]) ).
cnf(refute_0_1771,plain,
( multiply(X_86,identity) != X_86
| least_upper_bound(multiply(X_86,identity),X_85) = least_upper_bound(X_86,X_85) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_86,identity),X_85),least_upper_bound(multiply(X_86,identity),X_85)) )],[refute_0_1769,refute_0_1770]) ).
cnf(refute_0_1772,plain,
least_upper_bound(multiply(X_86,identity),X_85) = least_upper_bound(X_86,X_85),
inference(resolve,[$cnf( $equal(multiply(X_86,identity),X_86) )],[refute_0_1768,refute_0_1771]) ).
cnf(refute_0_1773,plain,
multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))) = least_upper_bound(multiply(X_86,identity),X_85),
inference(subst,[],[refute_0_829:[bind(X_46,$fot(X_85)),bind(X_82,$fot(X_86)),bind(X_83,$fot(identity))]]) ).
cnf(refute_0_1774,plain,
( multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))) != least_upper_bound(multiply(X_86,identity),X_85)
| least_upper_bound(multiply(X_86,identity),X_85) != least_upper_bound(X_86,X_85)
| multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))) = least_upper_bound(X_86,X_85) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))))),bind(Y0,$fot(least_upper_bound(multiply(X_86,identity),X_85))),bind(Z0,$fot(least_upper_bound(X_86,X_85)))]]) ).
cnf(refute_0_1775,plain,
( least_upper_bound(multiply(X_86,identity),X_85) != least_upper_bound(X_86,X_85)
| multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))) = least_upper_bound(X_86,X_85) ),
inference(resolve,[$cnf( $equal(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))),least_upper_bound(multiply(X_86,identity),X_85)) )],[refute_0_1773,refute_0_1774]) ).
cnf(refute_0_1776,plain,
multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))) = least_upper_bound(X_86,X_85),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_86,identity),X_85),least_upper_bound(X_86,X_85)) )],[refute_0_1772,refute_0_1775]) ).
cnf(refute_0_1777,plain,
inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))) = inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))))]]) ).
cnf(refute_0_1778,plain,
( multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))) != least_upper_bound(X_86,X_85)
| inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))) != inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))))
| inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))) = inverse(least_upper_bound(X_86,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))),inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))))) ),[1,0],$fot(least_upper_bound(X_86,X_85))]]) ).
cnf(refute_0_1779,plain,
( multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))) != least_upper_bound(X_86,X_85)
| inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))) = inverse(least_upper_bound(X_86,X_85)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))),inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))))) )],[refute_0_1777,refute_0_1778]) ).
cnf(refute_0_1780,plain,
inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))) = inverse(least_upper_bound(X_86,X_85)),
inference(resolve,[$cnf( $equal(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))),least_upper_bound(X_86,X_85)) )],[refute_0_1776,refute_0_1779]) ).
cnf(refute_0_1781,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) = inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(X_86)),bind(X_46,$fot(least_upper_bound(identity,multiply(inverse(X_86),X_85))))]]) ).
cnf(refute_0_1782,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) != inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))))
| inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))) != inverse(least_upper_bound(X_86,X_85))
| multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) = inverse(least_upper_bound(X_86,X_85)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)))),bind(Y0,$fot(inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))))),bind(Z0,$fot(inverse(least_upper_bound(X_86,X_85))))]]) ).
cnf(refute_0_1783,plain,
( inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))) != inverse(least_upper_bound(X_86,X_85))
| multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) = inverse(least_upper_bound(X_86,X_85)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)),inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85))))) )],[refute_0_1781,refute_0_1782]) ).
cnf(refute_0_1784,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) = inverse(least_upper_bound(X_86,X_85)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_86,least_upper_bound(identity,multiply(inverse(X_86),X_85)))),inverse(least_upper_bound(X_86,X_85))) )],[refute_0_1780,refute_0_1783]) ).
cnf(refute_0_1785,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)) != inverse(least_upper_bound(X_86,X_85))
| inverse(least_upper_bound(X_85,X_86)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86))
| inverse(least_upper_bound(X_85,X_86)) = inverse(least_upper_bound(X_86,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_85,X_86)),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86))) ),[1],$fot(inverse(least_upper_bound(X_86,X_85)))]]) ).
cnf(refute_0_1786,plain,
( inverse(least_upper_bound(X_85,X_86)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86))
| inverse(least_upper_bound(X_85,X_86)) = inverse(least_upper_bound(X_86,X_85)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86)),inverse(least_upper_bound(X_86,X_85))) )],[refute_0_1784,refute_0_1785]) ).
cnf(refute_0_1787,plain,
inverse(least_upper_bound(X_85,X_86)) = inverse(least_upper_bound(X_86,X_85)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_85,X_86)),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),inverse(X_86))) )],[refute_0_1767,refute_0_1786]) ).
cnf(refute_0_1788,plain,
inverse(least_upper_bound(X_375,least_upper_bound(X_31,X_30))) = inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)),
inference(subst,[],[refute_0_1787:[bind(X_85,$fot(X_375)),bind(X_86,$fot(least_upper_bound(X_31,X_30)))]]) ).
cnf(refute_0_1789,plain,
least_upper_bound(X_30,least_upper_bound(X_31,X_375)) = least_upper_bound(X_375,least_upper_bound(X_31,X_30)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(X_375))]]) ).
cnf(refute_0_1790,plain,
( least_upper_bound(X_30,least_upper_bound(X_31,X_375)) != least_upper_bound(X_375,least_upper_bound(X_31,X_30))
| least_upper_bound(X_375,least_upper_bound(X_31,X_30)) = least_upper_bound(X_30,least_upper_bound(X_31,X_375)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_30,least_upper_bound(X_31,X_375)))),bind(Y0,$fot(least_upper_bound(X_375,least_upper_bound(X_31,X_30))))]]) ).
cnf(refute_0_1791,plain,
least_upper_bound(X_375,least_upper_bound(X_31,X_30)) = least_upper_bound(X_30,least_upper_bound(X_31,X_375)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_30,least_upper_bound(X_31,X_375)),least_upper_bound(X_375,least_upper_bound(X_31,X_30))) )],[refute_0_1789,refute_0_1790]) ).
cnf(refute_0_1792,plain,
( inverse(least_upper_bound(X_375,least_upper_bound(X_31,X_30))) != inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))
| least_upper_bound(X_375,least_upper_bound(X_31,X_30)) != least_upper_bound(X_30,least_upper_bound(X_31,X_375))
| inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) = inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_375,least_upper_bound(X_31,X_30))),inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))) ),[0,0],$fot(least_upper_bound(X_30,least_upper_bound(X_31,X_375)))]]) ).
cnf(refute_0_1793,plain,
( inverse(least_upper_bound(X_375,least_upper_bound(X_31,X_30))) != inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))
| inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) = inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_375,least_upper_bound(X_31,X_30)),least_upper_bound(X_30,least_upper_bound(X_31,X_375))) )],[refute_0_1791,refute_0_1792]) ).
cnf(refute_0_1794,plain,
inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) = inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_375,least_upper_bound(X_31,X_30))),inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))) )],[refute_0_1788,refute_0_1793]) ).
cnf(refute_0_1795,plain,
least_upper_bound(least_upper_bound(X_31,X_30),X_375) = least_upper_bound(X_31,least_upper_bound(X_30,X_375)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_31)),bind(Y,$fot(X_30)),bind(Z,$fot(X_375))]]) ).
cnf(refute_0_1796,plain,
inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) = inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)))]]) ).
cnf(refute_0_1797,plain,
( inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) != inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))
| least_upper_bound(least_upper_bound(X_31,X_30),X_375) != least_upper_bound(X_31,least_upper_bound(X_30,X_375))
| inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) = inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)),inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))) ),[1,0],$fot(least_upper_bound(X_31,least_upper_bound(X_30,X_375)))]]) ).
cnf(refute_0_1798,plain,
( least_upper_bound(least_upper_bound(X_31,X_30),X_375) != least_upper_bound(X_31,least_upper_bound(X_30,X_375))
| inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) = inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)),inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))) )],[refute_0_1796,refute_0_1797]) ).
cnf(refute_0_1799,plain,
inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) = inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_31,X_30),X_375),least_upper_bound(X_31,least_upper_bound(X_30,X_375))) )],[refute_0_1795,refute_0_1798]) ).
cnf(refute_0_1800,plain,
( inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) != inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))
| inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)) != inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375)))
| inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) = inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))),inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375)))) ),[0],$fot(inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)))]]) ).
cnf(refute_0_1801,plain,
( inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) != inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))
| inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) = inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375)),inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375)))) )],[refute_0_1799,refute_0_1800]) ).
cnf(refute_0_1802,plain,
inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) = inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))),inverse(least_upper_bound(least_upper_bound(X_31,X_30),X_375))) )],[refute_0_1794,refute_0_1801]) ).
cnf(refute_0_1803,plain,
( inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) != inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375)))
| inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))) = inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))))),bind(Y0,$fot(inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375)))))]]) ).
cnf(refute_0_1804,plain,
inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375))) = inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_30,least_upper_bound(X_31,X_375))),inverse(least_upper_bound(X_31,least_upper_bound(X_30,X_375)))) )],[refute_0_1802,refute_0_1803]) ).
cnf(refute_0_1805,plain,
inverse(least_upper_bound(b,least_upper_bound(a,b))) = inverse(least_upper_bound(a,least_upper_bound(b,b))),
inference(subst,[],[refute_0_1804:[bind(X_30,$fot(a)),bind(X_31,$fot(b)),bind(X_375,$fot(b))]]) ).
cnf(refute_0_1806,plain,
( inverse(least_upper_bound(a,least_upper_bound(b,b))) != inverse(least_upper_bound(a,b))
| inverse(least_upper_bound(b,least_upper_bound(a,b))) != inverse(least_upper_bound(a,least_upper_bound(b,b)))
| inverse(least_upper_bound(b,least_upper_bound(a,b))) = inverse(least_upper_bound(a,b)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(b,least_upper_bound(a,b))))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(b,b))))),bind(Z0,$fot(inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_1807,plain,
( inverse(least_upper_bound(a,least_upper_bound(b,b))) != inverse(least_upper_bound(a,b))
| inverse(least_upper_bound(b,least_upper_bound(a,b))) = inverse(least_upper_bound(a,b)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(b,least_upper_bound(a,b))),inverse(least_upper_bound(a,least_upper_bound(b,b)))) )],[refute_0_1805,refute_0_1806]) ).
cnf(refute_0_1808,plain,
inverse(least_upper_bound(b,least_upper_bound(a,b))) = inverse(least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(b,b))),inverse(least_upper_bound(a,b))) )],[refute_0_1763,refute_0_1807]) ).
cnf(refute_0_1809,plain,
multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))),
introduced(tautology,[refl,[$fot(multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))))]]) ).
cnf(refute_0_1810,plain,
( multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))) != multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b))))
| inverse(least_upper_bound(b,least_upper_bound(a,b))) != inverse(least_upper_bound(a,b))
| multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(a,b))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))),multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b))))) ),[1,1],$fot(inverse(least_upper_bound(a,b)))]]) ).
cnf(refute_0_1811,plain,
( inverse(least_upper_bound(b,least_upper_bound(a,b))) != inverse(least_upper_bound(a,b))
| multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(a,b))) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))),multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b))))) )],[refute_0_1809,refute_0_1810]) ).
cnf(refute_0_1812,plain,
multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(a,b))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(b,least_upper_bound(a,b))),inverse(least_upper_bound(a,b))) )],[refute_0_1808,refute_0_1811]) ).
cnf(refute_0_1813,plain,
inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))) = multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(least_upper_bound(identity,X_119))),bind(X_46,$fot(inverse(X_119)))]]) ).
cnf(refute_0_1814,plain,
multiply(least_upper_bound(identity,X_99),inverse(X_99)) = least_upper_bound(identity,multiply(identity,inverse(X_99))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(identity)),bind(X_91,$fot(X_99))]]) ).
cnf(refute_0_1815,plain,
multiply(identity,inverse(X_99)) = inverse(X_99),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_99)))]]) ).
cnf(refute_0_1816,plain,
( multiply(identity,inverse(X_99)) != inverse(X_99)
| multiply(least_upper_bound(identity,X_99),inverse(X_99)) != least_upper_bound(identity,multiply(identity,inverse(X_99)))
| multiply(least_upper_bound(identity,X_99),inverse(X_99)) = least_upper_bound(identity,inverse(X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_99),inverse(X_99)),least_upper_bound(identity,multiply(identity,inverse(X_99)))) ),[1,1],$fot(inverse(X_99))]]) ).
cnf(refute_0_1817,plain,
( multiply(least_upper_bound(identity,X_99),inverse(X_99)) != least_upper_bound(identity,multiply(identity,inverse(X_99)))
| multiply(least_upper_bound(identity,X_99),inverse(X_99)) = least_upper_bound(identity,inverse(X_99)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_99)),inverse(X_99)) )],[refute_0_1815,refute_0_1816]) ).
cnf(refute_0_1818,plain,
multiply(least_upper_bound(identity,X_99),inverse(X_99)) = least_upper_bound(identity,inverse(X_99)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_99),inverse(X_99)),least_upper_bound(identity,multiply(identity,inverse(X_99)))) )],[refute_0_1814,refute_0_1817]) ).
cnf(refute_0_1819,plain,
multiply(least_upper_bound(identity,X_119),inverse(X_119)) = least_upper_bound(identity,inverse(X_119)),
inference(subst,[],[refute_0_1818:[bind(X_99,$fot(X_119))]]) ).
cnf(refute_0_1820,plain,
( multiply(least_upper_bound(identity,X_119),inverse(X_119)) != least_upper_bound(identity,inverse(X_119))
| inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))) != multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))
| inverse(least_upper_bound(identity,inverse(X_119))) = multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))),multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_119)))]]) ).
cnf(refute_0_1821,plain,
( inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))) != multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))
| inverse(least_upper_bound(identity,inverse(X_119))) = multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_119),inverse(X_119)),least_upper_bound(identity,inverse(X_119))) )],[refute_0_1819,refute_0_1820]) ).
cnf(refute_0_1822,plain,
inverse(least_upper_bound(identity,inverse(X_119))) = multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))),multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))) )],[refute_0_1813,refute_0_1821]) ).
cnf(refute_0_1823,plain,
inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))) = multiply(X_119,inverse(least_upper_bound(identity,X_119))),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(X_119)),bind(X_73,$fot(least_upper_bound(identity,X_119)))]]) ).
cnf(refute_0_1824,plain,
multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) = inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(least_upper_bound(identity,X_119))),bind(X_46,$fot(inverse(X_119)))]]) ).
cnf(refute_0_1825,plain,
( multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) != inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119)))
| inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))) != multiply(X_119,inverse(least_upper_bound(identity,X_119)))
| multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) = multiply(X_119,inverse(least_upper_bound(identity,X_119))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))))),bind(Z0,$fot(multiply(X_119,inverse(least_upper_bound(identity,X_119)))))]]) ).
cnf(refute_0_1826,plain,
( inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))) != multiply(X_119,inverse(least_upper_bound(identity,X_119)))
| multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) = multiply(X_119,inverse(least_upper_bound(identity,X_119))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))),inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119)))) )],[refute_0_1824,refute_0_1825]) ).
cnf(refute_0_1827,plain,
multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) = multiply(X_119,inverse(least_upper_bound(identity,X_119))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_119),inverse(X_119))),multiply(X_119,inverse(least_upper_bound(identity,X_119)))) )],[refute_0_1823,refute_0_1826]) ).
cnf(refute_0_1828,plain,
( multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))) != multiply(X_119,inverse(least_upper_bound(identity,X_119)))
| inverse(least_upper_bound(identity,inverse(X_119))) != multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))
| inverse(least_upper_bound(identity,inverse(X_119))) = multiply(X_119,inverse(least_upper_bound(identity,X_119))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))) ),[1],$fot(multiply(X_119,inverse(least_upper_bound(identity,X_119))))]]) ).
cnf(refute_0_1829,plain,
( inverse(least_upper_bound(identity,inverse(X_119))) != multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))
| inverse(least_upper_bound(identity,inverse(X_119))) = multiply(X_119,inverse(least_upper_bound(identity,X_119))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119))),multiply(X_119,inverse(least_upper_bound(identity,X_119)))) )],[refute_0_1827,refute_0_1828]) ).
cnf(refute_0_1830,plain,
inverse(least_upper_bound(identity,inverse(X_119))) = multiply(X_119,inverse(least_upper_bound(identity,X_119))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),multiply(inverse(inverse(X_119)),inverse(least_upper_bound(identity,X_119)))) )],[refute_0_1822,refute_0_1829]) ).
cnf(refute_0_1831,plain,
inverse(inverse(greatest_lower_bound(X_119,identity))) = greatest_lower_bound(X_119,identity),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(X_119,identity)))]]) ).
cnf(refute_0_1832,plain,
least_upper_bound(identity,inverse(X_119)) = inverse(greatest_lower_bound(X_119,identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(X_119))]]) ).
cnf(refute_0_1833,plain,
inverse(least_upper_bound(identity,inverse(X_119))) = inverse(least_upper_bound(identity,inverse(X_119))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(X_119))))]]) ).
cnf(refute_0_1834,plain,
( inverse(least_upper_bound(identity,inverse(X_119))) != inverse(least_upper_bound(identity,inverse(X_119)))
| least_upper_bound(identity,inverse(X_119)) != inverse(greatest_lower_bound(X_119,identity))
| inverse(least_upper_bound(identity,inverse(X_119))) = inverse(inverse(greatest_lower_bound(X_119,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),inverse(least_upper_bound(identity,inverse(X_119)))) ),[1,0],$fot(inverse(greatest_lower_bound(X_119,identity)))]]) ).
cnf(refute_0_1835,plain,
( least_upper_bound(identity,inverse(X_119)) != inverse(greatest_lower_bound(X_119,identity))
| inverse(least_upper_bound(identity,inverse(X_119))) = inverse(inverse(greatest_lower_bound(X_119,identity))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),inverse(least_upper_bound(identity,inverse(X_119)))) )],[refute_0_1833,refute_0_1834]) ).
cnf(refute_0_1836,plain,
inverse(least_upper_bound(identity,inverse(X_119))) = inverse(inverse(greatest_lower_bound(X_119,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_119)),inverse(greatest_lower_bound(X_119,identity))) )],[refute_0_1832,refute_0_1835]) ).
cnf(refute_0_1837,plain,
( inverse(inverse(greatest_lower_bound(X_119,identity))) != greatest_lower_bound(X_119,identity)
| inverse(least_upper_bound(identity,inverse(X_119))) != inverse(inverse(greatest_lower_bound(X_119,identity)))
| inverse(least_upper_bound(identity,inverse(X_119))) = greatest_lower_bound(X_119,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_119))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(X_119,identity))))),bind(Z0,$fot(greatest_lower_bound(X_119,identity)))]]) ).
cnf(refute_0_1838,plain,
( inverse(inverse(greatest_lower_bound(X_119,identity))) != greatest_lower_bound(X_119,identity)
| inverse(least_upper_bound(identity,inverse(X_119))) = greatest_lower_bound(X_119,identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),inverse(inverse(greatest_lower_bound(X_119,identity)))) )],[refute_0_1836,refute_0_1837]) ).
cnf(refute_0_1839,plain,
inverse(least_upper_bound(identity,inverse(X_119))) = greatest_lower_bound(X_119,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_119,identity))),greatest_lower_bound(X_119,identity)) )],[refute_0_1831,refute_0_1838]) ).
cnf(refute_0_1840,plain,
( inverse(least_upper_bound(identity,inverse(X_119))) != multiply(X_119,inverse(least_upper_bound(identity,X_119)))
| inverse(least_upper_bound(identity,inverse(X_119))) != greatest_lower_bound(X_119,identity)
| greatest_lower_bound(X_119,identity) = multiply(X_119,inverse(least_upper_bound(identity,X_119))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),multiply(X_119,inverse(least_upper_bound(identity,X_119)))) ),[0],$fot(greatest_lower_bound(X_119,identity))]]) ).
cnf(refute_0_1841,plain,
( inverse(least_upper_bound(identity,inverse(X_119))) != multiply(X_119,inverse(least_upper_bound(identity,X_119)))
| greatest_lower_bound(X_119,identity) = multiply(X_119,inverse(least_upper_bound(identity,X_119))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),greatest_lower_bound(X_119,identity)) )],[refute_0_1839,refute_0_1840]) ).
cnf(refute_0_1842,plain,
greatest_lower_bound(X_119,identity) = multiply(X_119,inverse(least_upper_bound(identity,X_119))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_119))),multiply(X_119,inverse(least_upper_bound(identity,X_119)))) )],[refute_0_1830,refute_0_1841]) ).
cnf(refute_0_1843,plain,
greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) = multiply(multiply(X_90,inverse(X_91)),inverse(least_upper_bound(identity,multiply(X_90,inverse(X_91))))),
inference(subst,[],[refute_0_1842:[bind(X_119,$fot(multiply(X_90,inverse(X_91))))]]) ).
cnf(refute_0_1844,plain,
( multiply(least_upper_bound(X_90,X_91),inverse(X_91)) != least_upper_bound(identity,multiply(X_90,inverse(X_91)))
| least_upper_bound(identity,multiply(X_90,inverse(X_91))) = multiply(least_upper_bound(X_90,X_91),inverse(X_91)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_90,inverse(X_91)))))]]) ).
cnf(refute_0_1845,plain,
least_upper_bound(identity,multiply(X_90,inverse(X_91))) = multiply(least_upper_bound(X_90,X_91),inverse(X_91)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),least_upper_bound(identity,multiply(X_90,inverse(X_91)))) )],[refute_0_172,refute_0_1844]) ).
cnf(refute_0_1846,plain,
( greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) != multiply(multiply(X_90,inverse(X_91)),inverse(least_upper_bound(identity,multiply(X_90,inverse(X_91)))))
| least_upper_bound(identity,multiply(X_90,inverse(X_91))) != multiply(least_upper_bound(X_90,X_91),inverse(X_91))
| greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) = multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_90,inverse(X_91)),identity),multiply(multiply(X_90,inverse(X_91)),inverse(least_upper_bound(identity,multiply(X_90,inverse(X_91)))))) ),[1,1,0],$fot(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))]]) ).
cnf(refute_0_1847,plain,
( greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) != multiply(multiply(X_90,inverse(X_91)),inverse(least_upper_bound(identity,multiply(X_90,inverse(X_91)))))
| greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) = multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_90,inverse(X_91))),multiply(least_upper_bound(X_90,X_91),inverse(X_91))) )],[refute_0_1845,refute_0_1846]) ).
cnf(refute_0_1848,plain,
greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) = multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_90,inverse(X_91)),identity),multiply(multiply(X_90,inverse(X_91)),inverse(least_upper_bound(identity,multiply(X_90,inverse(X_91)))))) )],[refute_0_1843,refute_0_1847]) ).
cnf(refute_0_1849,plain,
multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) = greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,inverse(X_153))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_153)),bind(Y,$fot(X_154)),bind(Z,$fot(inverse(X_153)))]]) ).
cnf(refute_0_1850,plain,
multiply(X_153,inverse(X_153)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_153))]]) ).
cnf(refute_0_1851,plain,
( multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,inverse(X_153)))
| multiply(X_153,inverse(X_153)) != identity
| multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) = greatest_lower_bound(multiply(X_153,X_154),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,inverse(X_153)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1852,plain,
( multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,inverse(X_153)))
| multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) = greatest_lower_bound(multiply(X_153,X_154),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_153,inverse(X_153)),identity) )],[refute_0_1850,refute_0_1851]) ).
cnf(refute_0_1853,plain,
multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) = greatest_lower_bound(multiply(X_153,X_154),identity),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,inverse(X_153)))) )],[refute_0_1849,refute_0_1852]) ).
cnf(refute_0_1854,plain,
greatest_lower_bound(multiply(X_153,X_154),identity) = greatest_lower_bound(identity,multiply(X_153,X_154)),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_153,X_154)))]]) ).
cnf(refute_0_1855,plain,
( multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) != greatest_lower_bound(multiply(X_153,X_154),identity)
| greatest_lower_bound(multiply(X_153,X_154),identity) != greatest_lower_bound(identity,multiply(X_153,X_154))
| multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) = greatest_lower_bound(identity,multiply(X_153,X_154)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))),greatest_lower_bound(identity,multiply(X_153,X_154))) ),[0],$fot(greatest_lower_bound(multiply(X_153,X_154),identity))]]) ).
cnf(refute_0_1856,plain,
( multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) != greatest_lower_bound(multiply(X_153,X_154),identity)
| multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) = greatest_lower_bound(identity,multiply(X_153,X_154)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),identity),greatest_lower_bound(identity,multiply(X_153,X_154))) )],[refute_0_1854,refute_0_1855]) ).
cnf(refute_0_1857,plain,
multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))) = greatest_lower_bound(identity,multiply(X_153,X_154)),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,inverse(X_153))),greatest_lower_bound(multiply(X_153,X_154),identity)) )],[refute_0_1853,refute_0_1856]) ).
cnf(refute_0_1858,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)),
inference(subst,[],[refute_0_1857:[bind(X_153,$fot(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_1859,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)))) = identity,
inference(subst,[],[refute_0_581:[bind(X_85,$fot(b)),bind(X_86,$fot(least_upper_bound(greatest_lower_bound(a,c),X_22)))]]) ).
cnf(refute_0_1860,plain,
least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)) = least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_22),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(greatest_lower_bound(a,c))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_1861,plain,
( least_upper_bound(b,greatest_lower_bound(a,c)) != b
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)) != least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_22)
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)) = least_upper_bound(b,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_22)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_1862,plain,
( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)) != least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_22)
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)) = least_upper_bound(b,X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_179,refute_0_1861]) ).
cnf(refute_0_1863,plain,
least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)) = least_upper_bound(b,X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_22)) )],[refute_0_1860,refute_0_1862]) ).
cnf(refute_0_1864,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)))) != identity
| least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)) != least_upper_bound(b,X_22)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,X_22))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)))),identity) ),[0,1,1],$fot(least_upper_bound(b,X_22))]]) ).
cnf(refute_0_1865,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)))) != identity
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,X_22))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,X_22)) )],[refute_0_1863,refute_0_1864]) ).
cnf(refute_0_1866,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,X_22))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),X_22)),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_22)))),identity) )],[refute_0_1859,refute_0_1865]) ).
cnf(refute_0_1867,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))) = identity,
inference(subst,[],[refute_0_1866:[bind(X_22,$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1868,plain,
inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) = multiply(inverse(least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(subst,[],[refute_0_495:[bind(X_69,$fot(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),bind(X_95,$fot(b))]]) ).
cnf(refute_0_1869,plain,
multiply(least_upper_bound(X_90,X_91),inverse(X_90)) = least_upper_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_90))),bind(Y,$fot(X_90)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_1870,plain,
multiply(X_90,inverse(X_90)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_90))]]) ).
cnf(refute_0_1871,plain,
( multiply(X_90,inverse(X_90)) != identity
| multiply(least_upper_bound(X_90,X_91),inverse(X_90)) != least_upper_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))
| multiply(least_upper_bound(X_90,X_91),inverse(X_90)) = least_upper_bound(identity,multiply(X_91,inverse(X_90))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),inverse(X_90)),least_upper_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1872,plain,
( multiply(least_upper_bound(X_90,X_91),inverse(X_90)) != least_upper_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))
| multiply(least_upper_bound(X_90,X_91),inverse(X_90)) = least_upper_bound(identity,multiply(X_91,inverse(X_90))) ),
inference(resolve,[$cnf( $equal(multiply(X_90,inverse(X_90)),identity) )],[refute_0_1870,refute_0_1871]) ).
cnf(refute_0_1873,plain,
multiply(least_upper_bound(X_90,X_91),inverse(X_90)) = least_upper_bound(identity,multiply(X_91,inverse(X_90))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),inverse(X_90)),least_upper_bound(multiply(X_90,inverse(X_90)),multiply(X_91,inverse(X_90)))) )],[refute_0_1869,refute_0_1872]) ).
cnf(refute_0_1874,plain,
multiply(least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)),inverse(X_100)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100))),
inference(subst,[],[refute_0_1873:[bind(X_90,$fot(X_100)),bind(X_91,$fot(greatest_lower_bound(X_11,X_100)))]]) ).
cnf(refute_0_1875,plain,
least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)) = X_100,
inference(subst,[],[refute_0_270:[bind(X_10,$fot(X_100))]]) ).
cnf(refute_0_1876,plain,
( multiply(least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)),inverse(X_100)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))
| least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)) != X_100
| multiply(X_100,inverse(X_100)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)),inverse(X_100)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))) ),[0,0],$fot(X_100)]]) ).
cnf(refute_0_1877,plain,
( multiply(least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)),inverse(X_100)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))
| multiply(X_100,inverse(X_100)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)),X_100) )],[refute_0_1875,refute_0_1876]) ).
cnf(refute_0_1878,plain,
multiply(X_100,inverse(X_100)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_100,greatest_lower_bound(X_11,X_100)),inverse(X_100)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))) )],[refute_0_1874,refute_0_1877]) ).
cnf(refute_0_1879,plain,
multiply(X_100,inverse(X_100)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_100))]]) ).
cnf(refute_0_1880,plain,
( multiply(X_100,inverse(X_100)) != identity
| multiply(X_100,inverse(X_100)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_100,inverse(X_100)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1881,plain,
( multiply(X_100,inverse(X_100)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100))) ),
inference(resolve,[$cnf( $equal(multiply(X_100,inverse(X_100)),identity) )],[refute_0_1879,refute_0_1880]) ).
cnf(refute_0_1882,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100))),
inference(resolve,[$cnf( $equal(multiply(X_100,inverse(X_100)),least_upper_bound(identity,multiply(greatest_lower_bound(X_11,X_100),inverse(X_100)))) )],[refute_0_1878,refute_0_1881]) ).
cnf(refute_0_1883,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),
inference(subst,[],[refute_0_1882:[bind(X_100,$fot(multiply(inverse(greatest_lower_bound(a,c)),b))),bind(X_11,$fot(multiply(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1884,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_213)),bind(X_56,$fot(identity)),bind(X_58,$fot(multiply(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1885,plain,
multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) = greatest_lower_bound(multiply(X_172,inverse(X_173)),multiply(X_173,inverse(X_173))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_173))),bind(Y,$fot(X_172)),bind(Z,$fot(X_173))]]) ).
cnf(refute_0_1886,plain,
multiply(X_173,inverse(X_173)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_173))]]) ).
cnf(refute_0_1887,plain,
( multiply(X_173,inverse(X_173)) != identity
| multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) != greatest_lower_bound(multiply(X_172,inverse(X_173)),multiply(X_173,inverse(X_173)))
| multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) = greatest_lower_bound(multiply(X_172,inverse(X_173)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)),greatest_lower_bound(multiply(X_172,inverse(X_173)),multiply(X_173,inverse(X_173)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1888,plain,
( multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) != greatest_lower_bound(multiply(X_172,inverse(X_173)),multiply(X_173,inverse(X_173)))
| multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) = greatest_lower_bound(multiply(X_172,inverse(X_173)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_173,inverse(X_173)),identity) )],[refute_0_1886,refute_0_1887]) ).
cnf(refute_0_1889,plain,
multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) = greatest_lower_bound(multiply(X_172,inverse(X_173)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)),greatest_lower_bound(multiply(X_172,inverse(X_173)),multiply(X_173,inverse(X_173)))) )],[refute_0_1885,refute_0_1888]) ).
cnf(refute_0_1890,plain,
greatest_lower_bound(multiply(X_172,inverse(X_173)),identity) = greatest_lower_bound(identity,multiply(X_172,inverse(X_173))),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_172,inverse(X_173))))]]) ).
cnf(refute_0_1891,plain,
( multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) != greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)
| greatest_lower_bound(multiply(X_172,inverse(X_173)),identity) != greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))
| multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) = greatest_lower_bound(identity,multiply(X_172,inverse(X_173))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)),greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) ),[0],$fot(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity))]]) ).
cnf(refute_0_1892,plain,
( multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) != greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)
| multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) = greatest_lower_bound(identity,multiply(X_172,inverse(X_173))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity),greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) )],[refute_0_1890,refute_0_1891]) ).
cnf(refute_0_1893,plain,
multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) = greatest_lower_bound(identity,multiply(X_172,inverse(X_173))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)),greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) )],[refute_0_1889,refute_0_1892]) ).
cnf(refute_0_1894,plain,
multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_1893:[bind(X_172,$fot(b)),bind(X_173,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_1895,plain,
( multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(b,least_upper_bound(a,c)) != b
| multiply(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) ),[0,0],$fot(b)]]) ).
cnf(refute_0_1896,plain,
( multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
| multiply(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),b) )],[refute_0_1170,refute_0_1895]) ).
cnf(refute_0_1897,plain,
multiply(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_1894,refute_0_1896]) ).
cnf(refute_0_1898,plain,
( multiply(b,inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_1899,plain,
greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_1897,refute_0_1898]) ).
cnf(refute_0_1900,plain,
( greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) = multiply(b,inverse(least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) ),[1],$fot(multiply(b,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_1901,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) = multiply(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_1899,refute_0_1900]) ).
cnf(refute_0_1902,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) = multiply(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_1884,refute_0_1901]) ).
cnf(refute_0_1903,plain,
greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(X_57,$fot(identity))]]) ).
cnf(refute_0_1904,plain,
( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))) ),[1,1],$fot(multiply(b,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_1905,plain,
( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_1899,refute_0_1904]) ).
cnf(refute_0_1906,plain,
greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_1903,refute_0_1905]) ).
cnf(refute_0_1907,plain,
greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(X_77,$fot(identity)),bind(X_78,$fot(X_56))]]) ).
cnf(refute_0_1908,plain,
( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_1909,plain,
( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_1907,refute_0_1908]) ).
cnf(refute_0_1910,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_1906,refute_0_1909]) ).
cnf(refute_0_1911,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_1910:[bind(X_56,$fot(least_upper_bound(identity,X_213)))]]) ).
cnf(refute_0_1912,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) != multiply(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1913,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) != multiply(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_1911,refute_0_1912]) ).
cnf(refute_0_1914,plain,
greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),multiply(b,inverse(least_upper_bound(a,c))))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_1902,refute_0_1913]) ).
cnf(refute_0_1915,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
inference(subst,[],[refute_0_1914:[bind(X_213,$fot(multiply(inverse(greatest_lower_bound(a,c)),b)))]]) ).
cnf(refute_0_1916,plain,
multiply(inverse(greatest_lower_bound(a,c)),least_upper_bound(b,greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(b)),bind(X_84,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_1917,plain,
( multiply(inverse(greatest_lower_bound(a,c)),least_upper_bound(b,greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))
| least_upper_bound(b,greatest_lower_bound(a,c)) != b
| multiply(inverse(greatest_lower_bound(a,c)),b) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),least_upper_bound(b,greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))) ),[0,1],$fot(b)]]) ).
cnf(refute_0_1918,plain,
( multiply(inverse(greatest_lower_bound(a,c)),least_upper_bound(b,greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))
| multiply(inverse(greatest_lower_bound(a,c)),b) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_179,refute_0_1917]) ).
cnf(refute_0_1919,plain,
multiply(inverse(greatest_lower_bound(a,c)),b) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),least_upper_bound(b,greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))) )],[refute_0_1916,refute_0_1918]) ).
cnf(refute_0_1920,plain,
( multiply(inverse(greatest_lower_bound(a,c)),b) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,c)),b))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))))]]) ).
cnf(refute_0_1921,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)) = multiply(inverse(greatest_lower_bound(a,c)),b),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))) )],[refute_0_1919,refute_0_1920]) ).
cnf(refute_0_1922,plain,
( greatest_lower_bound(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)) != multiply(inverse(greatest_lower_bound(a,c)),b)
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0,0],$fot(multiply(inverse(greatest_lower_bound(a,c)),b))]]) ).
cnf(refute_0_1923,plain,
( greatest_lower_bound(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),multiply(inverse(greatest_lower_bound(a,c)),b)) )],[refute_0_1921,refute_0_1922]) ).
cnf(refute_0_1924,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b)),multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_1915,refute_0_1923]) ).
cnf(refute_0_1925,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)),
inference(subst,[],[refute_0_106:[bind(X,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(Y,$fot(multiply(inverse(greatest_lower_bound(a,c)),b)))]]) ).
cnf(refute_0_1926,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b))
| greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)) = multiply(b,inverse(least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)))]]) ).
cnf(refute_0_1927,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)) = multiply(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b))) )],[refute_0_1925,refute_0_1926]) ).
cnf(refute_0_1928,plain,
greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)) = multiply(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_1924,refute_0_1927]) ).
cnf(refute_0_1929,plain,
( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)) != multiply(b,inverse(least_upper_bound(a,c)))
| identity != least_upper_bound(identity,multiply(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))
| identity = least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) ),[1,1,0],$fot(multiply(b,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_1930,plain,
( identity != least_upper_bound(identity,multiply(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))
| identity = least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_1928,refute_0_1929]) ).
cnf(refute_0_1931,plain,
identity = least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),b)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) )],[refute_0_1883,refute_0_1930]) ).
cnf(refute_0_1932,plain,
inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) = multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(greatest_lower_bound(a,c))),bind(X_74,$fot(multiply(b,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1933,plain,
multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(greatest_lower_bound(a,c)))),bind(Y,$fot(b)),bind(Z,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_1934,plain,
inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) = inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))))]]) ).
cnf(refute_0_1935,plain,
( multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)) != multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))
| inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) != inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)))
| inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) = inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))),inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)))) ),[1,0],$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1936,plain,
( multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)) != multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))
| inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) = inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))),inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)))) )],[refute_0_1934,refute_0_1935]) ).
cnf(refute_0_1937,plain,
inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) = inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) )],[refute_0_1933,refute_0_1936]) ).
cnf(refute_0_1938,plain,
( inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) != inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) = multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))))),bind(Y0,$fot(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))),bind(Z0,$fot(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_1939,plain,
( inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) = multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) )],[refute_0_1937,refute_0_1938]) ).
cnf(refute_0_1940,plain,
inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) = multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) )],[refute_0_1932,refute_0_1939]) ).
cnf(refute_0_1941,plain,
multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(multiply(inverse(greatest_lower_bound(a,c)),b))),bind(X_46,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_1942,plain,
( multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) != inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)))
| inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))),bind(Y0,$fot(inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))))),bind(Z0,$fot(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_1943,plain,
( inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))),inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c)))) )],[refute_0_1941,refute_0_1942]) ).
cnf(refute_0_1944,plain,
multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(greatest_lower_bound(a,c)),b),least_upper_bound(a,c))),multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) )],[refute_0_1940,refute_0_1943]) ).
cnf(refute_0_1945,plain,
multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),
introduced(tautology,[refl,[$fot(multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))))]]) ).
cnf(refute_0_1946,plain,
( multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) != multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))
| multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) ),[1,1],$fot(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_1947,plain,
( multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) )],[refute_0_1945,refute_0_1946]) ).
cnf(refute_0_1948,plain,
multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))),multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) )],[refute_0_1944,refute_0_1947]) ).
cnf(refute_0_1949,plain,
multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),
inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(inverse(least_upper_bound(a,c)))),bind(Z,$fot(inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))]]) ).
cnf(refute_0_1950,plain,
( multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) != multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))
| multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) != multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))),bind(Y0,$fot(multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))))),bind(Z0,$fot(multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_1951,plain,
( multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) != multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))),multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) )],[refute_0_1949,refute_0_1950]) ).
cnf(refute_0_1952,plain,
multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) = multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(b,multiply(inverse(least_upper_bound(a,c)),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_1948,refute_0_1951]) ).
cnf(refute_0_1953,plain,
least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))))]]) ).
cnf(refute_0_1954,plain,
( multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) != multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) != least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))
| least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) ),[1,1],$fot(multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_1955,plain,
( multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))) != multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) )],[refute_0_1953,refute_0_1954]) ).
cnf(refute_0_1956,plain,
least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) = least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))),multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_1952,refute_0_1955]) ).
cnf(refute_0_1957,plain,
( identity != least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))
| least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))) != least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| identity = least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),[0],$fot(least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))))]]) ).
cnf(refute_0_1958,plain,
( identity != least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))
| identity = least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b)))),least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_1956,refute_0_1957]) ).
cnf(refute_0_1959,plain,
identity = least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(multiply(b,inverse(least_upper_bound(a,c))),inverse(multiply(inverse(greatest_lower_bound(a,c)),b))))) )],[refute_0_1931,refute_0_1958]) ).
cnf(refute_0_1960,plain,
( identity != least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_1961,plain,
least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_1959,refute_0_1960]) ).
cnf(refute_0_1962,plain,
( inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != identity
| inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) = multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),multiply(inverse(least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_1963,plain,
( inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) = multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),identity) )],[refute_0_1961,refute_0_1962]) ).
cnf(refute_0_1964,plain,
inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) = multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),multiply(inverse(least_upper_bound(identity,multiply(b,multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_1868,refute_0_1963]) ).
cnf(refute_0_1965,plain,
inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) = multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(multiply(b,least_upper_bound(a,c)))),bind(X_74,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_1966,plain,
( inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))
| inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) = multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1967,plain,
( inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) = multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) )],[refute_0_1965,refute_0_1966]) ).
cnf(refute_0_1968,plain,
multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_1969,plain,
least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_1970,plain,
( inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))
| least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),[1,1],$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1971,plain,
( inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))
| least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_1969,refute_0_1970]) ).
cnf(refute_0_1972,plain,
least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) )],[refute_0_1965,refute_0_1971]) ).
cnf(refute_0_1973,plain,
multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
introduced(tautology,[refl,[$fot(multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_1974,plain,
( multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[1,1],$fot(least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_1975,plain,
( least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_1973,refute_0_1974]) ).
cnf(refute_0_1976,plain,
multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) )],[refute_0_1972,refute_0_1975]) ).
cnf(refute_0_1977,plain,
multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_1978,plain,
( multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1979,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_1977,refute_0_1978]) ).
cnf(refute_0_1980,plain,
multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_1979]) ).
cnf(refute_0_1981,plain,
( multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),bind(Z0,$fot(multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_1982,plain,
( multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_1980,refute_0_1981]) ).
cnf(refute_0_1983,plain,
multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))) )],[refute_0_1976,refute_0_1982]) ).
cnf(refute_0_1984,plain,
( multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) != least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))))),bind(Z0,$fot(least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_1985,plain,
( multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) != least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))) )],[refute_0_1983,refute_0_1984]) ).
cnf(refute_0_1986,plain,
multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) )],[refute_0_1968,refute_0_1985]) ).
cnf(refute_0_1987,plain,
( multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) != multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) ),[0],$fot(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_1988,plain,
( multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) != multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) )],[refute_0_1986,refute_0_1987]) ).
cnf(refute_0_1989,plain,
( inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) != multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))),multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_1967,refute_0_1988]) ).
cnf(refute_0_1990,plain,
multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) = least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))),multiply(inverse(identity),least_upper_bound(b,inverse(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_1964,refute_0_1989]) ).
cnf(refute_0_1991,plain,
( multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) != least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) = multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),bind(Y0,$fot(least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_1992,plain,
least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) = multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) )],[refute_0_1990,refute_0_1991]) ).
cnf(refute_0_1993,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))) != identity
| least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) != multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))),identity) ),[0,1,1],$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))]]) ).
cnf(refute_0_1994,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))) != identity
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) )],[refute_0_1992,refute_0_1993]) ).
cnf(refute_0_1995,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),least_upper_bound(b,multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))),identity) )],[refute_0_1867,refute_0_1994]) ).
cnf(refute_0_1996,plain,
multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) = multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(multiply(b,least_upper_bound(a,c))))),bind(Y,$fot(greatest_lower_bound(a,c))),bind(Z,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_1997,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) = multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_1998,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) != multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))
| inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) = multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)),multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) ),[1,0],$fot(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_1999,plain,
( inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) != multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))
| multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) = multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)),multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) )],[refute_0_1997,refute_0_1998]) ).
cnf(refute_0_2000,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) = multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c))) )],[refute_0_1932,refute_0_1999]) ).
cnf(refute_0_2001,plain,
( multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) != multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))
| multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) != multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c))
| multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) = multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))),bind(Y0,$fot(multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)))),bind(Z0,$fot(multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_2002,plain,
( multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) != multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))
| multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) = multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)),multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) )],[refute_0_2000,refute_0_2001]) ).
cnf(refute_0_2003,plain,
multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) = multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(b,least_upper_bound(a,c))),greatest_lower_bound(a,c)),greatest_lower_bound(a,c)),multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) )],[refute_0_1996,refute_0_2002]) ).
cnf(refute_0_2004,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_2005,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) != multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) ),[1,1],$fot(multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_2006,plain,
( multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)) != multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) )],[refute_0_2004,refute_0_2005]) ).
cnf(refute_0_2007,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)),multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) )],[refute_0_2003,refute_0_2006]) ).
cnf(refute_0_2008,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_2009,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))),inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))) ),[1,0],$fot(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_2010,plain,
( least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))),inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))) )],[refute_0_2008,refute_0_2009]) ).
cnf(refute_0_2011,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) )],[refute_0_2007,refute_0_2010]) ).
cnf(refute_0_2012,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))),
inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_213)),bind(X_56,$fot(identity)),bind(X_58,$fot(inverse(least_upper_bound(identity,X_88))))]]) ).
cnf(refute_0_2013,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))) = inverse(least_upper_bound(identity,X_88)),
inference(subst,[],[refute_0_262:[bind(X,$fot(inverse(least_upper_bound(identity,X_88)))),bind(Y,$fot(identity))]]) ).
cnf(refute_0_2014,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_88))),
inference(subst,[],[refute_0_434:[bind(X_18,$fot(X_88))]]) ).
cnf(refute_0_2015,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))
| least_upper_bound(identity,inverse(least_upper_bound(identity,X_88))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))))]]) ).
cnf(refute_0_2016,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X_88))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))) )],[refute_0_2014,refute_0_2015]) ).
cnf(refute_0_2017,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))) != inverse(least_upper_bound(identity,X_88))
| least_upper_bound(identity,inverse(least_upper_bound(identity,X_88))) != identity
| greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity) = inverse(least_upper_bound(identity,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))),inverse(least_upper_bound(identity,X_88))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_2018,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))) != inverse(least_upper_bound(identity,X_88))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity) = inverse(least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(identity,X_88))),identity) )],[refute_0_2016,refute_0_2017]) ).
cnf(refute_0_2019,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity) = inverse(least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_88)))),inverse(least_upper_bound(identity,X_88))) )],[refute_0_2013,refute_0_2018]) ).
cnf(refute_0_2020,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(inverse(least_upper_bound(identity,X_88))))]]) ).
cnf(refute_0_2021,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88)))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity) != inverse(least_upper_bound(identity,X_88))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity),inverse(least_upper_bound(identity,X_88))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))))]]) ).
cnf(refute_0_2022,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity) != inverse(least_upper_bound(identity,X_88))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88)))) )],[refute_0_2020,refute_0_2021]) ).
cnf(refute_0_2023,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_88)),identity),inverse(least_upper_bound(identity,X_88))) )],[refute_0_2019,refute_0_2022]) ).
cnf(refute_0_2024,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88)))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))) != inverse(least_upper_bound(identity,X_88))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) = inverse(least_upper_bound(identity,X_88)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))),inverse(least_upper_bound(identity,X_88))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))))]]) ).
cnf(refute_0_2025,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) = inverse(least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88))),inverse(least_upper_bound(identity,X_88))) )],[refute_0_2023,refute_0_2024]) ).
cnf(refute_0_2026,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) = inverse(least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_88)))) )],[refute_0_2012,refute_0_2025]) ).
cnf(refute_0_2027,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182)))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(inverse(least_upper_bound(identity,X_182)))),bind(X_57,$fot(identity))]]) ).
cnf(refute_0_2028,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182))) = inverse(least_upper_bound(identity,X_182)),
inference(subst,[],[refute_0_2023:[bind(X_88,$fot(X_182))]]) ).
cnf(refute_0_2029,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182))) != inverse(least_upper_bound(identity,X_182))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182))))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182))))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_182)))]]) ).
cnf(refute_0_2030,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182))))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182))),inverse(least_upper_bound(identity,X_182))) )],[refute_0_2028,refute_0_2029]) ).
cnf(refute_0_2031,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_182))))) )],[refute_0_2027,refute_0_2030]) ).
cnf(refute_0_2032,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(inverse(least_upper_bound(identity,X_182)))),bind(X_77,$fot(identity)),bind(X_78,$fot(X_56))]]) ).
cnf(refute_0_2033,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))
| greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))) = greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))))]]) ).
cnf(refute_0_2034,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))) = greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))))) )],[refute_0_2032,refute_0_2033]) ).
cnf(refute_0_2035,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))) = greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,X_182)),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,inverse(least_upper_bound(identity,X_182)))) )],[refute_0_2031,refute_0_2034]) ).
cnf(refute_0_2036,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) = greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88))),
inference(subst,[],[refute_0_2035:[bind(X_182,$fot(X_88)),bind(X_56,$fot(least_upper_bound(identity,X_213)))]]) ).
cnf(refute_0_2037,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) != greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) != inverse(least_upper_bound(identity,X_88))
| greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))),inverse(least_upper_bound(identity,X_88))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88))))]]) ).
cnf(refute_0_2038,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) != inverse(least_upper_bound(identity,X_88))
| greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))),greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))) )],[refute_0_2036,refute_0_2037]) ).
cnf(refute_0_2039,plain,
greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_213),inverse(least_upper_bound(identity,X_88)))),inverse(least_upper_bound(identity,X_88))) )],[refute_0_2026,refute_0_2038]) ).
cnf(refute_0_2040,plain,
greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),
inference(subst,[],[refute_0_2039:[bind(X_213,$fot(X_327)),bind(X_88,$fot(multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_2041,plain,
( multiply(inverse(X_84),least_upper_bound(X_83,X_84)) != least_upper_bound(identity,multiply(inverse(X_84),X_83))
| least_upper_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(X_84),least_upper_bound(X_83,X_84)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_84),X_83))))]]) ).
cnf(refute_0_2042,plain,
least_upper_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(X_84),least_upper_bound(X_83,X_84)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_83,X_84)),least_upper_bound(identity,multiply(inverse(X_84),X_83))) )],[refute_0_67,refute_0_2041]) ).
cnf(refute_0_2043,plain,
( greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| least_upper_bound(identity,multiply(inverse(X_84),X_83)) != multiply(inverse(X_84),least_upper_bound(X_83,X_84))
| greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) ),[1,0],$fot(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))]]) ).
cnf(refute_0_2044,plain,
( greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_84),X_83)),multiply(inverse(X_84),least_upper_bound(X_83,X_84))) )],[refute_0_2042,refute_0_2043]) ).
cnf(refute_0_2045,plain,
greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) = inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) )],[refute_0_2040,refute_0_2044]) ).
cnf(refute_0_2046,plain,
( greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))
| greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))
| inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) = inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) ),[0],$fot(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))))]]) ).
cnf(refute_0_2047,plain,
( greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))
| inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) = inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) )],[refute_0_2040,refute_0_2046]) ).
cnf(refute_0_2048,plain,
inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))) = multiply(inverse(least_upper_bound(X_83,X_84)),X_84),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(X_84)),bind(X_74,$fot(least_upper_bound(X_83,X_84)))]]) ).
cnf(refute_0_2049,plain,
( inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))) != multiply(inverse(least_upper_bound(X_83,X_84)),X_84)
| inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) != inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))
| inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(inverse(least_upper_bound(X_83,X_84)),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_83,X_84)),X_84))]]) ).
cnf(refute_0_2050,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) != inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))
| inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(inverse(least_upper_bound(X_83,X_84)),X_84) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(least_upper_bound(X_83,X_84)),X_84)) )],[refute_0_2048,refute_0_2049]) ).
cnf(refute_0_2051,plain,
( greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))) != inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))
| inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(inverse(least_upper_bound(X_83,X_84)),X_84) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) )],[refute_0_2047,refute_0_2050]) ).
cnf(refute_0_2052,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) = multiply(inverse(least_upper_bound(X_83,X_84)),X_84),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_327),inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83)))),inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) )],[refute_0_2045,refute_0_2051]) ).
cnf(refute_0_2053,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) != multiply(inverse(least_upper_bound(X_83,X_84)),X_84)
| multiply(inverse(least_upper_bound(X_83,X_84)),X_84) = inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_83,X_84)),X_84)))]]) ).
cnf(refute_0_2054,plain,
multiply(inverse(least_upper_bound(X_83,X_84)),X_84) = inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(least_upper_bound(X_83,X_84)),X_84)) )],[refute_0_2052,refute_0_2053]) ).
cnf(refute_0_2055,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_2054:[bind(X_83,$fot(greatest_lower_bound(a,c))),bind(X_84,$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2056,plain,
multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86)))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)),
inference(subst,[],[refute_0_110:[bind(X_154,$fot(identity)),bind(X_155,$fot(multiply(inverse(X_86),least_upper_bound(X_85,X_86))))]]) ).
cnf(refute_0_2057,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86)))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86))) != identity
| multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86)))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_2058,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86)))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) )],[refute_0_581,refute_0_2057]) ).
cnf(refute_0_2059,plain,
multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),greatest_lower_bound(identity,multiply(inverse(X_86),least_upper_bound(X_85,X_86)))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))) )],[refute_0_2056,refute_0_2058]) ).
cnf(refute_0_2060,plain,
inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(X_86)),bind(X_74,$fot(least_upper_bound(X_85,X_86)))]]) ).
cnf(refute_0_2061,plain,
multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) = inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86)))))]]) ).
cnf(refute_0_2062,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) != inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86)))
| inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))),bind(Y0,$fot(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_85,X_86)),X_86)))]]) ).
cnf(refute_0_2063,plain,
( inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity),inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86)))) )],[refute_0_2061,refute_0_2062]) ).
cnf(refute_0_2064,plain,
multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) )],[refute_0_2060,refute_0_2063]) ).
cnf(refute_0_2065,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| multiply(inverse(least_upper_bound(X_85,X_86)),X_86) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))) ),[0],$fot(multiply(inverse(least_upper_bound(X_85,X_86)),X_86))]]) ).
cnf(refute_0_2066,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| multiply(inverse(least_upper_bound(X_85,X_86)),X_86) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity),multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) )],[refute_0_2064,refute_0_2065]) ).
cnf(refute_0_2067,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)))]]) ).
cnf(refute_0_2068,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))) ),[1,1],$fot(multiply(inverse(least_upper_bound(X_85,X_86)),X_86))]]) ).
cnf(refute_0_2069,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))) )],[refute_0_2067,refute_0_2068]) ).
cnf(refute_0_2070,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity),multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) )],[refute_0_2064,refute_0_2069]) ).
cnf(refute_0_2071,plain,
( multiply(inverse(least_upper_bound(X_85,X_86)),X_86) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86))
| multiply(inverse(least_upper_bound(X_85,X_86)),X_86) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(X_85,X_86)),X_86),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)))]]) ).
cnf(refute_0_2072,plain,
( multiply(inverse(least_upper_bound(X_85,X_86)),X_86) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| multiply(inverse(least_upper_bound(X_85,X_86)),X_86) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86))) )],[refute_0_2070,refute_0_2071]) ).
cnf(refute_0_2073,plain,
( multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))
| multiply(inverse(least_upper_bound(X_85,X_86)),X_86) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_86)),X_86),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))) )],[refute_0_2066,refute_0_2072]) ).
cnf(refute_0_2074,plain,
multiply(inverse(least_upper_bound(X_85,X_86)),X_86) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),identity))) )],[refute_0_2059,refute_0_2073]) ).
cnf(refute_0_2075,plain,
( multiply(inverse(least_upper_bound(X_85,X_86)),X_86) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_85,X_86)),X_86))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86))))]]) ).
cnf(refute_0_2076,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_86)),X_86),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_85,X_86)),X_86))) )],[refute_0_2074,refute_0_2075]) ).
cnf(refute_0_2077,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),
inference(subst,[],[refute_0_2076:[bind(X_85,$fot(greatest_lower_bound(a,c))),bind(X_86,$fot(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2078,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) != multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_2079,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) )],[refute_0_2077,refute_0_2078]) ).
cnf(refute_0_2080,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))) )],[refute_0_2055,refute_0_2079]) ).
cnf(refute_0_2081,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))))]]) ).
cnf(refute_0_2082,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c))))) )],[refute_0_2080,refute_0_2081]) ).
cnf(refute_0_2083,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c)))),greatest_lower_bound(a,c)))),inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))) )],[refute_0_2011,refute_0_2082]) ).
cnf(refute_0_2084,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) != identity
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),identity) ),[0],$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_2085,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))) != identity
| inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))) )],[refute_0_2083,refute_0_2084]) ).
cnf(refute_0_2086,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),multiply(inverse(greatest_lower_bound(a,c)),multiply(b,least_upper_bound(a,c))))),identity) )],[refute_0_1995,refute_0_2085]) ).
cnf(refute_0_2087,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) != identity
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154))) ),[0,1,1],$fot(identity)]]) ).
cnf(refute_0_2088,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),identity) )],[refute_0_2086,refute_0_2087]) ).
cnf(refute_0_2089,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154))) )],[refute_0_1858,refute_0_2088]) ).
cnf(refute_0_2090,plain,
multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)) = greatest_lower_bound(multiply(X_153,inverse(X_153)),multiply(X_153,X_155)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_153)),bind(Y,$fot(inverse(X_153))),bind(Z,$fot(X_155))]]) ).
cnf(refute_0_2091,plain,
( multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)) != greatest_lower_bound(multiply(X_153,inverse(X_153)),multiply(X_153,X_155))
| multiply(X_153,inverse(X_153)) != identity
| multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)) = greatest_lower_bound(identity,multiply(X_153,X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)),greatest_lower_bound(multiply(X_153,inverse(X_153)),multiply(X_153,X_155))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2092,plain,
( multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)) != greatest_lower_bound(multiply(X_153,inverse(X_153)),multiply(X_153,X_155))
| multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)) = greatest_lower_bound(identity,multiply(X_153,X_155)) ),
inference(resolve,[$cnf( $equal(multiply(X_153,inverse(X_153)),identity) )],[refute_0_1850,refute_0_2091]) ).
cnf(refute_0_2093,plain,
multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)) = greatest_lower_bound(identity,multiply(X_153,X_155)),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(inverse(X_153),X_155)),greatest_lower_bound(multiply(X_153,inverse(X_153)),multiply(X_153,X_155))) )],[refute_0_2090,refute_0_2092]) ).
cnf(refute_0_2094,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),X_155)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155)),
inference(subst,[],[refute_0_2093:[bind(X_153,$fot(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_2095,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),X_155)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) != identity
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),X_155)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155))) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_2096,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),X_155)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),identity) )],[refute_0_2086,refute_0_2095]) ).
cnf(refute_0_2097,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),X_155)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155))) )],[refute_0_2094,refute_0_2096]) ).
cnf(refute_0_2098,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155))))]]) ).
cnf(refute_0_2099,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_155)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_155))) )],[refute_0_2097,refute_0_2098]) ).
cnf(refute_0_2100,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)),
inference(subst,[],[refute_0_2099:[bind(X_155,$fot(X_154))]]) ).
cnf(refute_0_2101,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154))
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) ),[0],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)))]]) ).
cnf(refute_0_2102,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) )],[refute_0_2100,refute_0_2101]) ).
cnf(refute_0_2103,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),X_154))) )],[refute_0_2089,refute_0_2102]) ).
cnf(refute_0_2104,plain,
multiply(identity,greatest_lower_bound(X_154,identity)) = greatest_lower_bound(X_154,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_154,identity)))]]) ).
cnf(refute_0_2105,plain,
inverse(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_2106,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))) != least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) != identity
| inverse(identity) = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_2107,plain,
( inverse(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))) != least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))
| inverse(identity) = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))),identity) )],[refute_0_2086,refute_0_2106]) ).
cnf(refute_0_2108,plain,
inverse(identity) = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) )],[refute_0_2105,refute_0_2107]) ).
cnf(refute_0_2109,plain,
( inverse(identity) != identity
| inverse(identity) != least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))
| identity = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(identity),least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_2110,plain,
( inverse(identity) != least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))
| identity = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_2109]) ).
cnf(refute_0_2111,plain,
identity = least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(identity),least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) )],[refute_0_2108,refute_0_2110]) ).
cnf(refute_0_2112,plain,
( identity != least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_2113,plain,
least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c))))) )],[refute_0_2111,refute_0_2112]) ).
cnf(refute_0_2114,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)))]]) ).
cnf(refute_0_2115,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity))
| least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) != identity
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = multiply(identity,greatest_lower_bound(X_154,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2116,plain,
( least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) != identity
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = multiply(identity,greatest_lower_bound(X_154,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity))) )],[refute_0_2114,refute_0_2115]) ).
cnf(refute_0_2117,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = multiply(identity,greatest_lower_bound(X_154,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),identity) )],[refute_0_2113,refute_0_2116]) ).
cnf(refute_0_2118,plain,
( multiply(identity,greatest_lower_bound(X_154,identity)) != greatest_lower_bound(X_154,identity)
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != multiply(identity,greatest_lower_bound(X_154,identity))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = greatest_lower_bound(X_154,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_154,identity)))),bind(Z0,$fot(greatest_lower_bound(X_154,identity)))]]) ).
cnf(refute_0_2119,plain,
( multiply(identity,greatest_lower_bound(X_154,identity)) != greatest_lower_bound(X_154,identity)
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = greatest_lower_bound(X_154,identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),multiply(identity,greatest_lower_bound(X_154,identity))) )],[refute_0_2117,refute_0_2118]) ).
cnf(refute_0_2120,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) = greatest_lower_bound(X_154,identity),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_154,identity)),greatest_lower_bound(X_154,identity)) )],[refute_0_2104,refute_0_2119]) ).
cnf(refute_0_2121,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != greatest_lower_bound(X_154,identity)
| greatest_lower_bound(X_154,identity) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) ),[0],$fot(greatest_lower_bound(X_154,identity))]]) ).
cnf(refute_0_2122,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))
| greatest_lower_bound(X_154,identity) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),greatest_lower_bound(X_154,identity)) )],[refute_0_2120,refute_0_2121]) ).
cnf(refute_0_2123,plain,
multiply(identity,greatest_lower_bound(identity,X_154)) = greatest_lower_bound(identity,X_154),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,X_154)))]]) ).
cnf(refute_0_2124,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)))]]) ).
cnf(refute_0_2125,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))
| least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) != identity
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) = multiply(identity,greatest_lower_bound(identity,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2126,plain,
( least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))) != identity
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) = multiply(identity,greatest_lower_bound(identity,X_154)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) )],[refute_0_2124,refute_0_2125]) ).
cnf(refute_0_2127,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) = multiply(identity,greatest_lower_bound(identity,X_154)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),identity) )],[refute_0_2113,refute_0_2126]) ).
cnf(refute_0_2128,plain,
( multiply(identity,greatest_lower_bound(identity,X_154)) != greatest_lower_bound(identity,X_154)
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) != multiply(identity,greatest_lower_bound(identity,X_154))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) = greatest_lower_bound(identity,X_154) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,X_154)))),bind(Z0,$fot(greatest_lower_bound(identity,X_154)))]]) ).
cnf(refute_0_2129,plain,
( multiply(identity,greatest_lower_bound(identity,X_154)) != greatest_lower_bound(identity,X_154)
| multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) = greatest_lower_bound(identity,X_154) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)),multiply(identity,greatest_lower_bound(identity,X_154))) )],[refute_0_2127,refute_0_2128]) ).
cnf(refute_0_2130,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) = greatest_lower_bound(identity,X_154),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,X_154)),greatest_lower_bound(identity,X_154)) )],[refute_0_2123,refute_0_2129]) ).
cnf(refute_0_2131,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)) != greatest_lower_bound(identity,X_154)
| greatest_lower_bound(X_154,identity) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))
| greatest_lower_bound(X_154,identity) = greatest_lower_bound(identity,X_154) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_154,identity),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) ),[1],$fot(greatest_lower_bound(identity,X_154))]]) ).
cnf(refute_0_2132,plain,
( greatest_lower_bound(X_154,identity) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))
| greatest_lower_bound(X_154,identity) = greatest_lower_bound(identity,X_154) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154)),greatest_lower_bound(identity,X_154)) )],[refute_0_2130,refute_0_2131]) ).
cnf(refute_0_2133,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)) != multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))
| greatest_lower_bound(X_154,identity) = greatest_lower_bound(identity,X_154) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_154,identity),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) )],[refute_0_2122,refute_0_2132]) ).
cnf(refute_0_2134,plain,
greatest_lower_bound(X_154,identity) = greatest_lower_bound(identity,X_154),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(X_154,identity)),multiply(least_upper_bound(identity,multiply(inverse(multiply(b,least_upper_bound(a,c))),multiply(greatest_lower_bound(a,c),greatest_lower_bound(a,c)))),greatest_lower_bound(identity,X_154))) )],[refute_0_2103,refute_0_2133]) ).
cnf(refute_0_2135,plain,
greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) = greatest_lower_bound(identity,multiply(X_90,inverse(X_91))),
inference(subst,[],[refute_0_2134:[bind(X_154,$fot(multiply(X_90,inverse(X_91))))]]) ).
cnf(refute_0_2136,plain,
( greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) != multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))
| greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) != greatest_lower_bound(identity,multiply(X_90,inverse(X_91)))
| greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) = multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_90,inverse(X_91)),identity),multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_90,inverse(X_91))))]]) ).
cnf(refute_0_2137,plain,
( greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) != multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))
| greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) = multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_90,inverse(X_91)),identity),greatest_lower_bound(identity,multiply(X_90,inverse(X_91)))) )],[refute_0_2135,refute_0_2136]) ).
cnf(refute_0_2138,plain,
multiply(least_upper_bound(X_90,X_91),identity) = least_upper_bound(X_90,X_91),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(least_upper_bound(X_90,X_91)))]]) ).
cnf(refute_0_2139,plain,
multiply(inverse(X_91),X_91) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_91))]]) ).
cnf(refute_0_2140,plain,
multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) = multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)))]]) ).
cnf(refute_0_2141,plain,
( multiply(inverse(X_91),X_91) != identity
| multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) != multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91))
| multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) = multiply(least_upper_bound(X_90,X_91),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)),multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2142,plain,
( multiply(inverse(X_91),X_91) != identity
| multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) = multiply(least_upper_bound(X_90,X_91),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)),multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91))) )],[refute_0_2140,refute_0_2141]) ).
cnf(refute_0_2143,plain,
multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) = multiply(least_upper_bound(X_90,X_91),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),X_91),identity) )],[refute_0_2139,refute_0_2142]) ).
cnf(refute_0_2144,plain,
( multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) != multiply(least_upper_bound(X_90,X_91),identity)
| multiply(least_upper_bound(X_90,X_91),identity) != least_upper_bound(X_90,X_91)
| multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) = least_upper_bound(X_90,X_91) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)))),bind(Y0,$fot(multiply(least_upper_bound(X_90,X_91),identity))),bind(Z0,$fot(least_upper_bound(X_90,X_91)))]]) ).
cnf(refute_0_2145,plain,
( multiply(least_upper_bound(X_90,X_91),identity) != least_upper_bound(X_90,X_91)
| multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) = least_upper_bound(X_90,X_91) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)),multiply(least_upper_bound(X_90,X_91),identity)) )],[refute_0_2143,refute_0_2144]) ).
cnf(refute_0_2146,plain,
multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) = least_upper_bound(X_90,X_91),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),identity),least_upper_bound(X_90,X_91)) )],[refute_0_2138,refute_0_2145]) ).
cnf(refute_0_2147,plain,
multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91) = multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_90,X_91))),bind(Y,$fot(inverse(X_91))),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_2148,plain,
( multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91) != multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91))
| multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) != least_upper_bound(X_90,X_91)
| multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91) = least_upper_bound(X_90,X_91) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91))),bind(Y0,$fot(multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)))),bind(Z0,$fot(least_upper_bound(X_90,X_91)))]]) ).
cnf(refute_0_2149,plain,
( multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)) != least_upper_bound(X_90,X_91)
| multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91) = least_upper_bound(X_90,X_91) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91),multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91))) )],[refute_0_2147,refute_0_2148]) ).
cnf(refute_0_2150,plain,
multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91) = least_upper_bound(X_90,X_91),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,X_91),multiply(inverse(X_91),X_91)),least_upper_bound(X_90,X_91)) )],[refute_0_2146,refute_0_2149]) ).
cnf(refute_0_2151,plain,
inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)) = inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)))]]) ).
cnf(refute_0_2152,plain,
( multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91) != least_upper_bound(X_90,X_91)
| inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)) != inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91))
| inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)) = inverse(least_upper_bound(X_90,X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)),inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91))) ),[1,0],$fot(least_upper_bound(X_90,X_91))]]) ).
cnf(refute_0_2153,plain,
( multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91) != least_upper_bound(X_90,X_91)
| inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)) = inverse(least_upper_bound(X_90,X_91)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)),inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91))) )],[refute_0_2151,refute_0_2152]) ).
cnf(refute_0_2154,plain,
inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)) = inverse(least_upper_bound(X_90,X_91)),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91),least_upper_bound(X_90,X_91)) )],[refute_0_2150,refute_0_2153]) ).
cnf(refute_0_2155,plain,
multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))),bind(X_46,$fot(X_91))]]) ).
cnf(refute_0_2156,plain,
( multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) != inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91))
| inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)) != inverse(least_upper_bound(X_90,X_91))
| multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = inverse(least_upper_bound(X_90,X_91)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))),bind(Y0,$fot(inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)))),bind(Z0,$fot(inverse(least_upper_bound(X_90,X_91))))]]) ).
cnf(refute_0_2157,plain,
( inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)) != inverse(least_upper_bound(X_90,X_91))
| multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = inverse(least_upper_bound(X_90,X_91)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))),inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91))) )],[refute_0_2155,refute_0_2156]) ).
cnf(refute_0_2158,plain,
multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = inverse(least_upper_bound(X_90,X_91)),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(X_90,X_91),inverse(X_91)),X_91)),inverse(least_upper_bound(X_90,X_91))) )],[refute_0_2154,refute_0_2157]) ).
cnf(refute_0_2159,plain,
multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) = multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))),
introduced(tautology,[refl,[$fot(multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))))]]) ).
cnf(refute_0_2160,plain,
( multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) != multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))
| multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) != inverse(least_upper_bound(X_90,X_91))
| multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))),multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))) ),[1,1],$fot(inverse(least_upper_bound(X_90,X_91)))]]) ).
cnf(refute_0_2161,plain,
( multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) != inverse(least_upper_bound(X_90,X_91))
| multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))) ),
inference(resolve,[$cnf( $equal(multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))),multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))) )],[refute_0_2159,refute_0_2160]) ).
cnf(refute_0_2162,plain,
multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))),inverse(least_upper_bound(X_90,X_91))) )],[refute_0_2158,refute_0_2161]) ).
cnf(refute_0_2163,plain,
multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))),
inference(subst,[],[associativity:[bind(X,$fot(X_90)),bind(Y,$fot(inverse(X_91))),bind(Z,$fot(inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))]]) ).
cnf(refute_0_2164,plain,
( multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) != multiply(X_90,inverse(least_upper_bound(X_90,X_91)))
| multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) != multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))
| multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))),bind(Y0,$fot(multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))))),bind(Z0,$fot(multiply(X_90,inverse(least_upper_bound(X_90,X_91)))))]]) ).
cnf(refute_0_2165,plain,
( multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) != multiply(X_90,inverse(least_upper_bound(X_90,X_91)))
| multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))),multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))))) )],[refute_0_2163,refute_0_2164]) ).
cnf(refute_0_2166,plain,
multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))),
inference(resolve,[$cnf( $equal(multiply(X_90,multiply(inverse(X_91),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))),multiply(X_90,inverse(least_upper_bound(X_90,X_91)))) )],[refute_0_2162,refute_0_2165]) ).
cnf(refute_0_2167,plain,
( multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))) != multiply(X_90,inverse(least_upper_bound(X_90,X_91)))
| greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) != multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))
| greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_90,inverse(X_91))),multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) ),[1],$fot(multiply(X_90,inverse(least_upper_bound(X_90,X_91))))]]) ).
cnf(refute_0_2168,plain,
( greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) != multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))
| greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))),multiply(X_90,inverse(least_upper_bound(X_90,X_91)))) )],[refute_0_2166,refute_0_2167]) ).
cnf(refute_0_2169,plain,
( greatest_lower_bound(multiply(X_90,inverse(X_91)),identity) != multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))
| greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_90,inverse(X_91))),multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) )],[refute_0_2137,refute_0_2168]) ).
cnf(refute_0_2170,plain,
greatest_lower_bound(identity,multiply(X_90,inverse(X_91))) = multiply(X_90,inverse(least_upper_bound(X_90,X_91))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_90,inverse(X_91)),identity),multiply(multiply(X_90,inverse(X_91)),inverse(multiply(least_upper_bound(X_90,X_91),inverse(X_91))))) )],[refute_0_1848,refute_0_2169]) ).
cnf(refute_0_2171,plain,
greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))),
inference(subst,[],[refute_0_2170:[bind(X_90,$fot(b)),bind(X_91,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_2172,plain,
( multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))) != multiply(b,inverse(least_upper_bound(a,b)))
| greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))) != multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b))))
| greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(a,b))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))))),bind(Y0,$fot(multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))))),bind(Z0,$fot(multiply(b,inverse(least_upper_bound(a,b)))))]]) ).
cnf(refute_0_2173,plain,
( multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))) != multiply(b,inverse(least_upper_bound(a,b)))
| greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(a,b))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b))))) )],[refute_0_2171,refute_0_2172]) ).
cnf(refute_0_2174,plain,
greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))) = multiply(b,inverse(least_upper_bound(a,b))),
inference(resolve,[$cnf( $equal(multiply(b,inverse(least_upper_bound(b,least_upper_bound(a,b)))),multiply(b,inverse(least_upper_bound(a,b)))) )],[refute_0_1812,refute_0_2173]) ).
cnf(refute_0_2175,plain,
multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) = multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)))]]) ).
cnf(refute_0_2176,plain,
( multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) != multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c))
| greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))) != multiply(b,inverse(least_upper_bound(a,b)))
| multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) = multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)),multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c))) ),[1,0],$fot(multiply(b,inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_2177,plain,
( greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))) != multiply(b,inverse(least_upper_bound(a,b)))
| multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) = multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)),multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c))) )],[refute_0_2175,refute_0_2176]) ).
cnf(refute_0_2178,plain,
multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) = multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),multiply(b,inverse(least_upper_bound(a,b)))) )],[refute_0_2174,refute_0_2177]) ).
cnf(refute_0_2179,plain,
( multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)) != multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) != multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c))
| multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) = multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)))),bind(Y0,$fot(multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)))),bind(Z0,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2180,plain,
( multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)) != multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) = multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)),multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c))) )],[refute_0_2178,refute_0_2179]) ).
cnf(refute_0_2181,plain,
multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) = multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(least_upper_bound(a,b))),least_upper_bound(a,c)),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) )],[refute_0_1754,refute_0_2180]) ).
cnf(refute_0_2182,plain,
multiply(greatest_lower_bound(X_172,identity),X_171) = greatest_lower_bound(multiply(X_172,X_171),multiply(identity,X_171)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_171)),bind(Y,$fot(X_172)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_2183,plain,
multiply(identity,X_171) = X_171,
inference(subst,[],[left_identity:[bind(X,$fot(X_171))]]) ).
cnf(refute_0_2184,plain,
( multiply(greatest_lower_bound(X_172,identity),X_171) != greatest_lower_bound(multiply(X_172,X_171),multiply(identity,X_171))
| multiply(identity,X_171) != X_171
| multiply(greatest_lower_bound(X_172,identity),X_171) = greatest_lower_bound(multiply(X_172,X_171),X_171) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_172,identity),X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(identity,X_171))) ),[1,1],$fot(X_171)]]) ).
cnf(refute_0_2185,plain,
( multiply(greatest_lower_bound(X_172,identity),X_171) != greatest_lower_bound(multiply(X_172,X_171),multiply(identity,X_171))
| multiply(greatest_lower_bound(X_172,identity),X_171) = greatest_lower_bound(multiply(X_172,X_171),X_171) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_171),X_171) )],[refute_0_2183,refute_0_2184]) ).
cnf(refute_0_2186,plain,
multiply(greatest_lower_bound(X_172,identity),X_171) = greatest_lower_bound(multiply(X_172,X_171),X_171),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,identity),X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(identity,X_171))) )],[refute_0_2182,refute_0_2185]) ).
cnf(refute_0_2187,plain,
greatest_lower_bound(multiply(X_172,X_171),X_171) = greatest_lower_bound(X_171,multiply(X_172,X_171)),
inference(subst,[],[refute_0_106:[bind(X,$fot(X_171)),bind(Y,$fot(multiply(X_172,X_171)))]]) ).
cnf(refute_0_2188,plain,
( multiply(greatest_lower_bound(X_172,identity),X_171) != greatest_lower_bound(multiply(X_172,X_171),X_171)
| greatest_lower_bound(multiply(X_172,X_171),X_171) != greatest_lower_bound(X_171,multiply(X_172,X_171))
| multiply(greatest_lower_bound(X_172,identity),X_171) = greatest_lower_bound(X_171,multiply(X_172,X_171)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_172,identity),X_171),greatest_lower_bound(X_171,multiply(X_172,X_171))) ),[0],$fot(greatest_lower_bound(multiply(X_172,X_171),X_171))]]) ).
cnf(refute_0_2189,plain,
( multiply(greatest_lower_bound(X_172,identity),X_171) != greatest_lower_bound(multiply(X_172,X_171),X_171)
| multiply(greatest_lower_bound(X_172,identity),X_171) = greatest_lower_bound(X_171,multiply(X_172,X_171)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),X_171),greatest_lower_bound(X_171,multiply(X_172,X_171))) )],[refute_0_2187,refute_0_2188]) ).
cnf(refute_0_2190,plain,
multiply(greatest_lower_bound(X_172,identity),X_171) = greatest_lower_bound(X_171,multiply(X_172,X_171)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,identity),X_171),greatest_lower_bound(multiply(X_172,X_171),X_171)) )],[refute_0_2186,refute_0_2189]) ).
cnf(refute_0_2191,plain,
multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) = greatest_lower_bound(X_174,multiply(multiply(X,Y),X_174)),
inference(subst,[],[refute_0_2190:[bind(X_171,$fot(X_174)),bind(X_172,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_2192,plain,
multiply(multiply(X,Y),X_174) = multiply(X,multiply(Y,X_174)),
inference(subst,[],[associativity:[bind(Z,$fot(X_174))]]) ).
cnf(refute_0_2193,plain,
( multiply(multiply(X,Y),X_174) != multiply(X,multiply(Y,X_174))
| multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) != greatest_lower_bound(X_174,multiply(multiply(X,Y),X_174))
| multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) = greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_174),greatest_lower_bound(X_174,multiply(multiply(X,Y),X_174))) ),[1,1],$fot(multiply(X,multiply(Y,X_174)))]]) ).
cnf(refute_0_2194,plain,
( multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) != greatest_lower_bound(X_174,multiply(multiply(X,Y),X_174))
| multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) = greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_174),multiply(X,multiply(Y,X_174))) )],[refute_0_2192,refute_0_2193]) ).
cnf(refute_0_2195,plain,
multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) = greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_174),greatest_lower_bound(X_174,multiply(multiply(X,Y),X_174))) )],[refute_0_2191,refute_0_2194]) ).
cnf(refute_0_2196,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_17,X_16),
inference(subst,[],[refute_0_570:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_2197,plain,
greatest_lower_bound(X_17,X_16) = greatest_lower_bound(X_16,X_17),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_2198,plain,
( greatest_lower_bound(X_17,X_16) != greatest_lower_bound(X_16,X_17)
| greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_17,X_16))),bind(Y0,$fot(greatest_lower_bound(X_16,X_17)))]]) ).
cnf(refute_0_2199,plain,
greatest_lower_bound(X_16,X_17) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_16),greatest_lower_bound(X_16,X_17)) )],[refute_0_2197,refute_0_2198]) ).
cnf(refute_0_2200,plain,
( greatest_lower_bound(X_16,X_17) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_17,X_16)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16) ),
introduced(tautology,[equality,[$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_2201,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( $equal(greatest_lower_bound(X_16,X_17),greatest_lower_bound(X_17,X_16)) )],[refute_0_2199,refute_0_2200]) ).
cnf(refute_0_2202,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_16)) = greatest_lower_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_17,X_16)) )],[refute_0_2196,refute_0_2201]) ).
cnf(refute_0_2203,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = greatest_lower_bound(X_17,multiply(X_175,X_17)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_175,X_17)))]]) ).
cnf(refute_0_2204,plain,
multiply(greatest_lower_bound(X_175,identity),X_17) = greatest_lower_bound(X_17,multiply(X_175,X_17)),
inference(subst,[],[refute_0_2190:[bind(X_171,$fot(X_17)),bind(X_172,$fot(X_175))]]) ).
cnf(refute_0_2205,plain,
( multiply(greatest_lower_bound(X_175,identity),X_17) != greatest_lower_bound(X_17,multiply(X_175,X_17))
| greatest_lower_bound(X_17,multiply(X_175,X_17)) = multiply(greatest_lower_bound(X_175,identity),X_17) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(X_175,identity),X_17))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(X_175,X_17))))]]) ).
cnf(refute_0_2206,plain,
greatest_lower_bound(X_17,multiply(X_175,X_17)) = multiply(greatest_lower_bound(X_175,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_175,identity),X_17),greatest_lower_bound(X_17,multiply(X_175,X_17))) )],[refute_0_2204,refute_0_2205]) ).
cnf(refute_0_2207,plain,
( greatest_lower_bound(X_17,multiply(X_175,X_17)) != multiply(greatest_lower_bound(X_175,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) != greatest_lower_bound(X_17,multiply(X_175,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(X_175,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))),greatest_lower_bound(X_17,multiply(X_175,X_17))) ),[1],$fot(multiply(greatest_lower_bound(X_175,identity),X_17))]]) ).
cnf(refute_0_2208,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) != greatest_lower_bound(X_17,multiply(X_175,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(X_175,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(X_175,X_17)),multiply(greatest_lower_bound(X_175,identity),X_17)) )],[refute_0_2206,refute_0_2207]) ).
cnf(refute_0_2209,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(X_175,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))),greatest_lower_bound(X_17,multiply(X_175,X_17))) )],[refute_0_2203,refute_0_2208]) ).
cnf(refute_0_2210,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)) = greatest_lower_bound(identity,X_175),
inference(subst,[],[refute_0_570:[bind(Y,$fot(X_175)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_2211,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17))]]) ).
cnf(refute_0_2212,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)
| greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)) != greatest_lower_bound(identity,X_175)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) = multiply(greatest_lower_bound(identity,X_175),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)) ),[1,0],$fot(greatest_lower_bound(identity,X_175))]]) ).
cnf(refute_0_2213,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)) != greatest_lower_bound(identity,X_175)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) = multiply(greatest_lower_bound(identity,X_175),X_17) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)) )],[refute_0_2211,refute_0_2212]) ).
cnf(refute_0_2214,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) = multiply(greatest_lower_bound(identity,X_175),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),greatest_lower_bound(identity,X_175)) )],[refute_0_2210,refute_0_2213]) ).
cnf(refute_0_2215,plain,
greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_173,X_171))),bind(X_17,$fot(multiply(X_172,X_171)))]]) ).
cnf(refute_0_2216,plain,
multiply(greatest_lower_bound(X_172,X_173),X_171) = greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_171)),bind(Y,$fot(X_172)),bind(Z,$fot(X_173))]]) ).
cnf(refute_0_2217,plain,
( multiply(greatest_lower_bound(X_172,X_173),X_171) != greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))
| greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)) = multiply(greatest_lower_bound(X_172,X_173),X_171) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(X_172,X_173),X_171))),bind(Y0,$fot(greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))))]]) ).
cnf(refute_0_2218,plain,
greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)) = multiply(greatest_lower_bound(X_172,X_173),X_171),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,X_173),X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) )],[refute_0_2216,refute_0_2217]) ).
cnf(refute_0_2219,plain,
( greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)) != multiply(greatest_lower_bound(X_172,X_173),X_171)
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_172,X_173),X_171) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) ),[1],$fot(multiply(greatest_lower_bound(X_172,X_173),X_171))]]) ).
cnf(refute_0_2220,plain,
( greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_172,X_173),X_171) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)),multiply(greatest_lower_bound(X_172,X_173),X_171)) )],[refute_0_2218,refute_0_2219]) ).
cnf(refute_0_2221,plain,
greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_172,X_173),X_171),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) )],[refute_0_2215,refute_0_2220]) ).
cnf(refute_0_2222,plain,
greatest_lower_bound(X_172,X_172) = X_172,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_172))]]) ).
cnf(refute_0_2223,plain,
greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)) = greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)))]]) ).
cnf(refute_0_2224,plain,
( greatest_lower_bound(X_172,X_172) != X_172
| greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)) != greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172))
| greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)) = greatest_lower_bound(X_173,X_172) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172))) ),[1,1],$fot(X_172)]]) ).
cnf(refute_0_2225,plain,
( greatest_lower_bound(X_172,X_172) != X_172
| greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)) = greatest_lower_bound(X_173,X_172) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172))) )],[refute_0_2223,refute_0_2224]) ).
cnf(refute_0_2226,plain,
greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)) = greatest_lower_bound(X_173,X_172),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_172,X_172),X_172) )],[refute_0_2222,refute_0_2225]) ).
cnf(refute_0_2227,plain,
multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) = multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171))]]) ).
cnf(refute_0_2228,plain,
( multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) != multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)
| greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)) != greatest_lower_bound(X_173,X_172)
| multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) = multiply(greatest_lower_bound(X_173,X_172),X_171) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171),multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)) ),[1,0],$fot(greatest_lower_bound(X_173,X_172))]]) ).
cnf(refute_0_2229,plain,
( greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)) != greatest_lower_bound(X_173,X_172)
| multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) = multiply(greatest_lower_bound(X_173,X_172),X_171) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171),multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)) )],[refute_0_2227,refute_0_2228]) ).
cnf(refute_0_2230,plain,
multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) = multiply(greatest_lower_bound(X_173,X_172),X_171),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),greatest_lower_bound(X_173,X_172)) )],[refute_0_2226,refute_0_2229]) ).
cnf(refute_0_2231,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_2232,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_2231]) ).
cnf(refute_0_2233,plain,
greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171)) = multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171),
inference(subst,[],[refute_0_2232:[bind(X,$fot(X_171)),bind(Y,$fot(X_173)),bind(Z,$fot(greatest_lower_bound(X_172,X_172)))]]) ).
cnf(refute_0_2234,plain,
greatest_lower_bound(X,greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X)),
inference(subst,[],[refute_0_1521:[bind(X_56,$fot(multiply(X_172,X_171))),bind(X_57,$fot(multiply(X_173,X_171)))]]) ).
cnf(refute_0_2235,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X))
| greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)) != multiply(greatest_lower_bound(X_172,X_173),X_171)
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)) = greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X))) ),[0,1],$fot(multiply(greatest_lower_bound(X_172,X_173),X_171))]]) ).
cnf(refute_0_2236,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X))
| greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)) = greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171)),multiply(greatest_lower_bound(X_172,X_173),X_171)) )],[refute_0_2218,refute_0_2235]) ).
cnf(refute_0_2237,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)) = greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X))) )],[refute_0_2234,refute_0_2236]) ).
cnf(refute_0_2238,plain,
( greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)) != greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X))
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X))))]]) ).
cnf(refute_0_2239,plain,
greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(greatest_lower_bound(X_172,X_173),X_171)),greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_173,X_171),X))) )],[refute_0_2237,refute_0_2238]) ).
cnf(refute_0_2240,plain,
greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171)),
inference(subst,[],[refute_0_2239:[bind(X,$fot(multiply(X_173,X_171))),bind(X_173,$fot(X_172))]]) ).
cnf(refute_0_2241,plain,
( greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171))
| greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171)) != multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)))]]) ).
cnf(refute_0_2242,plain,
( greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171)) != multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171))) )],[refute_0_2240,refute_0_2241]) ).
cnf(refute_0_2243,plain,
greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_173,X_171),multiply(greatest_lower_bound(X_172,X_172),X_171)),multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)) )],[refute_0_2233,refute_0_2242]) ).
cnf(refute_0_2244,plain,
( multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) != multiply(greatest_lower_bound(X_173,X_172),X_171)
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_173,X_172),X_171) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171))),bind(Z0,$fot(multiply(greatest_lower_bound(X_173,X_172),X_171)))]]) ).
cnf(refute_0_2245,plain,
( multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171) != multiply(greatest_lower_bound(X_173,X_172),X_171)
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_173,X_172),X_171) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171)) )],[refute_0_2243,refute_0_2244]) ).
cnf(refute_0_2246,plain,
greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) = multiply(greatest_lower_bound(X_173,X_172),X_171),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_173,greatest_lower_bound(X_172,X_172)),X_171),multiply(greatest_lower_bound(X_173,X_172),X_171)) )],[refute_0_2230,refute_0_2245]) ).
cnf(refute_0_2247,plain,
( greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != multiply(greatest_lower_bound(X_172,X_173),X_171)
| greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != multiply(greatest_lower_bound(X_173,X_172),X_171)
| multiply(greatest_lower_bound(X_173,X_172),X_171) = multiply(greatest_lower_bound(X_172,X_173),X_171) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),multiply(greatest_lower_bound(X_172,X_173),X_171)) ),[0],$fot(multiply(greatest_lower_bound(X_173,X_172),X_171))]]) ).
cnf(refute_0_2248,plain,
( greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))) != multiply(greatest_lower_bound(X_172,X_173),X_171)
| multiply(greatest_lower_bound(X_173,X_172),X_171) = multiply(greatest_lower_bound(X_172,X_173),X_171) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),multiply(greatest_lower_bound(X_173,X_172),X_171)) )],[refute_0_2246,refute_0_2247]) ).
cnf(refute_0_2249,plain,
multiply(greatest_lower_bound(X_173,X_172),X_171) = multiply(greatest_lower_bound(X_172,X_173),X_171),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(X_173,X_171))),multiply(greatest_lower_bound(X_172,X_173),X_171)) )],[refute_0_2221,refute_0_2248]) ).
cnf(refute_0_2250,plain,
( multiply(greatest_lower_bound(X_173,X_172),X_171) != multiply(greatest_lower_bound(X_172,X_173),X_171)
| multiply(greatest_lower_bound(X_172,X_173),X_171) = multiply(greatest_lower_bound(X_173,X_172),X_171) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(X_173,X_172),X_171))),bind(Y0,$fot(multiply(greatest_lower_bound(X_172,X_173),X_171)))]]) ).
cnf(refute_0_2251,plain,
multiply(greatest_lower_bound(X_172,X_173),X_171) = multiply(greatest_lower_bound(X_173,X_172),X_171),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_173,X_172),X_171),multiply(greatest_lower_bound(X_172,X_173),X_171)) )],[refute_0_2249,refute_0_2250]) ).
cnf(refute_0_2252,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17),
inference(subst,[],[refute_0_2251:[bind(X_171,$fot(X_17)),bind(X_172,$fot(greatest_lower_bound(X_175,identity))),bind(X_173,$fot(identity))]]) ).
cnf(refute_0_2253,plain,
( multiply(greatest_lower_bound(X_172,identity),X_171) != greatest_lower_bound(X_171,multiply(X_172,X_171))
| greatest_lower_bound(X_171,multiply(X_172,X_171)) = multiply(greatest_lower_bound(X_172,identity),X_171) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(X_172,identity),X_171))),bind(Y0,$fot(greatest_lower_bound(X_171,multiply(X_172,X_171))))]]) ).
cnf(refute_0_2254,plain,
greatest_lower_bound(X_171,multiply(X_172,X_171)) = multiply(greatest_lower_bound(X_172,identity),X_171),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,identity),X_171),greatest_lower_bound(X_171,multiply(X_172,X_171))) )],[refute_0_2190,refute_0_2253]) ).
cnf(refute_0_2255,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)) = multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17),
inference(subst,[],[refute_0_2254:[bind(X_171,$fot(X_17)),bind(X_172,$fot(greatest_lower_bound(X_175,identity)))]]) ).
cnf(refute_0_2256,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)) != multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)))),bind(Y0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)))]]) ).
cnf(refute_0_2257,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)
| greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)),multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17)) )],[refute_0_2255,refute_0_2256]) ).
cnf(refute_0_2258,plain,
greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_175,identity),identity),X_17),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)) )],[refute_0_2252,refute_0_2257]) ).
cnf(refute_0_2259,plain,
greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,multiply(X_175,X_57))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(multiply(X_175,X_57)))]]) ).
cnf(refute_0_2260,plain,
multiply(greatest_lower_bound(X_175,identity),X_57) = greatest_lower_bound(X_57,multiply(X_175,X_57)),
inference(subst,[],[refute_0_2190:[bind(X_171,$fot(X_57)),bind(X_172,$fot(X_175))]]) ).
cnf(refute_0_2261,plain,
( multiply(greatest_lower_bound(X_175,identity),X_57) != greatest_lower_bound(X_57,multiply(X_175,X_57))
| greatest_lower_bound(X_57,multiply(X_175,X_57)) = multiply(greatest_lower_bound(X_175,identity),X_57) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(X_175,identity),X_57))),bind(Y0,$fot(greatest_lower_bound(X_57,multiply(X_175,X_57))))]]) ).
cnf(refute_0_2262,plain,
greatest_lower_bound(X_57,multiply(X_175,X_57)) = multiply(greatest_lower_bound(X_175,identity),X_57),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_175,identity),X_57),greatest_lower_bound(X_57,multiply(X_175,X_57))) )],[refute_0_2260,refute_0_2261]) ).
cnf(refute_0_2263,plain,
( greatest_lower_bound(X_57,multiply(X_175,X_57)) != multiply(greatest_lower_bound(X_175,identity),X_57)
| greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,multiply(X_175,X_57)))
| greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,multiply(X_175,X_57)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_175,identity),X_57))]]) ).
cnf(refute_0_2264,plain,
( greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,multiply(X_175,X_57)))
| greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_57,multiply(X_175,X_57)),multiply(greatest_lower_bound(X_175,identity),X_57)) )],[refute_0_2262,refute_0_2263]) ).
cnf(refute_0_2265,plain,
greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,multiply(X_175,X_57)))) )],[refute_0_2259,refute_0_2264]) ).
cnf(refute_0_2266,plain,
greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,multiply(X_175,X_57))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(multiply(X_175,X_57))),bind(X_77,$fot(X_57)),bind(X_78,$fot(X_56))]]) ).
cnf(refute_0_2267,plain,
( greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57))
| greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,multiply(X_175,X_57)))
| greatest_lower_bound(X_57,greatest_lower_bound(X_56,multiply(X_175,X_57))) = greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57))) ),[0],$fot(greatest_lower_bound(X_57,greatest_lower_bound(X_56,multiply(X_175,X_57))))]]) ).
cnf(refute_0_2268,plain,
( greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57))
| greatest_lower_bound(X_57,greatest_lower_bound(X_56,multiply(X_175,X_57))) = greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,multiply(X_175,X_57)))) )],[refute_0_2266,refute_0_2267]) ).
cnf(refute_0_2269,plain,
greatest_lower_bound(X_57,greatest_lower_bound(X_56,multiply(X_175,X_57))) = greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_175,X_57),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,multiply(greatest_lower_bound(X_175,identity),X_57))) )],[refute_0_2265,refute_0_2268]) ).
cnf(refute_0_2270,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)),
inference(subst,[],[refute_0_2269:[bind(X_56,$fot(X_17)),bind(X_57,$fot(X_17))]]) ).
cnf(refute_0_2271,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) != greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))))),bind(Y0,$fot(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)))]]) ).
cnf(refute_0_2272,plain,
( greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))),greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17))) )],[refute_0_2270,refute_0_2271]) ).
cnf(refute_0_2273,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,multiply(greatest_lower_bound(X_175,identity),X_17)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)) )],[refute_0_2258,refute_0_2272]) ).
cnf(refute_0_2274,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) != multiply(greatest_lower_bound(identity,X_175),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(identity,X_175),X_17) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_175),X_17)))]]) ).
cnf(refute_0_2275,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17) != multiply(greatest_lower_bound(identity,X_175),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(identity,X_175),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17)) )],[refute_0_2273,refute_0_2274]) ).
cnf(refute_0_2276,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) = multiply(greatest_lower_bound(identity,X_175),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_175,identity)),X_17),multiply(greatest_lower_bound(identity,X_175),X_17)) )],[refute_0_2214,refute_0_2275]) ).
cnf(refute_0_2277,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) != multiply(greatest_lower_bound(X_175,identity),X_17)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) != multiply(greatest_lower_bound(identity,X_175),X_17)
| multiply(greatest_lower_bound(identity,X_175),X_17) = multiply(greatest_lower_bound(X_175,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))),multiply(greatest_lower_bound(X_175,identity),X_17)) ),[0],$fot(multiply(greatest_lower_bound(identity,X_175),X_17))]]) ).
cnf(refute_0_2278,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))) != multiply(greatest_lower_bound(X_175,identity),X_17)
| multiply(greatest_lower_bound(identity,X_175),X_17) = multiply(greatest_lower_bound(X_175,identity),X_17) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))),multiply(greatest_lower_bound(identity,X_175),X_17)) )],[refute_0_2276,refute_0_2277]) ).
cnf(refute_0_2279,plain,
multiply(greatest_lower_bound(identity,X_175),X_17) = multiply(greatest_lower_bound(X_175,identity),X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,multiply(X_175,X_17))),multiply(greatest_lower_bound(X_175,identity),X_17)) )],[refute_0_2209,refute_0_2278]) ).
cnf(refute_0_2280,plain,
( multiply(greatest_lower_bound(identity,X_175),X_17) != multiply(greatest_lower_bound(X_175,identity),X_17)
| multiply(greatest_lower_bound(X_175,identity),X_17) = multiply(greatest_lower_bound(identity,X_175),X_17) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_175),X_17))),bind(Y0,$fot(multiply(greatest_lower_bound(X_175,identity),X_17)))]]) ).
cnf(refute_0_2281,plain,
multiply(greatest_lower_bound(X_175,identity),X_17) = multiply(greatest_lower_bound(identity,X_175),X_17),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_175),X_17),multiply(greatest_lower_bound(X_175,identity),X_17)) )],[refute_0_2279,refute_0_2280]) ).
cnf(refute_0_2282,plain,
multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) = multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174),
inference(subst,[],[refute_0_2281:[bind(X_17,$fot(X_174)),bind(X_175,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_2283,plain,
( multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) != multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174)
| multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) != greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174)))
| multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174) = greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_174),greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174)))) ),[0],$fot(multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174))]]) ).
cnf(refute_0_2284,plain,
( multiply(greatest_lower_bound(multiply(X,Y),identity),X_174) != greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174)))
| multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174) = greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_174),multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174)) )],[refute_0_2282,refute_0_2283]) ).
cnf(refute_0_2285,plain,
multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174) = greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_174),greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174)))) )],[refute_0_2195,refute_0_2284]) ).
cnf(refute_0_2286,plain,
( multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174) != greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174)))
| greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))) = multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174))),bind(Y0,$fot(greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174)))))]]) ).
cnf(refute_0_2287,plain,
greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174))) = multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X,Y)),X_174),greatest_lower_bound(X_174,multiply(X,multiply(Y,X_174)))) )],[refute_0_2285,refute_0_2286]) ).
cnf(refute_0_2288,plain,
greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)),
inference(subst,[],[refute_0_2287:[bind(X,$fot(b)),bind(Y,$fot(inverse(least_upper_bound(a,b)))),bind(X_174,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_2289,plain,
( multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) != multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c))
| greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)))),bind(Z0,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2290,plain,
( multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)) != multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c))) )],[refute_0_2288,refute_0_2289]) ).
cnf(refute_0_2291,plain,
greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,b)))),least_upper_bound(a,c)),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) )],[refute_0_2181,refute_0_2290]) ).
cnf(refute_0_2292,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),
introduced(tautology,[refl,[$fot(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_2293,plain,
( greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),[1,1],$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))]]) ).
cnf(refute_0_2294,plain,
( greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) )],[refute_0_2292,refute_0_2293]) ).
cnf(refute_0_2295,plain,
least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) )],[refute_0_2291,refute_0_2294]) ).
cnf(refute_0_2296,plain,
( least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(a,c)
| least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))
| least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = least_upper_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(a,c)) ),[0],$fot(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2297,plain,
( least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(a,c)
| least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) )],[refute_0_2295,refute_0_2296]) ).
cnf(refute_0_2298,plain,
least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(a,c)) )],[refute_0_1753,refute_0_2297]) ).
cnf(refute_0_2299,plain,
( multiply(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != least_upper_bound(a,c)
| multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),[0,0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_2300,plain,
( multiply(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),least_upper_bound(a,c)) )],[refute_0_2298,refute_0_2299]) ).
cnf(refute_0_2301,plain,
multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_1156,refute_0_2300]) ).
cnf(refute_0_2302,plain,
inverse(multiply(b,inverse(least_upper_bound(a,b)))) = multiply(least_upper_bound(a,b),inverse(b)),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(least_upper_bound(a,b))),bind(X_73,$fot(b))]]) ).
cnf(refute_0_2303,plain,
multiply(X_253,inverse(multiply(multiply(X,Y),X_253))) = inverse(multiply(X,Y)),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(multiply(X,Y))),bind(X_55,$fot(X_253))]]) ).
cnf(refute_0_2304,plain,
multiply(multiply(X,Y),X_253) = multiply(X,multiply(Y,X_253)),
inference(subst,[],[associativity:[bind(Z,$fot(X_253))]]) ).
cnf(refute_0_2305,plain,
( multiply(X_253,inverse(multiply(multiply(X,Y),X_253))) != inverse(multiply(X,Y))
| multiply(multiply(X,Y),X_253) != multiply(X,multiply(Y,X_253))
| multiply(X_253,inverse(multiply(X,multiply(Y,X_253)))) = inverse(multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_253,inverse(multiply(multiply(X,Y),X_253))),inverse(multiply(X,Y))) ),[0,1,0],$fot(multiply(X,multiply(Y,X_253)))]]) ).
cnf(refute_0_2306,plain,
( multiply(X_253,inverse(multiply(multiply(X,Y),X_253))) != inverse(multiply(X,Y))
| multiply(X_253,inverse(multiply(X,multiply(Y,X_253)))) = inverse(multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_253),multiply(X,multiply(Y,X_253))) )],[refute_0_2304,refute_0_2305]) ).
cnf(refute_0_2307,plain,
multiply(X_253,inverse(multiply(X,multiply(Y,X_253)))) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(multiply(X_253,inverse(multiply(multiply(X,Y),X_253))),inverse(multiply(X,Y))) )],[refute_0_2303,refute_0_2306]) ).
cnf(refute_0_2308,plain,
multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = inverse(multiply(b,inverse(least_upper_bound(a,b)))),
inference(subst,[],[refute_0_2307:[bind(X,$fot(b)),bind(Y,$fot(inverse(least_upper_bound(a,b)))),bind(X_253,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_2309,plain,
( multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != inverse(multiply(b,inverse(least_upper_bound(a,b))))
| inverse(multiply(b,inverse(least_upper_bound(a,b)))) != multiply(least_upper_bound(a,b),inverse(b))
| multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,b),inverse(b)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),bind(Y0,$fot(inverse(multiply(b,inverse(least_upper_bound(a,b)))))),bind(Z0,$fot(multiply(least_upper_bound(a,b),inverse(b))))]]) ).
cnf(refute_0_2310,plain,
( inverse(multiply(b,inverse(least_upper_bound(a,b)))) != multiply(least_upper_bound(a,b),inverse(b))
| multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,b),inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(b,inverse(least_upper_bound(a,b))))) )],[refute_0_2308,refute_0_2309]) ).
cnf(refute_0_2311,plain,
multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,b),inverse(b)),
inference(resolve,[$cnf( $equal(inverse(multiply(b,inverse(least_upper_bound(a,b)))),multiply(least_upper_bound(a,b),inverse(b))) )],[refute_0_2302,refute_0_2310]) ).
cnf(refute_0_2312,plain,
( multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != multiply(least_upper_bound(a,b),inverse(b))
| multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(least_upper_bound(a,b),inverse(b)) = least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),[0],$fot(multiply(least_upper_bound(a,b),inverse(b)))]]) ).
cnf(refute_0_2313,plain,
( multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(least_upper_bound(a,b),inverse(b)) = least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),multiply(least_upper_bound(a,b),inverse(b))) )],[refute_0_2311,refute_0_2312]) ).
cnf(refute_0_2314,plain,
multiply(least_upper_bound(a,b),inverse(b)) = least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_2301,refute_0_2313]) ).
cnf(refute_0_2315,plain,
( multiply(least_upper_bound(a,b),inverse(b)) != least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),inverse(b)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(a,b),inverse(b)))),bind(Y0,$fot(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_2316,plain,
least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),inverse(b)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),inverse(b)),least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_2314,refute_0_2315]) ).
cnf(refute_0_2317,plain,
( multiply(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(least_upper_bound(a,b),inverse(b))
| multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),[0,0],$fot(multiply(least_upper_bound(a,b),inverse(b)))]]) ).
cnf(refute_0_2318,plain,
( multiply(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(least_upper_bound(a,b),inverse(b))) )],[refute_0_2316,refute_0_2317]) ).
cnf(refute_0_2319,plain,
multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) )],[refute_0_1155,refute_0_2318]) ).
cnf(refute_0_2320,plain,
multiply(multiply(least_upper_bound(a,c),inverse(c)),b) = multiply(least_upper_bound(a,c),multiply(inverse(c),b)),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(inverse(c))),bind(Z,$fot(b))]]) ).
cnf(refute_0_2321,plain,
inverse(multiply(c,inverse(least_upper_bound(a,c)))) = multiply(least_upper_bound(a,c),inverse(c)),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(least_upper_bound(a,c))),bind(X_73,$fot(c))]]) ).
cnf(refute_0_2322,plain,
inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_2323,plain,
( inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != least_upper_bound(a,c)
| inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = inverse(least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),[1,0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_2324,plain,
( least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != least_upper_bound(a,c)
| inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = inverse(least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) )],[refute_0_2322,refute_0_2323]) ).
cnf(refute_0_2325,plain,
inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = inverse(least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),least_upper_bound(a,c)) )],[refute_0_2298,refute_0_2324]) ).
cnf(refute_0_2326,plain,
multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
introduced(tautology,[refl,[$fot(multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_2327,plain,
( multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != inverse(least_upper_bound(a,c))
| multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),[1,1],$fot(inverse(least_upper_bound(a,c)))]]) ).
cnf(refute_0_2328,plain,
( inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != inverse(least_upper_bound(a,c))
| multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_2326,refute_0_2327]) ).
cnf(refute_0_2329,plain,
multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(least_upper_bound(a,c))) )],[refute_0_2325,refute_0_2328]) ).
cnf(refute_0_2330,plain,
greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_2170:[bind(X_90,$fot(c)),bind(X_91,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2331,plain,
( multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Y0,$fot(multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Z0,$fot(multiply(c,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2332,plain,
( multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_2330,refute_0_2331]) ).
cnf(refute_0_2333,plain,
greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(c,inverse(least_upper_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(c,inverse(least_upper_bound(a,c)))) )],[refute_0_2329,refute_0_2332]) ).
cnf(refute_0_2334,plain,
inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_2335,plain,
( greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(least_upper_bound(a,c)))
| inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(multiply(c,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) ),[1,0],$fot(multiply(c,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_2336,plain,
( greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(least_upper_bound(a,c)))
| inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(multiply(c,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2334,refute_0_2335]) ).
cnf(refute_0_2337,plain,
inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(multiply(c,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(c,inverse(least_upper_bound(a,c)))) )],[refute_0_2333,refute_0_2336]) ).
cnf(refute_0_2338,plain,
( inverse(multiply(c,inverse(least_upper_bound(a,c)))) != multiply(least_upper_bound(a,c),inverse(c))
| inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != inverse(multiply(c,inverse(least_upper_bound(a,c))))
| inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))),bind(Y0,$fot(inverse(multiply(c,inverse(least_upper_bound(a,c)))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),inverse(c))))]]) ).
cnf(refute_0_2339,plain,
( inverse(multiply(c,inverse(least_upper_bound(a,c)))) != multiply(least_upper_bound(a,c),inverse(c))
| inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),inverse(multiply(c,inverse(least_upper_bound(a,c))))) )],[refute_0_2337,refute_0_2338]) ).
cnf(refute_0_2340,plain,
inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = multiply(least_upper_bound(a,c),inverse(c)),
inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(least_upper_bound(a,c)))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2321,refute_0_2339]) ).
cnf(refute_0_2341,plain,
inverse(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))) = inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))),
inference(subst,[],[refute_0_1787:[bind(X_85,$fot(greatest_lower_bound(X_16,X_11))),bind(X_86,$fot(greatest_lower_bound(X_11,X_16)))]]) ).
cnf(refute_0_2342,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))) != inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) != greatest_lower_bound(X_16,X_11)
| inverse(greatest_lower_bound(X_16,X_11)) = inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))),inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))) ),[0,0],$fot(greatest_lower_bound(X_16,X_11))]]) ).
cnf(refute_0_2343,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))) != inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))
| inverse(greatest_lower_bound(X_16,X_11)) = inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)),greatest_lower_bound(X_16,X_11)) )],[refute_0_1609,refute_0_2342]) ).
cnf(refute_0_2344,plain,
inverse(greatest_lower_bound(X_16,X_11)) = inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))),inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))) )],[refute_0_2341,refute_0_2343]) ).
cnf(refute_0_2345,plain,
least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)) = greatest_lower_bound(X_11,X_16),
inference(subst,[],[refute_0_1609:[bind(X_11,$fot(X_16)),bind(X_16,$fot(X_11))]]) ).
cnf(refute_0_2346,plain,
inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) = inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))))]]) ).
cnf(refute_0_2347,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) != inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))
| least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)) != greatest_lower_bound(X_11,X_16)
| inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) = inverse(greatest_lower_bound(X_11,X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))),inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))) ),[1,0],$fot(greatest_lower_bound(X_11,X_16))]]) ).
cnf(refute_0_2348,plain,
( least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)) != greatest_lower_bound(X_11,X_16)
| inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) = inverse(greatest_lower_bound(X_11,X_16)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))),inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))) )],[refute_0_2346,refute_0_2347]) ).
cnf(refute_0_2349,plain,
inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) = inverse(greatest_lower_bound(X_11,X_16)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)),greatest_lower_bound(X_11,X_16)) )],[refute_0_2345,refute_0_2348]) ).
cnf(refute_0_2350,plain,
( inverse(greatest_lower_bound(X_16,X_11)) != inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))
| inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))) != inverse(greatest_lower_bound(X_11,X_16))
| inverse(greatest_lower_bound(X_16,X_11)) = inverse(greatest_lower_bound(X_11,X_16)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_16,X_11)),inverse(greatest_lower_bound(X_11,X_16))) ),[0],$fot(inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))))]]) ).
cnf(refute_0_2351,plain,
( inverse(greatest_lower_bound(X_16,X_11)) != inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))
| inverse(greatest_lower_bound(X_16,X_11)) = inverse(greatest_lower_bound(X_11,X_16)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11))),inverse(greatest_lower_bound(X_11,X_16))) )],[refute_0_2349,refute_0_2350]) ).
cnf(refute_0_2352,plain,
inverse(greatest_lower_bound(X_16,X_11)) = inverse(greatest_lower_bound(X_11,X_16)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_16,X_11)),inverse(least_upper_bound(greatest_lower_bound(X_11,X_16),greatest_lower_bound(X_16,X_11)))) )],[refute_0_2344,refute_0_2351]) ).
cnf(refute_0_2353,plain,
( inverse(greatest_lower_bound(X_16,X_11)) != inverse(greatest_lower_bound(X_11,X_16))
| inverse(greatest_lower_bound(X_11,X_16)) = inverse(greatest_lower_bound(X_16,X_11)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(X_16,X_11)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_11,X_16))))]]) ).
cnf(refute_0_2354,plain,
inverse(greatest_lower_bound(X_11,X_16)) = inverse(greatest_lower_bound(X_16,X_11)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_16,X_11)),inverse(greatest_lower_bound(X_11,X_16))) )],[refute_0_2352,refute_0_2353]) ).
cnf(refute_0_2355,plain,
inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity)) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),bind(X_16,$fot(identity))]]) ).
cnf(refute_0_2356,plain,
least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_2357,plain,
( inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity)) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity))
| least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))),bind(Y0,$fot(inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))))]]) ).
cnf(refute_0_2358,plain,
( inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity)) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity))) )],[refute_0_2356,refute_0_2357]) ).
cnf(refute_0_2359,plain,
least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),identity)),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2355,refute_0_2358]) ).
cnf(refute_0_2360,plain,
multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity) = least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))))]]) ).
cnf(refute_0_2361,plain,
( multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity) != least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))))]]) ).
cnf(refute_0_2362,plain,
( least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity),least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2360,refute_0_2361]) ).
cnf(refute_0_2363,plain,
multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2359,refute_0_2362]) ).
cnf(refute_0_2364,plain,
least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
inference(subst,[],[refute_0_933:[bind(Y,$fot(X_357)),bind(X_31,$fot(multiply(Y,X))),bind(X_32,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_2365,plain,
( least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
| least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))),least_upper_bound(multiply(Y,X),multiply(Z,X))) ),[1],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_2366,plain,
( least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_630,refute_0_2365]) ).
cnf(refute_0_2367,plain,
least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[refute_0_2364,refute_0_2366]) ).
cnf(refute_0_2368,plain,
least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
inference(subst,[],[refute_0_549:[bind(Y,$fot(X_310)),bind(X_20,$fot(multiply(Y,X))),bind(X_22,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_2369,plain,
( least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
| least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))),least_upper_bound(multiply(Y,X),multiply(Z,X))) ),[1],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_2370,plain,
( least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_630,refute_0_2369]) ).
cnf(refute_0_2371,plain,
least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[refute_0_2368,refute_0_2370]) ).
cnf(refute_0_2372,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))) = least_upper_bound(X_20,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89))),
inference(subst,[],[refute_0_747:[bind(Y,$fot(multiply(X_90,X_89))),bind(X_22,$fot(multiply(X_91,X_89)))]]) ).
cnf(refute_0_2373,plain,
( least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)) != multiply(least_upper_bound(X_90,X_91),X_89)
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))) != least_upper_bound(X_20,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)))
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))) = least_upper_bound(X_20,multiply(least_upper_bound(X_90,X_91),X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))),least_upper_bound(X_20,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)))) ),[1,1],$fot(multiply(least_upper_bound(X_90,X_91),X_89))]]) ).
cnf(refute_0_2374,plain,
( least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))) != least_upper_bound(X_20,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)))
| least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))) = least_upper_bound(X_20,multiply(least_upper_bound(X_90,X_91),X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)),multiply(least_upper_bound(X_90,X_91),X_89)) )],[refute_0_660,refute_0_2373]) ).
cnf(refute_0_2375,plain,
least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))) = least_upper_bound(X_20,multiply(least_upper_bound(X_90,X_91),X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),least_upper_bound(X_20,multiply(X_91,X_89))),least_upper_bound(X_20,least_upper_bound(multiply(X_90,X_89),multiply(X_91,X_89)))) )],[refute_0_2372,refute_0_2374]) ).
cnf(refute_0_2376,plain,
least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) = least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(least_upper_bound(Y,Z),X)),
inference(subst,[],[refute_0_2375:[bind(X_20,$fot(greatest_lower_bound(multiply(Y,X),X_310))),bind(X_89,$fot(X)),bind(X_90,$fot(Y)),bind(X_91,$fot(Z))]]) ).
cnf(refute_0_2377,plain,
( least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) != multiply(least_upper_bound(Y,Z),X)
| least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) != least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(least_upper_bound(Y,Z),X))
| least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))),multiply(least_upper_bound(Y,Z),X)) ),[0],$fot(least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_2378,plain,
( least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))) != multiply(least_upper_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(least_upper_bound(Y,Z),X))) )],[refute_0_2376,refute_0_2377]) ).
cnf(refute_0_2379,plain,
least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(greatest_lower_bound(multiply(Y,X),X_310),multiply(Z,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_2371,refute_0_2378]) ).
cnf(refute_0_2380,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Z,Y),X),
inference(subst,[],[refute_0_2379:[bind(Y,$fot(Z)),bind(Z,$fot(Y)),bind(X_310,$fot(X_357))]]) ).
cnf(refute_0_2381,plain,
least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X)),
inference(subst,[],[refute_0_686:[bind(X,$fot(greatest_lower_bound(multiply(Z,X),X_357))),bind(X_89,$fot(X)),bind(X_90,$fot(Z)),bind(X_91,$fot(Y))]]) ).
cnf(refute_0_2382,plain,
( least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) != least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Z,Y),X)
| least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = multiply(least_upper_bound(Z,Y),X) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X)))),bind(Z0,$fot(multiply(least_upper_bound(Z,Y),X)))]]) ).
cnf(refute_0_2383,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Z,Y),X)
| least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))),least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_2381,refute_0_2382]) ).
cnf(refute_0_2384,plain,
least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),X_357),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_2380,refute_0_2383]) ).
cnf(refute_0_2385,plain,
( least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) != multiply(least_upper_bound(Y,Z),X)
| least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))),multiply(least_upper_bound(Y,Z),X)) ),[0],$fot(multiply(least_upper_bound(Z,Y),X))]]) ).
cnf(refute_0_2386,plain,
( least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))) != multiply(least_upper_bound(Y,Z),X)
| multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_2384,refute_0_2385]) ).
cnf(refute_0_2387,plain,
multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),least_upper_bound(multiply(Y,X),greatest_lower_bound(multiply(Z,X),X_357))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_2367,refute_0_2386]) ).
cnf(refute_0_2388,plain,
( multiply(least_upper_bound(Z,Y),X) != multiply(least_upper_bound(Y,Z),X)
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(Z,Y),X))),bind(Y0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_2389,plain,
multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Z,Y),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_2387,refute_0_2388]) ).
cnf(refute_0_2390,plain,
multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity) = multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity),
inference(subst,[],[refute_0_2389:[bind(X,$fot(identity)),bind(Y,$fot(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_2391,plain,
( multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity) != multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity)
| multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))))]]) ).
cnf(refute_0_2392,plain,
( multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity),multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity)) )],[refute_0_2390,refute_0_2391]) ).
cnf(refute_0_2393,plain,
multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),identity),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2363,refute_0_2392]) ).
cnf(refute_0_2394,plain,
least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) = multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity),
inference(subst,[],[refute_0_701:[bind(X_89,$fot(identity)),bind(X_90,$fot(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_2395,plain,
( multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) != multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity)
| least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))))]]) ).
cnf(refute_0_2396,plain,
( multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity)) )],[refute_0_2394,refute_0_2395]) ).
cnf(refute_0_2397,plain,
least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity),identity),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2393,refute_0_2396]) ).
cnf(refute_0_2398,plain,
( inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != multiply(least_upper_bound(a,c),inverse(c))
| least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),inverse(c))))]]) ).
cnf(refute_0_2399,plain,
( inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != multiply(least_upper_bound(a,c),inverse(c))
| least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2397,refute_0_2398]) ).
cnf(refute_0_2400,plain,
least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) = multiply(least_upper_bound(a,c),inverse(c)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2340,refute_0_2399]) ).
cnf(refute_0_2401,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) = multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b))]]) ).
cnf(refute_0_2402,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) != multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)
| least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) != multiply(least_upper_bound(a,c),inverse(c))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) = multiply(multiply(least_upper_bound(a,c),inverse(c)),b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b),multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) ),[1,0],$fot(multiply(least_upper_bound(a,c),inverse(c)))]]) ).
cnf(refute_0_2403,plain,
( least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)) != multiply(least_upper_bound(a,c),inverse(c))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) = multiply(multiply(least_upper_bound(a,c),inverse(c)),b) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b),multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) )],[refute_0_2401,refute_0_2402]) ).
cnf(refute_0_2404,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) = multiply(multiply(least_upper_bound(a,c),inverse(c)),b),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2400,refute_0_2403]) ).
cnf(refute_0_2405,plain,
( multiply(multiply(least_upper_bound(a,c),inverse(c)),b) != multiply(least_upper_bound(a,c),multiply(inverse(c),b))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) != multiply(multiply(least_upper_bound(a,c),inverse(c)),b)
| multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) = multiply(least_upper_bound(a,c),multiply(inverse(c),b)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b))),bind(Y0,$fot(multiply(multiply(least_upper_bound(a,c),inverse(c)),b))),bind(Z0,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))]]) ).
cnf(refute_0_2406,plain,
( multiply(multiply(least_upper_bound(a,c),inverse(c)),b) != multiply(least_upper_bound(a,c),multiply(inverse(c),b))
| multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) = multiply(least_upper_bound(a,c),multiply(inverse(c),b)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b),multiply(multiply(least_upper_bound(a,c),inverse(c)),b)) )],[refute_0_2404,refute_0_2405]) ).
cnf(refute_0_2407,plain,
multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) = multiply(least_upper_bound(a,c),multiply(inverse(c),b)),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,c),inverse(c)),b),multiply(least_upper_bound(a,c),multiply(inverse(c),b))) )],[refute_0_2320,refute_0_2406]) ).
cnf(refute_0_2408,plain,
inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) = inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)),
introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)))]]) ).
cnf(refute_0_2409,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) != multiply(least_upper_bound(a,c),multiply(inverse(c),b))
| inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) != inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b))
| inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) = inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)),inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b))) ),[1,0],$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))]]) ).
cnf(refute_0_2410,plain,
( multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b) != multiply(least_upper_bound(a,c),multiply(inverse(c),b))
| inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) = inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)),inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b))) )],[refute_0_2408,refute_0_2409]) ).
cnf(refute_0_2411,plain,
inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) = inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b),multiply(least_upper_bound(a,c),multiply(inverse(c),b))) )],[refute_0_2407,refute_0_2410]) ).
cnf(refute_0_2412,plain,
multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),bind(X_46,$fot(b))]]) ).
cnf(refute_0_2413,plain,
( multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b))
| inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) != inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))
| multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)))),bind(Z0,$fot(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))]]) ).
cnf(refute_0_2414,plain,
( inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)) != inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))
| multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b))) )],[refute_0_2412,refute_0_2413]) ).
cnf(refute_0_2415,plain,
multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)),b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) )],[refute_0_2411,refute_0_2414]) ).
cnf(refute_0_2416,plain,
multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))) = multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))))]]) ).
cnf(refute_0_2417,plain,
( multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))
| multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))) != multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))
| multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))) = multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))),multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))) ),[1,1],$fot(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))]]) ).
cnf(refute_0_2418,plain,
( multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))
| multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))) = multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))),multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))) )],[refute_0_2416,refute_0_2417]) ).
cnf(refute_0_2419,plain,
multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))) = multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),
inference(resolve,[$cnf( $equal(multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) )],[refute_0_2415,refute_0_2418]) ).
cnf(refute_0_2420,plain,
multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(a,b))),bind(Y,$fot(inverse(b))),bind(Z,$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))]]) ).
cnf(refute_0_2421,plain,
( multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))
| multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))) != multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))
| multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))),bind(Y0,$fot(multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))))),bind(Z0,$fot(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))]]) ).
cnf(refute_0_2422,plain,
( multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))) != multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))
| multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))))) )],[refute_0_2420,refute_0_2421]) ).
cnf(refute_0_2423,plain,
multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) = multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),multiply(inverse(b),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity))))),multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) )],[refute_0_2419,refute_0_2422]) ).
cnf(refute_0_2424,plain,
( multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))
| multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) = multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),[0],$fot(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))]]) ).
cnf(refute_0_2425,plain,
( multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))) != multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) = multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) )],[refute_0_2423,refute_0_2424]) ).
cnf(refute_0_2426,plain,
multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) = multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,b),inverse(b)),inverse(least_upper_bound(identity,multiply(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),identity)))),multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) )],[refute_0_2319,refute_0_2425]) ).
cnf(refute_0_2427,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))
| multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) != multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))) ),[1,0,1],$fot(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_2428,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) )],[refute_0_2426,refute_0_2427]) ).
cnf(refute_0_2429,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))) )],[refute_0_1147,refute_0_2428]) ).
cnf(refute_0_2430,plain,
inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(least_upper_bound(a,b))),bind(X_46,$fot(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))]]) ).
cnf(refute_0_2431,plain,
( multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))) != multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))) ),[0,0],$fot(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_2432,plain,
( inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) )],[refute_0_2426,refute_0_2431]) ).
cnf(refute_0_2433,plain,
inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))) )],[refute_0_2430,refute_0_2432]) ).
cnf(refute_0_2434,plain,
multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)) = multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(least_upper_bound(a,b)))),bind(Y,$fot(least_upper_bound(a,c))),bind(Z,$fot(inverse(c)))]]) ).
cnf(refute_0_2435,plain,
multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) = multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))),
introduced(tautology,[refl,[$fot(multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))))]]) ).
cnf(refute_0_2436,plain,
( multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)) != multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))
| multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) != multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))
| multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))),multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))) ),[1,1],$fot(multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))]]) ).
cnf(refute_0_2437,plain,
( multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)) != multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))
| multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))),multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))) )],[refute_0_2435,refute_0_2436]) ).
cnf(refute_0_2438,plain,
multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)),multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) )],[refute_0_2434,refute_0_2437]) ).
cnf(refute_0_2439,plain,
multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c)) = multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))),
inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),bind(Z,$fot(inverse(c)))]]) ).
cnf(refute_0_2440,plain,
inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c)),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),bind(X_73,$fot(c))]]) ).
cnf(refute_0_2441,plain,
( multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c)) != multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Y0,$fot(multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c)))),bind(Z0,$fot(multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))))]]) ).
cnf(refute_0_2442,plain,
( multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c)) != multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c))) )],[refute_0_2440,refute_0_2441]) ).
cnf(refute_0_2443,plain,
inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))),
inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),inverse(c)),multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))) )],[refute_0_2439,refute_0_2442]) ).
cnf(refute_0_2444,plain,
( multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Y0,$fot(multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))))),bind(Z0,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_2445,plain,
( multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c)))) )],[refute_0_2443,refute_0_2444]) ).
cnf(refute_0_2446,plain,
inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),
inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)),inverse(c))),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) )],[refute_0_2438,refute_0_2445]) ).
cnf(refute_0_2447,plain,
( inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))
| multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) = multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))) ),[0],$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))]]) ).
cnf(refute_0_2448,plain,
( inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))
| multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) = multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) )],[refute_0_2446,refute_0_2447]) ).
cnf(refute_0_2449,plain,
multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))) = multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(c))),bind(Y,$fot(b)),bind(Z,$fot(inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_2450,plain,
multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))))]]) ).
cnf(refute_0_2451,plain,
( multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))) != multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))) ),[1,1],$fot(multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))]]) ).
cnf(refute_0_2452,plain,
( multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))) != multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))) )],[refute_0_2450,refute_0_2451]) ).
cnf(refute_0_2453,plain,
multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) )],[refute_0_2449,refute_0_2452]) ).
cnf(refute_0_2454,plain,
multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(multiply(inverse(c),b))),bind(Z,$fot(inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_2455,plain,
inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b))),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),bind(X_73,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_2456,plain,
( multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))
| inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b)))
| inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))),bind(Y0,$fot(multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))))]]) ).
cnf(refute_0_2457,plain,
( multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))
| inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b)))) )],[refute_0_2455,refute_0_2456]) ).
cnf(refute_0_2458,plain,
inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(least_upper_bound(a,b))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))) )],[refute_0_2454,refute_0_2457]) ).
cnf(refute_0_2459,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) = inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(least_upper_bound(a,b))),bind(X_46,$fot(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))]]) ).
cnf(refute_0_2460,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) != inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))
| inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))))]]) ).
cnf(refute_0_2461,plain,
( inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))) )],[refute_0_2459,refute_0_2460]) ).
cnf(refute_0_2462,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(a,b),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))) )],[refute_0_2458,refute_0_2461]) ).
cnf(refute_0_2463,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) != multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))))]]) ).
cnf(refute_0_2464,plain,
( multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))) != multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b))))) )],[refute_0_2462,refute_0_2463]) ).
cnf(refute_0_2465,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(least_upper_bound(a,b)))),multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))) )],[refute_0_2453,refute_0_2464]) ).
cnf(refute_0_2466,plain,
( multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) != multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))) != multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))
| multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))) ),[0],$fot(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_2467,plain,
( multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) != multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))
| multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b))),multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))) )],[refute_0_2465,refute_0_2466]) ).
cnf(refute_0_2468,plain,
( inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))
| multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
inference(resolve,[$cnf( $equal(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))) )],[refute_0_2448,refute_0_2467]) ).
cnf(refute_0_2469,plain,
multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))),
inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),inverse(least_upper_bound(a,b)))) )],[refute_0_2433,refute_0_2468]) ).
cnf(refute_0_2470,plain,
( multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) != multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))
| multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))))]]) ).
cnf(refute_0_2471,plain,
multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),
inference(resolve,[$cnf( $equal(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))) )],[refute_0_2469,refute_0_2470]) ).
cnf(refute_0_2472,plain,
inverse(inverse(inverse(least_upper_bound(a,b)))) = inverse(least_upper_bound(a,b)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_2473,plain,
multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))),
introduced(tautology,[refl,[$fot(multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))))]]) ).
cnf(refute_0_2474,plain,
( multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))
| inverse(inverse(inverse(least_upper_bound(a,b)))) != inverse(least_upper_bound(a,b))
| multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(b,inverse(least_upper_bound(a,b))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) ),[1,1],$fot(inverse(least_upper_bound(a,b)))]]) ).
cnf(refute_0_2475,plain,
( inverse(inverse(inverse(least_upper_bound(a,b)))) != inverse(least_upper_bound(a,b))
| multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(b,inverse(least_upper_bound(a,b))) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) )],[refute_0_2473,refute_0_2474]) ).
cnf(refute_0_2476,plain,
multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(b,inverse(least_upper_bound(a,b))),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(least_upper_bound(a,b)))),inverse(least_upper_bound(a,b))) )],[refute_0_2472,refute_0_2475]) ).
cnf(refute_0_2477,plain,
multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))))]]) ).
cnf(refute_0_2478,plain,
( multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(b,inverse(least_upper_bound(a,b)))
| multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) != multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))))
| multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))),multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))))) ),[1,1],$fot(multiply(b,inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_2479,plain,
( multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(b,inverse(least_upper_bound(a,b)))
| multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))),multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))))) )],[refute_0_2477,refute_0_2478]) ).
cnf(refute_0_2480,plain,
multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))),
inference(resolve,[$cnf( $equal(multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))),multiply(b,inverse(least_upper_bound(a,b)))) )],[refute_0_2476,refute_0_2479]) ).
cnf(refute_0_2481,plain,
multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(c))),bind(Y,$fot(b)),bind(Z,$fot(inverse(inverse(inverse(least_upper_bound(a,b))))))]]) ).
cnf(refute_0_2482,plain,
( multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))))
| multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) != multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))
| multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))))),bind(Y0,$fot(multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))))),bind(Z0,$fot(multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))))]]) ).
cnf(refute_0_2483,plain,
( multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))) != multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))
| multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))),multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b))))))) )],[refute_0_2481,refute_0_2482]) ).
cnf(refute_0_2484,plain,
multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))),
inference(resolve,[$cnf( $equal(multiply(inverse(c),multiply(b,inverse(inverse(inverse(least_upper_bound(a,b)))))),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) )],[refute_0_2480,refute_0_2483]) ).
cnf(refute_0_2485,plain,
multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))))]]) ).
cnf(refute_0_2486,plain,
( multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))))) ),[1,1],$fot(multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))]]) ).
cnf(refute_0_2487,plain,
( multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))))) )],[refute_0_2485,refute_0_2486]) ).
cnf(refute_0_2488,plain,
multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) )],[refute_0_2484,refute_0_2487]) ).
cnf(refute_0_2489,plain,
( multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) != multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))
| multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))))),bind(Z0,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_2490,plain,
( multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))),multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b)))))) )],[refute_0_2488,refute_0_2489]) ).
cnf(refute_0_2491,plain,
multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(inverse(c),multiply(b,inverse(least_upper_bound(a,b))))),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) )],[refute_0_2471,refute_0_2490]) ).
cnf(refute_0_2492,plain,
multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(multiply(inverse(c),b))),bind(Z,$fot(inverse(inverse(inverse(least_upper_bound(a,b))))))]]) ).
cnf(refute_0_2493,plain,
( multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))))
| multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))))),bind(Z0,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_2494,plain,
( multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))),multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b))))))) )],[refute_0_2492,refute_0_2493]) ).
cnf(refute_0_2495,plain,
multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))) = multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(multiply(inverse(c),b),inverse(inverse(inverse(least_upper_bound(a,b)))))),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) )],[refute_0_2491,refute_0_2494]) ).
cnf(refute_0_2496,plain,
least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) = least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))))]]) ).
cnf(refute_0_2497,plain,
( multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) != least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))
| least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) = least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))),least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))) ),[1,1],$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))]]) ).
cnf(refute_0_2498,plain,
( multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))) != multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))
| least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) = least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))),least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))) )],[refute_0_2496,refute_0_2497]) ).
cnf(refute_0_2499,plain,
least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) = least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) )],[refute_0_2495,refute_0_2498]) ).
cnf(refute_0_2500,plain,
multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))),
inference(subst,[],[refute_0_1146:[bind(X_45,$fot(X_474)),bind(X_86,$fot(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))]]) ).
cnf(refute_0_2501,plain,
inverse(inverse(X_100)) = multiply(inverse(multiply(least_upper_bound(X_100,X_101),inverse(X_100))),least_upper_bound(X_100,X_101)),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(least_upper_bound(X_100,X_101))),bind(X_69,$fot(inverse(X_100)))]]) ).
cnf(refute_0_2502,plain,
multiply(least_upper_bound(X_100,X_101),inverse(X_100)) = least_upper_bound(identity,multiply(X_101,inverse(X_100))),
inference(subst,[],[refute_0_1873:[bind(X_90,$fot(X_100)),bind(X_91,$fot(X_101))]]) ).
cnf(refute_0_2503,plain,
( multiply(least_upper_bound(X_100,X_101),inverse(X_100)) != least_upper_bound(identity,multiply(X_101,inverse(X_100)))
| inverse(inverse(X_100)) != multiply(inverse(multiply(least_upper_bound(X_100,X_101),inverse(X_100))),least_upper_bound(X_100,X_101))
| inverse(inverse(X_100)) = multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_100)),multiply(inverse(multiply(least_upper_bound(X_100,X_101),inverse(X_100))),least_upper_bound(X_100,X_101))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_101,inverse(X_100))))]]) ).
cnf(refute_0_2504,plain,
( inverse(inverse(X_100)) != multiply(inverse(multiply(least_upper_bound(X_100,X_101),inverse(X_100))),least_upper_bound(X_100,X_101))
| inverse(inverse(X_100)) = multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_100,X_101),inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) )],[refute_0_2502,refute_0_2503]) ).
cnf(refute_0_2505,plain,
inverse(inverse(X_100)) = multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_100)),multiply(inverse(multiply(least_upper_bound(X_100,X_101),inverse(X_100))),least_upper_bound(X_100,X_101))) )],[refute_0_2501,refute_0_2504]) ).
cnf(refute_0_2506,plain,
inverse(inverse(X_100)) = X_100,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_100))]]) ).
cnf(refute_0_2507,plain,
( inverse(inverse(X_100)) != X_100
| inverse(inverse(X_100)) != multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101))
| X_100 = multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_100)),multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101))) ),[0],$fot(X_100)]]) ).
cnf(refute_0_2508,plain,
( inverse(inverse(X_100)) != multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101))
| X_100 = multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_100)),X_100) )],[refute_0_2506,refute_0_2507]) ).
cnf(refute_0_2509,plain,
X_100 = multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_100)),multiply(inverse(least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(X_100,X_101))) )],[refute_0_2505,refute_0_2508]) ).
cnf(refute_0_2510,plain,
X_323 = multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),
inference(subst,[],[refute_0_2509:[bind(X_100,$fot(X_323)),bind(X_101,$fot(inverse(least_upper_bound(inverse(X_323),X_18))))]]) ).
cnf(refute_0_2511,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323))),
inference(subst,[],[refute_0_844:[bind(X_85,$fot(inverse(X_323)))]]) ).
cnf(refute_0_2512,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))))]]) ).
cnf(refute_0_2513,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))) )],[refute_0_2511,refute_0_2512]) ).
cnf(refute_0_2514,plain,
( X_323 != multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323))) != identity
| X_323 = multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_323,multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_2515,plain,
( X_323 != multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))
| X_323 = multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323))),identity) )],[refute_0_2513,refute_0_2514]) ).
cnf(refute_0_2516,plain,
X_323 = multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),
inference(resolve,[$cnf( $equal(X_323,multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(inverse(X_323),X_18)),inverse(X_323)))),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))) )],[refute_0_2510,refute_0_2515]) ).
cnf(refute_0_2517,plain,
multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))))]]) ).
cnf(refute_0_2518,plain,
multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))))]]) ).
cnf(refute_0_2519,plain,
( multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) != multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_2520,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))) )],[refute_0_2518,refute_0_2519]) ).
cnf(refute_0_2521,plain,
multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_2520]) ).
cnf(refute_0_2522,plain,
( multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) != least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))
| multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) != multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))
| multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))))),bind(Z0,$fot(least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))))]]) ).
cnf(refute_0_2523,plain,
( multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) != least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))
| multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))) )],[refute_0_2521,refute_0_2522]) ).
cnf(refute_0_2524,plain,
multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) = least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) )],[refute_0_2517,refute_0_2523]) ).
cnf(refute_0_2525,plain,
( X_323 != multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))
| multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) != least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))
| X_323 = least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_323,least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) ),[0],$fot(multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))))]]) ).
cnf(refute_0_2526,plain,
( X_323 != multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))
| X_323 = least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18)))) )],[refute_0_2524,refute_0_2525]) ).
cnf(refute_0_2527,plain,
X_323 = least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))),
inference(resolve,[$cnf( $equal(X_323,multiply(inverse(identity),least_upper_bound(X_323,inverse(least_upper_bound(inverse(X_323),X_18))))) )],[refute_0_2516,refute_0_2526]) ).
cnf(refute_0_2528,plain,
inverse(X_474) = least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),
inference(subst,[],[refute_0_2527:[bind(X_323,$fot(inverse(X_474)))]]) ).
cnf(refute_0_2529,plain,
( inverse(X_474) != least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))
| least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = inverse(X_474) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(X_474))),bind(Y0,$fot(least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))]]) ).
cnf(refute_0_2530,plain,
least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = inverse(X_474),
inference(resolve,[$cnf( $equal(inverse(X_474),least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) )],[refute_0_2528,refute_0_2529]) ).
cnf(refute_0_2531,plain,
( multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) != inverse(X_474)
| multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) ),[0,1],$fot(inverse(X_474))]]) ).
cnf(refute_0_2532,plain,
( multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) )],[refute_0_2530,refute_0_2531]) ).
cnf(refute_0_2533,plain,
multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),least_upper_bound(inverse(X_474),inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) )],[refute_0_2500,refute_0_2532]) ).
cnf(refute_0_2534,plain,
multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474)) = least_upper_bound(identity,multiply(X_18,inverse(X_474))),
inference(subst,[],[refute_0_98:[bind(X_89,$fot(inverse(X_474))),bind(X_91,$fot(X_18))]]) ).
cnf(refute_0_2535,plain,
inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474)),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(least_upper_bound(inverse(inverse(X_474)),X_18))),bind(X_73,$fot(X_474))]]) ).
cnf(refute_0_2536,plain,
( multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474)) != least_upper_bound(identity,multiply(X_18,inverse(X_474)))
| inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474))
| inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = least_upper_bound(identity,multiply(X_18,inverse(X_474))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))),bind(Y0,$fot(multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474)))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_18,inverse(X_474)))))]]) ).
cnf(refute_0_2537,plain,
( multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474)) != least_upper_bound(identity,multiply(X_18,inverse(X_474)))
| inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = least_upper_bound(identity,multiply(X_18,inverse(X_474))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474))) )],[refute_0_2535,refute_0_2536]) ).
cnf(refute_0_2538,plain,
inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = least_upper_bound(identity,multiply(X_18,inverse(X_474))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X_474)),X_18),inverse(X_474)),least_upper_bound(identity,multiply(X_18,inverse(X_474)))) )],[refute_0_2534,refute_0_2537]) ).
cnf(refute_0_2539,plain,
multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) = inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(X_474)),bind(X_46,$fot(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))]]) ).
cnf(refute_0_2540,plain,
( multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) != inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))
| inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != least_upper_bound(identity,multiply(X_18,inverse(X_474)))
| multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) = least_upper_bound(identity,multiply(X_18,inverse(X_474))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)))),bind(Y0,$fot(inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_18,inverse(X_474)))))]]) ).
cnf(refute_0_2541,plain,
( inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != least_upper_bound(identity,multiply(X_18,inverse(X_474)))
| multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) = least_upper_bound(identity,multiply(X_18,inverse(X_474))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)),inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) )],[refute_0_2539,refute_0_2540]) ).
cnf(refute_0_2542,plain,
multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) = least_upper_bound(identity,multiply(X_18,inverse(X_474))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),least_upper_bound(identity,multiply(X_18,inverse(X_474)))) )],[refute_0_2538,refute_0_2541]) ).
cnf(refute_0_2543,plain,
( multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) != least_upper_bound(identity,multiply(X_18,inverse(X_474)))
| least_upper_bound(identity,multiply(X_18,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) ),[0],$fot(least_upper_bound(identity,multiply(X_18,inverse(X_474))))]]) ).
cnf(refute_0_2544,plain,
( multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| least_upper_bound(identity,multiply(X_18,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)),least_upper_bound(identity,multiply(X_18,inverse(X_474)))) )],[refute_0_2542,refute_0_2543]) ).
cnf(refute_0_2545,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_474,inverse(X_18)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2546,plain,
multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))),
inference(subst,[],[refute_0_2093:[bind(X_153,$fot(X_474)),bind(X_155,$fot(inverse(X_18)))]]) ).
cnf(refute_0_2547,plain,
inverse(least_upper_bound(inverse(X_474),X_475)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),
inference(subst,[],[refute_0_495:[bind(X_69,$fot(least_upper_bound(inverse(X_474),X_475))),bind(X_95,$fot(inverse(X_475)))]]) ).
cnf(refute_0_2548,plain,
multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)) = inverse(greatest_lower_bound(identity,multiply(X_474,X_475))),
inference(subst,[],[refute_0_1146:[bind(X_45,$fot(X_474)),bind(X_86,$fot(X_475))]]) ).
cnf(refute_0_2549,plain,
( multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| inverse(least_upper_bound(inverse(X_474),X_475)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))
| inverse(least_upper_bound(inverse(X_474),X_475)) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_474),X_475)),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) ),[1,0,0,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))]]) ).
cnf(refute_0_2550,plain,
( inverse(least_upper_bound(inverse(X_474),X_475)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))
| inverse(least_upper_bound(inverse(X_474),X_475)) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)),inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) )],[refute_0_2548,refute_0_2549]) ).
cnf(refute_0_2551,plain,
inverse(least_upper_bound(inverse(X_474),X_475)) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_474),X_475)),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_2547,refute_0_2550]) ).
cnf(refute_0_2552,plain,
multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))) = inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(inverse(greatest_lower_bound(X_464,inverse(X_465))))),bind(X_55,$fot(greatest_lower_bound(identity,multiply(X_464,X_465))))]]) ).
cnf(refute_0_2553,plain,
X_46 = multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46)),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(greatest_lower_bound(X_343,inverse(X_46))))]]) ).
cnf(refute_0_2554,plain,
multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) = greatest_lower_bound(multiply(X_172,X_171),multiply(inverse(X_171),X_171)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_171)),bind(Y,$fot(X_172)),bind(Z,$fot(inverse(X_171)))]]) ).
cnf(refute_0_2555,plain,
multiply(inverse(X_171),X_171) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_171))]]) ).
cnf(refute_0_2556,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) != greatest_lower_bound(multiply(X_172,X_171),multiply(inverse(X_171),X_171))
| multiply(inverse(X_171),X_171) != identity
| multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) = greatest_lower_bound(multiply(X_172,X_171),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(inverse(X_171),X_171))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2557,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) != greatest_lower_bound(multiply(X_172,X_171),multiply(inverse(X_171),X_171))
| multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) = greatest_lower_bound(multiply(X_172,X_171),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_171),X_171),identity) )],[refute_0_2555,refute_0_2556]) ).
cnf(refute_0_2558,plain,
multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) = greatest_lower_bound(multiply(X_172,X_171),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171),greatest_lower_bound(multiply(X_172,X_171),multiply(inverse(X_171),X_171))) )],[refute_0_2554,refute_0_2557]) ).
cnf(refute_0_2559,plain,
greatest_lower_bound(multiply(X_172,X_171),identity) = greatest_lower_bound(identity,multiply(X_172,X_171)),
inference(subst,[],[refute_0_106:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_172,X_171)))]]) ).
cnf(refute_0_2560,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) != greatest_lower_bound(multiply(X_172,X_171),identity)
| greatest_lower_bound(multiply(X_172,X_171),identity) != greatest_lower_bound(identity,multiply(X_172,X_171))
| multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) = greatest_lower_bound(identity,multiply(X_172,X_171)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171),greatest_lower_bound(identity,multiply(X_172,X_171))) ),[0],$fot(greatest_lower_bound(multiply(X_172,X_171),identity))]]) ).
cnf(refute_0_2561,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) != greatest_lower_bound(multiply(X_172,X_171),identity)
| multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) = greatest_lower_bound(identity,multiply(X_172,X_171)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,X_171),identity),greatest_lower_bound(identity,multiply(X_172,X_171))) )],[refute_0_2559,refute_0_2560]) ).
cnf(refute_0_2562,plain,
multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171) = greatest_lower_bound(identity,multiply(X_172,X_171)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,inverse(X_171)),X_171),greatest_lower_bound(multiply(X_172,X_171),identity)) )],[refute_0_2558,refute_0_2561]) ).
cnf(refute_0_2563,plain,
multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46) = greatest_lower_bound(identity,multiply(X_343,X_46)),
inference(subst,[],[refute_0_2562:[bind(X_171,$fot(X_46)),bind(X_172,$fot(X_343))]]) ).
cnf(refute_0_2564,plain,
( X_46 != multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46))
| multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46) != greatest_lower_bound(identity,multiply(X_343,X_46))
| X_46 = multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),greatest_lower_bound(identity,multiply(X_343,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_343,X_46)))]]) ).
cnf(refute_0_2565,plain,
( X_46 != multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46))
| X_46 = multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),greatest_lower_bound(identity,multiply(X_343,X_46))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46),greatest_lower_bound(identity,multiply(X_343,X_46))) )],[refute_0_2563,refute_0_2564]) ).
cnf(refute_0_2566,plain,
X_46 = multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),greatest_lower_bound(identity,multiply(X_343,X_46))),
inference(resolve,[$cnf( $equal(X_46,multiply(inverse(greatest_lower_bound(X_343,inverse(X_46))),multiply(greatest_lower_bound(X_343,inverse(X_46)),X_46))) )],[refute_0_2553,refute_0_2565]) ).
cnf(refute_0_2567,plain,
X_465 = multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))),
inference(subst,[],[refute_0_2566:[bind(X_343,$fot(X_464)),bind(X_46,$fot(X_465))]]) ).
cnf(refute_0_2568,plain,
( X_465 != multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465)))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) = X_465 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_465)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465)))))]]) ).
cnf(refute_0_2569,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) = X_465,
inference(resolve,[$cnf( $equal(X_465,multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465)))) )],[refute_0_2567,refute_0_2568]) ).
cnf(refute_0_2570,plain,
( multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))) != inverse(inverse(greatest_lower_bound(X_464,inverse(X_465))))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) != X_465
| multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) = inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))),inverse(inverse(greatest_lower_bound(X_464,inverse(X_465))))) ),[0,1,0],$fot(X_465)]]) ).
cnf(refute_0_2571,plain,
( multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))) != inverse(inverse(greatest_lower_bound(X_464,inverse(X_465))))
| multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) = inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))),X_465) )],[refute_0_2569,refute_0_2570]) ).
cnf(refute_0_2572,plain,
multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) = inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))),inverse(inverse(greatest_lower_bound(X_464,inverse(X_465))))) )],[refute_0_2552,refute_0_2571]) ).
cnf(refute_0_2573,plain,
inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))) = greatest_lower_bound(X_464,inverse(X_465)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(X_464,inverse(X_465))))]]) ).
cnf(refute_0_2574,plain,
( multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) != inverse(inverse(greatest_lower_bound(X_464,inverse(X_465))))
| inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))) != greatest_lower_bound(X_464,inverse(X_465))
| multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) = greatest_lower_bound(X_464,inverse(X_465)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)),greatest_lower_bound(X_464,inverse(X_465))) ),[0],$fot(inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))))]]) ).
cnf(refute_0_2575,plain,
( multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) != inverse(inverse(greatest_lower_bound(X_464,inverse(X_465))))
| multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) = greatest_lower_bound(X_464,inverse(X_465)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_464,inverse(X_465)))),greatest_lower_bound(X_464,inverse(X_465))) )],[refute_0_2573,refute_0_2574]) ).
cnf(refute_0_2576,plain,
multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)) = greatest_lower_bound(X_464,inverse(X_465)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_464,X_465)),inverse(X_465)),inverse(inverse(greatest_lower_bound(X_464,inverse(X_465))))) )],[refute_0_2572,refute_0_2575]) ).
cnf(refute_0_2577,plain,
multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)) = greatest_lower_bound(X_474,inverse(X_475)),
inference(subst,[],[refute_0_2576:[bind(X_464,$fot(X_474)),bind(X_465,$fot(X_475))]]) ).
cnf(refute_0_2578,plain,
least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))) = inverse(X_475),
inference(subst,[],[refute_0_881:[bind(X_331,$fot(inverse(X_474))),bind(X_332,$fot(X_475))]]) ).
cnf(refute_0_2579,plain,
multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))))]]) ).
cnf(refute_0_2580,plain,
( multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))
| least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))) != inverse(X_475)
| multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) ),[1,1],$fot(inverse(X_475))]]) ).
cnf(refute_0_2581,plain,
( least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))) != inverse(X_475)
| multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_2579,refute_0_2580]) ).
cnf(refute_0_2582,plain,
multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))),inverse(X_475)) )],[refute_0_2578,refute_0_2581]) ).
cnf(refute_0_2583,plain,
inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = greatest_lower_bound(identity,multiply(X_474,X_475)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(identity,multiply(X_474,X_475))))]]) ).
cnf(refute_0_2584,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))) = greatest_lower_bound(identity,multiply(X_474,X_475)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_474,X_475))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2585,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))))]]) ).
cnf(refute_0_2586,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))) != greatest_lower_bound(identity,multiply(X_474,X_475))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_475))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_474,X_475)))]]) ).
cnf(refute_0_2587,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))) != greatest_lower_bound(identity,multiply(X_474,X_475))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_475))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))) )],[refute_0_2585,refute_0_2586]) ).
cnf(refute_0_2588,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_475))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))),greatest_lower_bound(identity,multiply(X_474,X_475))) )],[refute_0_2584,refute_0_2587]) ).
cnf(refute_0_2589,plain,
inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(greatest_lower_bound(identity,multiply(X_474,X_475)))),bind(X_16,$fot(identity))]]) ).
cnf(refute_0_2590,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(greatest_lower_bound(identity,multiply(X_474,X_475))))]]) ).
cnf(refute_0_2591,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))))]]) ).
cnf(refute_0_2592,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity))) )],[refute_0_2590,refute_0_2591]) ).
cnf(refute_0_2593,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_475)),identity)),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))) )],[refute_0_2589,refute_0_2592]) ).
cnf(refute_0_2594,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_475))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))]]) ).
cnf(refute_0_2595,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_475))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475))))) )],[refute_0_2593,refute_0_2594]) ).
cnf(refute_0_2596,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_475))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) )],[refute_0_2588,refute_0_2595]) ).
cnf(refute_0_2597,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))]]) ).
cnf(refute_0_2598,plain,
( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))]]) ).
cnf(refute_0_2599,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) )],[refute_0_2597,refute_0_2598]) ).
cnf(refute_0_2600,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) )],[refute_0_2596,refute_0_2599]) ).
cnf(refute_0_2601,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != greatest_lower_bound(identity,multiply(X_474,X_475))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = greatest_lower_bound(identity,multiply(X_474,X_475)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X_474,X_475))))]]) ).
cnf(refute_0_2602,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != greatest_lower_bound(identity,multiply(X_474,X_475))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = greatest_lower_bound(identity,multiply(X_474,X_475)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) )],[refute_0_2600,refute_0_2601]) ).
cnf(refute_0_2603,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = greatest_lower_bound(identity,multiply(X_474,X_475)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),greatest_lower_bound(identity,multiply(X_474,X_475))) )],[refute_0_2583,refute_0_2602]) ).
cnf(refute_0_2604,plain,
multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))))]]) ).
cnf(refute_0_2605,plain,
( multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != greatest_lower_bound(identity,multiply(X_474,X_475))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_474,X_475)))]]) ).
cnf(refute_0_2606,plain,
( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != greatest_lower_bound(identity,multiply(X_474,X_475))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_2604,refute_0_2605]) ).
cnf(refute_0_2607,plain,
multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),greatest_lower_bound(identity,multiply(X_474,X_475))) )],[refute_0_2603,refute_0_2606]) ).
cnf(refute_0_2608,plain,
( multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475))))]]) ).
cnf(refute_0_2609,plain,
( multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_2607,refute_0_2608]) ).
cnf(refute_0_2610,plain,
multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475))) )],[refute_0_2582,refute_0_2609]) ).
cnf(refute_0_2611,plain,
( multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)) != greatest_lower_bound(X_474,inverse(X_475))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_474,inverse(X_475)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)))),bind(Z0,$fot(greatest_lower_bound(X_474,inverse(X_475))))]]) ).
cnf(refute_0_2612,plain,
( multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)) != greatest_lower_bound(X_474,inverse(X_475))
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_474,inverse(X_475)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475))) )],[refute_0_2610,refute_0_2611]) ).
cnf(refute_0_2613,plain,
multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_474,inverse(X_475)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_474,X_475)),inverse(X_475)),greatest_lower_bound(X_474,inverse(X_475))) )],[refute_0_2577,refute_0_2612]) ).
cnf(refute_0_2614,plain,
( multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != greatest_lower_bound(X_474,inverse(X_475))
| inverse(least_upper_bound(inverse(X_474),X_475)) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))
| inverse(least_upper_bound(inverse(X_474),X_475)) = greatest_lower_bound(X_474,inverse(X_475)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_474),X_475)),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) ),[1],$fot(greatest_lower_bound(X_474,inverse(X_475)))]]) ).
cnf(refute_0_2615,plain,
( inverse(least_upper_bound(inverse(X_474),X_475)) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))
| inverse(least_upper_bound(inverse(X_474),X_475)) = greatest_lower_bound(X_474,inverse(X_475)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),greatest_lower_bound(X_474,inverse(X_475))) )],[refute_0_2613,refute_0_2614]) ).
cnf(refute_0_2616,plain,
inverse(least_upper_bound(inverse(X_474),X_475)) = greatest_lower_bound(X_474,inverse(X_475)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_474),X_475)),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_2551,refute_0_2615]) ).
cnf(refute_0_2617,plain,
inverse(least_upper_bound(inverse(inverse(X_474)),X_18)) = greatest_lower_bound(inverse(X_474),inverse(X_18)),
inference(subst,[],[refute_0_2616:[bind(X_474,$fot(inverse(X_474))),bind(X_475,$fot(X_18))]]) ).
cnf(refute_0_2618,plain,
multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),
introduced(tautology,[refl,[$fot(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))]]) ).
cnf(refute_0_2619,plain,
( multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) != multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))
| inverse(least_upper_bound(inverse(inverse(X_474)),X_18)) != greatest_lower_bound(inverse(X_474),inverse(X_18))
| multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) ),[1,1],$fot(greatest_lower_bound(inverse(X_474),inverse(X_18)))]]) ).
cnf(refute_0_2620,plain,
( inverse(least_upper_bound(inverse(inverse(X_474)),X_18)) != greatest_lower_bound(inverse(X_474),inverse(X_18))
| multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))) ),
inference(resolve,[$cnf( $equal(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) )],[refute_0_2618,refute_0_2619]) ).
cnf(refute_0_2621,plain,
multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X_474)),X_18)),greatest_lower_bound(inverse(X_474),inverse(X_18))) )],[refute_0_2617,refute_0_2620]) ).
cnf(refute_0_2622,plain,
( multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) != multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18)))
| multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))),bind(Y0,$fot(multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))))]]) ).
cnf(refute_0_2623,plain,
( multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))) ),
inference(resolve,[$cnf( $equal(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18)))) )],[refute_0_2621,refute_0_2622]) ).
cnf(refute_0_2624,plain,
multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))),
inference(resolve,[$cnf( $equal(multiply(X_474,greatest_lower_bound(inverse(X_474),inverse(X_18))),greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) )],[refute_0_2546,refute_0_2623]) ).
cnf(refute_0_2625,plain,
greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))]]) ).
cnf(refute_0_2626,plain,
( multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))
| greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))]]) ).
cnf(refute_0_2627,plain,
( multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) )],[refute_0_2625,refute_0_2626]) ).
cnf(refute_0_2628,plain,
greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))),
inference(resolve,[$cnf( $equal(multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) )],[refute_0_2624,refute_0_2627]) ).
cnf(refute_0_2629,plain,
( greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))
| greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))))]]) ).
cnf(refute_0_2630,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))) )],[refute_0_2628,refute_0_2629]) ).
cnf(refute_0_2631,plain,
greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) = greatest_lower_bound(identity,multiply(X_474,inverse(X_18))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))),greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) )],[refute_0_2545,refute_0_2630]) ).
cnf(refute_0_2632,plain,
inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))))]]) ).
cnf(refute_0_2633,plain,
( greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))]]) ).
cnf(refute_0_2634,plain,
( greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))) != greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))
| inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) )],[refute_0_2632,refute_0_2633]) ).
cnf(refute_0_2635,plain,
inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))),greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) )],[refute_0_2631,refute_0_2634]) ).
cnf(refute_0_2636,plain,
( inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))
| least_upper_bound(identity,multiply(X_18,inverse(X_474))) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| least_upper_bound(identity,multiply(X_18,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_18,inverse(X_474))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) ),[1],$fot(inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))))]]) ).
cnf(refute_0_2637,plain,
( least_upper_bound(identity,multiply(X_18,inverse(X_474))) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| least_upper_bound(identity,multiply(X_18,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18))))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))) )],[refute_0_2635,refute_0_2636]) ).
cnf(refute_0_2638,plain,
( multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))
| least_upper_bound(identity,multiply(X_18,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_18,inverse(X_474))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) )],[refute_0_2544,refute_0_2637]) ).
cnf(refute_0_2639,plain,
least_upper_bound(identity,multiply(X_18,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(inverse(X_474)),X_18))),inverse(X_474)),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(least_upper_bound(inverse(inverse(X_474)),X_18)))))) )],[refute_0_2533,refute_0_2638]) ).
cnf(refute_0_2640,plain,
( least_upper_bound(identity,multiply(X_18,inverse(X_474))) != inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))
| inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) = least_upper_bound(identity,multiply(X_18,inverse(X_474))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(identity,multiply(X_18,inverse(X_474))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))))]]) ).
cnf(refute_0_2641,plain,
inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18)))) = least_upper_bound(identity,multiply(X_18,inverse(X_474))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_18,inverse(X_474))),inverse(greatest_lower_bound(identity,multiply(X_474,inverse(X_18))))) )],[refute_0_2639,refute_0_2640]) ).
cnf(refute_0_2642,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))) = least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))),
inference(subst,[],[refute_0_2641:[bind(X_18,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),bind(X_474,$fot(inverse(inverse(least_upper_bound(a,b)))))]]) ).
cnf(refute_0_2643,plain,
multiply(inverse(X_475),least_upper_bound(inverse(inverse(X_50)),X_475)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475))),
inference(subst,[],[refute_0_1146:[bind(X_45,$fot(inverse(X_50))),bind(X_86,$fot(X_475))]]) ).
cnf(refute_0_2644,plain,
( multiply(inverse(X_475),least_upper_bound(inverse(inverse(X_50)),X_475)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475)))
| inverse(inverse(X_50)) != X_50
| multiply(inverse(X_475),least_upper_bound(X_50,X_475)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_475),least_upper_bound(inverse(inverse(X_50)),X_475)),inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475)))) ),[0,1,0],$fot(X_50)]]) ).
cnf(refute_0_2645,plain,
( multiply(inverse(X_475),least_upper_bound(inverse(inverse(X_50)),X_475)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475)))
| multiply(inverse(X_475),least_upper_bound(X_50,X_475)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_50)),X_50) )],[refute_0_88,refute_0_2644]) ).
cnf(refute_0_2646,plain,
multiply(inverse(X_475),least_upper_bound(X_50,X_475)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_475),least_upper_bound(inverse(inverse(X_50)),X_475)),inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475)))) )],[refute_0_2643,refute_0_2645]) ).
cnf(refute_0_2647,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))),
inference(subst,[],[refute_0_2646:[bind(X_475,$fot(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),bind(X_50,$fot(inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_2648,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))
| inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))) != least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))))),bind(Z0,$fot(least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))))]]) ).
cnf(refute_0_2649,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))) != least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))) )],[refute_0_2647,refute_0_2648]) ).
cnf(refute_0_2650,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(a,b))),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))))),least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))) )],[refute_0_2642,refute_0_2649]) ).
cnf(refute_0_2651,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))
| least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) != least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))))),bind(Y0,$fot(least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))))),bind(Z0,$fot(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))))]]) ).
cnf(refute_0_2652,plain,
( least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))) != least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b))))))) )],[refute_0_2650,refute_0_2651]) ).
cnf(refute_0_2653,plain,
multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) = least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(least_upper_bound(a,c),multiply(inverse(c),b)),inverse(inverse(inverse(least_upper_bound(a,b)))))),least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) )],[refute_0_2499,refute_0_2652]) ).
cnf(refute_0_2654,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) ),[0],$fot(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_2655,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) )],[refute_0_2653,refute_0_2654]) ).
cnf(refute_0_2656,plain,
( inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) != multiply(least_upper_bound(a,c),inverse(c))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = multiply(least_upper_bound(a,c),inverse(c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) ),[1],$fot(multiply(least_upper_bound(a,c),inverse(c)))]]) ).
cnf(refute_0_2657,plain,
( least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2340,refute_0_2656]) ).
cnf(refute_0_2658,plain,
( multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))) != inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2655,refute_0_2657]) ).
cnf(refute_0_2659,plain,
least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = multiply(least_upper_bound(a,c),inverse(c)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b)))),least_upper_bound(inverse(least_upper_bound(a,b)),inverse(multiply(least_upper_bound(a,c),multiply(inverse(c),b))))),inverse(greatest_lower_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) )],[refute_0_2429,refute_0_2658]) ).
cnf(refute_0_2660,plain,
( least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != multiply(least_upper_bound(a,c),inverse(c))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) != least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(least_upper_bound(a,c),inverse(c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) ),[1],$fot(multiply(least_upper_bound(a,c),inverse(c)))]]) ).
cnf(refute_0_2661,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) != least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2659,refute_0_2660]) ).
cnf(refute_0_2662,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(least_upper_bound(a,c),inverse(c)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) )],[refute_0_550,refute_0_2661]) ).
cnf(refute_0_2663,plain,
inverse(greatest_lower_bound(c,a)) = inverse(greatest_lower_bound(a,c)),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(c)),bind(X_16,$fot(a))]]) ).
cnf(refute_0_2664,plain,
multiply(a,inverse(greatest_lower_bound(c,a))) = multiply(a,inverse(greatest_lower_bound(c,a))),
introduced(tautology,[refl,[$fot(multiply(a,inverse(greatest_lower_bound(c,a))))]]) ).
cnf(refute_0_2665,plain,
( multiply(a,inverse(greatest_lower_bound(c,a))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| inverse(greatest_lower_bound(c,a)) != inverse(greatest_lower_bound(a,c))
| multiply(a,inverse(greatest_lower_bound(c,a))) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(c,a))),multiply(a,inverse(greatest_lower_bound(c,a)))) ),[1,1],$fot(inverse(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_2666,plain,
( inverse(greatest_lower_bound(c,a)) != inverse(greatest_lower_bound(a,c))
| multiply(a,inverse(greatest_lower_bound(c,a))) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(c,a))),multiply(a,inverse(greatest_lower_bound(c,a)))) )],[refute_0_2664,refute_0_2665]) ).
cnf(refute_0_2667,plain,
multiply(a,inverse(greatest_lower_bound(c,a))) = multiply(a,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(c,a)),inverse(greatest_lower_bound(a,c))) )],[refute_0_2663,refute_0_2666]) ).
cnf(refute_0_2668,plain,
multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))),
inference(subst,[],[refute_0_1146:[bind(X_45,$fot(greatest_lower_bound(X_172,X_173))),bind(X_86,$fot(inverse(X_173)))]]) ).
cnf(refute_0_2669,plain,
( multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) != greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))))) ),[1,0,1],$fot(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))]]) ).
cnf(refute_0_2670,plain,
( multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)),greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) )],[refute_0_1893,refute_0_2669]) ).
cnf(refute_0_2671,plain,
multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))))) )],[refute_0_2668,refute_0_2670]) ).
cnf(refute_0_2672,plain,
multiply(least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)),inverse(greatest_lower_bound(X_11,X_98))) = least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98)))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(X_98)),bind(X_91,$fot(greatest_lower_bound(X_11,X_98)))]]) ).
cnf(refute_0_2673,plain,
least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)) = X_98,
inference(subst,[],[refute_0_270:[bind(X_10,$fot(X_98))]]) ).
cnf(refute_0_2674,plain,
( multiply(least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)),inverse(greatest_lower_bound(X_11,X_98))) != least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))
| least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)) != X_98
| multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))) = least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)),inverse(greatest_lower_bound(X_11,X_98))),least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))) ),[0,0],$fot(X_98)]]) ).
cnf(refute_0_2675,plain,
( multiply(least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)),inverse(greatest_lower_bound(X_11,X_98))) != least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))
| multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))) = least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)),X_98) )],[refute_0_2673,refute_0_2674]) ).
cnf(refute_0_2676,plain,
multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))) = least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_98,greatest_lower_bound(X_11,X_98)),inverse(greatest_lower_bound(X_11,X_98))),least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))) )],[refute_0_2672,refute_0_2675]) ).
cnf(refute_0_2677,plain,
( multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))) != least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))
| least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98)))) = multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))))]]) ).
cnf(refute_0_2678,plain,
least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98)))) = multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))),
inference(resolve,[$cnf( $equal(multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))),least_upper_bound(identity,multiply(X_98,inverse(greatest_lower_bound(X_11,X_98))))) )],[refute_0_2676,refute_0_2677]) ).
cnf(refute_0_2679,plain,
least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),
inference(subst,[],[refute_0_2678:[bind(X_11,$fot(X_172)),bind(X_98,$fot(X_173))]]) ).
cnf(refute_0_2680,plain,
inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))) = inverse(greatest_lower_bound(X_172,X_173)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(inverse(greatest_lower_bound(X_172,X_173))))]]) ).
cnf(refute_0_2681,plain,
multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))) = multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))),
introduced(tautology,[refl,[$fot(multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))]]) ).
cnf(refute_0_2682,plain,
( multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))) != multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))
| inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))) != inverse(greatest_lower_bound(X_172,X_173))
| multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))),multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_172,X_173)))]]) ).
cnf(refute_0_2683,plain,
( inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))) != inverse(greatest_lower_bound(X_172,X_173))
| multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(resolve,[$cnf( $equal(multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))),multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) )],[refute_0_2681,refute_0_2682]) ).
cnf(refute_0_2684,plain,
multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))),inverse(greatest_lower_bound(X_172,X_173))) )],[refute_0_2680,refute_0_2683]) ).
cnf(refute_0_2685,plain,
least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) = least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))))]]) ).
cnf(refute_0_2686,plain,
( multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) != least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))
| least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) = least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))),least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))) ),[1,1],$fot(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))))]]) ).
cnf(refute_0_2687,plain,
( multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) = least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))),least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))) )],[refute_0_2685,refute_0_2686]) ).
cnf(refute_0_2688,plain,
least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) = least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))),
inference(resolve,[$cnf( $equal(multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))),multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) )],[refute_0_2684,refute_0_2687]) ).
cnf(refute_0_2689,plain,
( least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) != least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))))
| least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))))),bind(Z0,$fot(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))))]]) ).
cnf(refute_0_2690,plain,
( least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))),least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))))) )],[refute_0_2688,refute_0_2689]) ).
cnf(refute_0_2691,plain,
least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))),multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) )],[refute_0_2679,refute_0_2690]) ).
cnf(refute_0_2692,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173)))) = least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))),
inference(subst,[],[refute_0_2641:[bind(X_18,$fot(X_173)),bind(X_474,$fot(inverse(inverse(greatest_lower_bound(X_172,X_173)))))]]) ).
cnf(refute_0_2693,plain,
multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173)))),
inference(subst,[],[refute_0_2646:[bind(X_475,$fot(inverse(X_173))),bind(X_50,$fot(inverse(greatest_lower_bound(X_172,X_173))))]]) ).
cnf(refute_0_2694,plain,
( multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173))))
| inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173)))) != least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))))]]) ).
cnf(refute_0_2695,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173)))) != least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173))))) )],[refute_0_2693,refute_0_2694]) ).
cnf(refute_0_2696,plain,
multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X_172,X_173))),inverse(X_173)))),least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))) )],[refute_0_2692,refute_0_2695]) ).
cnf(refute_0_2697,plain,
( multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))
| least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))))),bind(Z0,$fot(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))))]]) ).
cnf(refute_0_2698,plain,
( least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))),least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173))))))) )],[refute_0_2696,refute_0_2697]) ).
cnf(refute_0_2699,plain,
multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_173,inverse(inverse(inverse(greatest_lower_bound(X_172,X_173)))))),multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) )],[refute_0_2691,refute_0_2698]) ).
cnf(refute_0_2700,plain,
( multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))
| multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))) ),[0],$fot(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))))]]) ).
cnf(refute_0_2701,plain,
( multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))
| multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))),multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) )],[refute_0_2699,refute_0_2700]) ).
cnf(refute_0_2702,plain,
inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))),
inference(subst,[],[refute_0_2641:[bind(X_18,$fot(X_173)),bind(X_474,$fot(X_172))]]) ).
cnf(refute_0_2703,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = greatest_lower_bound(identity,multiply(X_172,inverse(X_173))),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_172,inverse(X_173)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2704,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))))]]) ).
cnf(refute_0_2705,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) != greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) = inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))]]) ).
cnf(refute_0_2706,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) != greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) = inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))) )],[refute_0_2704,refute_0_2705]) ).
cnf(refute_0_2707,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) = inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) )],[refute_0_2703,refute_0_2706]) ).
cnf(refute_0_2708,plain,
( inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) != least_upper_bound(identity,multiply(X_173,inverse(X_172)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) != inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_173,inverse(X_172)))))]]) ).
cnf(refute_0_2709,plain,
( inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) != least_upper_bound(identity,multiply(X_173,inverse(X_172)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))),inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) )],[refute_0_2707,refute_0_2708]) ).
cnf(refute_0_2710,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),least_upper_bound(identity,multiply(X_173,inverse(X_172)))) )],[refute_0_2702,refute_0_2709]) ).
cnf(refute_0_2711,plain,
( multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) != least_upper_bound(identity,multiply(X_173,inverse(X_172)))
| multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),least_upper_bound(identity,multiply(X_173,inverse(X_172)))) ),[0],$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))))]]) ).
cnf(refute_0_2712,plain,
( multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))
| multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))),least_upper_bound(identity,multiply(X_173,inverse(X_172)))) )],[refute_0_2710,refute_0_2711]) ).
cnf(refute_0_2713,plain,
( multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))
| multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))) ),
inference(resolve,[$cnf( $equal(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))) )],[refute_0_2701,refute_0_2712]) ).
cnf(refute_0_2714,plain,
multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = least_upper_bound(identity,multiply(X_173,inverse(X_172))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_173)),least_upper_bound(inverse(greatest_lower_bound(X_172,X_173)),inverse(X_173))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))) )],[refute_0_2671,refute_0_2713]) ).
cnf(refute_0_2715,plain,
( multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) != least_upper_bound(identity,multiply(X_173,inverse(X_172)))
| least_upper_bound(identity,multiply(X_173,inverse(X_172))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_173,inverse(X_172)))))]]) ).
cnf(refute_0_2716,plain,
least_upper_bound(identity,multiply(X_173,inverse(X_172))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),
inference(resolve,[$cnf( $equal(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),least_upper_bound(identity,multiply(X_173,inverse(X_172)))) )],[refute_0_2714,refute_0_2715]) ).
cnf(refute_0_2717,plain,
least_upper_bound(identity,multiply(a,inverse(c))) = multiply(a,inverse(greatest_lower_bound(c,a))),
inference(subst,[],[refute_0_2716:[bind(X_172,$fot(c)),bind(X_173,$fot(a))]]) ).
cnf(refute_0_2718,plain,
multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(subst,[],[refute_0_98:[bind(X_89,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_2719,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = identity,
inference(subst,[],[refute_0_1866:[bind(X_22,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_2720,plain,
least_upper_bound(b,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))),
inference(subst,[],[refute_0_1163:[bind(X,$fot(a)),bind(X_21,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_2721,plain,
least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_270:[bind(X_10,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),bind(X_11,$fot(least_upper_bound(a,least_upper_bound(c,identity))))]]) ).
cnf(refute_0_2722,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465)))),
inference(subst,[],[refute_0_785:[bind(X_153,$fot(inverse(greatest_lower_bound(X_464,inverse(X_465))))),bind(X_154,$fot(greatest_lower_bound(identity,multiply(X_464,X_465))))]]) ).
cnf(refute_0_2723,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) != greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) != X_465
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)),greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))) ),[1,1],$fot(X_465)]]) ).
cnf(refute_0_2724,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) != greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))),X_465) )],[refute_0_2569,refute_0_2723]) ).
cnf(refute_0_2725,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)),greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))) )],[refute_0_2722,refute_0_2724]) ).
cnf(refute_0_2726,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))) = greatest_lower_bound(identity,multiply(X_464,X_465)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_464,X_465))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2727,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) = multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))))]]) ).
cnf(refute_0_2728,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) != multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))))
| greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))) != greatest_lower_bound(identity,multiply(X_464,X_465))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) = multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_464,X_465)))]]) ).
cnf(refute_0_2729,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))) != greatest_lower_bound(identity,multiply(X_464,X_465))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) = multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))))) )],[refute_0_2727,refute_0_2728]) ).
cnf(refute_0_2730,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) = multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) )],[refute_0_2726,refute_0_2729]) ).
cnf(refute_0_2731,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) != X_465
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) != multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465)))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) = X_465 ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))))),bind(Z0,$fot(X_465))]]) ).
cnf(refute_0_2732,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))) != X_465
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) = X_465 ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465)))) )],[refute_0_2730,refute_0_2731]) ).
cnf(refute_0_2733,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) = X_465,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,multiply(X_464,X_465))),X_465) )],[refute_0_2569,refute_0_2732]) ).
cnf(refute_0_2734,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_1609:[bind(X_11,$fot(multiply(X,Y))),bind(X_16,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_2735,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_2736,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_296,refute_0_2735]) ).
cnf(refute_0_2737,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_2734,refute_0_2736]) ).
cnf(refute_0_2738,plain,
least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) = greatest_lower_bound(Y,Z),
inference(subst,[],[refute_0_1609:[bind(X_11,$fot(Z)),bind(X_16,$fot(Y))]]) ).
cnf(refute_0_2739,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_2740,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_2741,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( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_2739,refute_0_2740]) ).
cnf(refute_0_2742,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_2738,refute_0_2741]) ).
cnf(refute_0_2743,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
inference(subst,[],[refute_0_286:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_2744,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Y0,$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_2745,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_2743,refute_0_2744]) ).
cnf(refute_0_2746,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_2742,refute_0_2745]) ).
cnf(refute_0_2747,plain,
greatest_lower_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(subst,[],[refute_0_296:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_2748,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_2749,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_2750,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_2748,refute_0_2749]) ).
cnf(refute_0_2751,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_2747,refute_0_2750]) ).
cnf(refute_0_2752,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_2753,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))) )],[refute_0_2751,refute_0_2752]) ).
cnf(refute_0_2754,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_2746,refute_0_2753]) ).
cnf(refute_0_2755,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_1395:[bind(X_137,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(X_20,$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_2756,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_2757,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_2755,refute_0_2756]) ).
cnf(refute_0_2758,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_2754,refute_0_2757]) ).
cnf(refute_0_2759,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_2760,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_2758,refute_0_2759]) ).
cnf(refute_0_2761,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),[0],$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_2762,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_2747,refute_0_2761]) ).
cnf(refute_0_2763,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_2760,refute_0_2762]) ).
cnf(refute_0_2764,plain,
multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_2737,refute_0_2763]) ).
cnf(refute_0_2765,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_2766,plain,
multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_2764,refute_0_2765]) ).
cnf(refute_0_2767,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))),
inference(subst,[],[refute_0_2766:[bind(X,$fot(inverse(greatest_lower_bound(X_464,inverse(X_465))))),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(identity,multiply(X_464,X_465))))]]) ).
cnf(refute_0_2768,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) != multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))))
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) != X_465
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = X_465 ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))))),bind(Z0,$fot(X_465))]]) ).
cnf(refute_0_2769,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))) != X_465
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = X_465 ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)),multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465))))) )],[refute_0_2767,refute_0_2768]) ).
cnf(refute_0_2770,plain,
multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) = X_465,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_464,X_465)))),X_465) )],[refute_0_2733,refute_0_2769]) ).
cnf(refute_0_2771,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) != X_465
| multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) != greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)
| X_465 = greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)),greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)) ),[0],$fot(X_465)]]) ).
cnf(refute_0_2772,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) != greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)
| X_465 = greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)),X_465) )],[refute_0_2770,refute_0_2771]) ).
cnf(refute_0_2773,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465) = greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465)))),
inference(subst,[],[refute_0_106:[bind(X,$fot(X_465)),bind(Y,$fot(inverse(greatest_lower_bound(X_464,inverse(X_465)))))]]) ).
cnf(refute_0_2774,plain,
( X_465 != greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)
| greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465) != greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465))))
| X_465 = greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_465,greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465))))) ),[0],$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465))]]) ).
cnf(refute_0_2775,plain,
( X_465 != greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)
| X_465 = greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465),greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465))))) )],[refute_0_2773,refute_0_2774]) ).
cnf(refute_0_2776,plain,
( multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)) != greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)
| X_465 = greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465)))) ),
inference(resolve,[$cnf( $equal(X_465,greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)) )],[refute_0_2772,refute_0_2775]) ).
cnf(refute_0_2777,plain,
X_465 = greatest_lower_bound(X_465,inverse(greatest_lower_bound(X_464,inverse(X_465)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_464,inverse(X_465))),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_464,X_465)),identity)),greatest_lower_bound(inverse(greatest_lower_bound(X_464,inverse(X_465))),X_465)) )],[refute_0_2725,refute_0_2776]) ).
cnf(refute_0_2778,plain,
least_upper_bound(a,least_upper_bound(c,identity)) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))))),
inference(subst,[],[refute_0_2777:[bind(X_464,$fot(b)),bind(X_465,$fot(least_upper_bound(a,least_upper_bound(c,identity))))]]) ).
cnf(refute_0_2779,plain,
greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))),Z),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(greatest_lower_bound(X_64,least_upper_bound(a,c))))]]) ).
cnf(refute_0_2780,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))) != greatest_lower_bound(b,X_64)
| greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))),Z)
| greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_64),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))),Z)) ),[1,0],$fot(greatest_lower_bound(b,X_64))]]) ).
cnf(refute_0_2781,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))),Z)
| greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_64),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))),greatest_lower_bound(b,X_64)) )],[refute_0_1572,refute_0_2780]) ).
cnf(refute_0_2782,plain,
greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_64),Z),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_64,least_upper_bound(a,c))),Z)) )],[refute_0_2779,refute_0_2781]) ).
cnf(refute_0_2783,plain,
greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z) = greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_64)),bind(Y,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_2784,plain,
greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)))]]) ).
cnf(refute_0_2785,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z))
| greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z) != greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))
| greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z))) ),[1,1],$fot(greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z)))]]) ).
cnf(refute_0_2786,plain,
( greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z) != greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))
| greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z))) )],[refute_0_2784,refute_0_2785]) ).
cnf(refute_0_2787,plain,
greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z),greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) )],[refute_0_2783,refute_0_2786]) ).
cnf(refute_0_2788,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) != greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z)))
| greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_64),Z)
| greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(greatest_lower_bound(b,X_64),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,X_64),Z)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))))]]) ).
cnf(refute_0_2789,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_64),Z)
| greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(greatest_lower_bound(b,X_64),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z)))) )],[refute_0_2787,refute_0_2788]) ).
cnf(refute_0_2790,plain,
greatest_lower_bound(greatest_lower_bound(b,X_64),Z) = greatest_lower_bound(b,greatest_lower_bound(X_64,Z)),
inference(subst,[],[refute_0_566:[bind(X,$fot(b)),bind(Y,$fot(X_64))]]) ).
cnf(refute_0_2791,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) != greatest_lower_bound(greatest_lower_bound(b,X_64),Z)
| greatest_lower_bound(greatest_lower_bound(b,X_64),Z) != greatest_lower_bound(b,greatest_lower_bound(X_64,Z))
| greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_64,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))),greatest_lower_bound(b,greatest_lower_bound(X_64,Z))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(b,X_64),Z))]]) ).
cnf(refute_0_2792,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) != greatest_lower_bound(greatest_lower_bound(b,X_64),Z)
| greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_64,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_64),Z),greatest_lower_bound(b,greatest_lower_bound(X_64,Z))) )],[refute_0_2790,refute_0_2791]) ).
cnf(refute_0_2793,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_64),Z)
| greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_64,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))),greatest_lower_bound(greatest_lower_bound(b,X_64),Z)) )],[refute_0_2789,refute_0_2792]) ).
cnf(refute_0_2794,plain,
greatest_lower_bound(b,greatest_lower_bound(X_64,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_64,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_64,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,X_64),Z)) )],[refute_0_2782,refute_0_2793]) ).
cnf(refute_0_2795,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_2794:[bind(Z,$fot(inverse(least_upper_bound(a,c)))),bind(X_64,$fot(least_upper_bound(b,identity)))]]) ).
cnf(refute_0_2796,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_1842:[bind(X_119,$fot(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2797,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))),bind(X_55,$fot(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_2798,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c)))),
inference(subst,[],[refute_0_149:[bind(X_89,$fot(greatest_lower_bound(identity,least_upper_bound(a,c)))),bind(X_90,$fot(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_2799,plain,
multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),multiply(inverse(X_163),greatest_lower_bound(identity,X_163))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(greatest_lower_bound(identity,X_163))),bind(Y,$fot(X_172)),bind(Z,$fot(inverse(X_163)))]]) ).
cnf(refute_0_2800,plain,
multiply(inverse(X_163),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(identity,multiply(inverse(X_163),identity)),
inference(subst,[],[refute_0_110:[bind(X_154,$fot(identity)),bind(X_155,$fot(X_163))]]) ).
cnf(refute_0_2801,plain,
inverse(X_163) = multiply(inverse(X_163),identity),
inference(subst,[],[refute_0_49:[bind(X_48,$fot(inverse(X_163)))]]) ).
cnf(refute_0_2802,plain,
( inverse(X_163) != multiply(inverse(X_163),identity)
| multiply(inverse(X_163),identity) = inverse(X_163) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(X_163))),bind(Y0,$fot(multiply(inverse(X_163),identity)))]]) ).
cnf(refute_0_2803,plain,
multiply(inverse(X_163),identity) = inverse(X_163),
inference(resolve,[$cnf( $equal(inverse(X_163),multiply(inverse(X_163),identity)) )],[refute_0_2801,refute_0_2802]) ).
cnf(refute_0_2804,plain,
( multiply(inverse(X_163),greatest_lower_bound(identity,X_163)) != greatest_lower_bound(identity,multiply(inverse(X_163),identity))
| multiply(inverse(X_163),identity) != inverse(X_163)
| multiply(inverse(X_163),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(identity,inverse(X_163)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_163),greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,multiply(inverse(X_163),identity))) ),[1,1],$fot(inverse(X_163))]]) ).
cnf(refute_0_2805,plain,
( multiply(inverse(X_163),greatest_lower_bound(identity,X_163)) != greatest_lower_bound(identity,multiply(inverse(X_163),identity))
| multiply(inverse(X_163),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(identity,inverse(X_163)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_163),identity),inverse(X_163)) )],[refute_0_2803,refute_0_2804]) ).
cnf(refute_0_2806,plain,
multiply(inverse(X_163),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(identity,inverse(X_163)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_163),greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,multiply(inverse(X_163),identity))) )],[refute_0_2800,refute_0_2805]) ).
cnf(refute_0_2807,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) != greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),multiply(inverse(X_163),greatest_lower_bound(identity,X_163)))
| multiply(inverse(X_163),greatest_lower_bound(identity,X_163)) != greatest_lower_bound(identity,inverse(X_163))
| multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)),greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),multiply(inverse(X_163),greatest_lower_bound(identity,X_163)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_163)))]]) ).
cnf(refute_0_2808,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) != greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),multiply(inverse(X_163),greatest_lower_bound(identity,X_163)))
| multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_163),greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) )],[refute_0_2806,refute_0_2807]) ).
cnf(refute_0_2809,plain,
multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)),greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),multiply(inverse(X_163),greatest_lower_bound(identity,X_163)))) )],[refute_0_2799,refute_0_2808]) ).
cnf(refute_0_2810,plain,
greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)))) = greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),
inference(subst,[],[refute_0_262:[bind(X,$fot(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))))]]) ).
cnf(refute_0_2811,plain,
least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))) = Y,
inference(subst,[],[refute_0_1352:[bind(X_10,$fot(Y)),bind(X_56,$fot(X_110)),bind(X_57,$fot(X_111))]]) ).
cnf(refute_0_2812,plain,
( greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)))) != greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))
| least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))) != Y
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)))),greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_2813,plain,
( greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)))) != greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))),Y) )],[refute_0_2811,refute_0_2812]) ).
cnf(refute_0_2814,plain,
greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),least_upper_bound(Y,greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)))),greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))) )],[refute_0_2810,refute_0_2813]) ).
cnf(refute_0_2815,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)) = greatest_lower_bound(Y,X_111),
inference(subst,[],[refute_0_570:[bind(Y,$fot(X_111)),bind(X_15,$fot(Y))]]) ).
cnf(refute_0_2816,plain,
greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) = greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))))]]) ).
cnf(refute_0_2817,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)) != greatest_lower_bound(Y,X_111)
| greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) != greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))
| greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))),greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))) ),[1,1],$fot(greatest_lower_bound(Y,X_111))]]) ).
cnf(refute_0_2818,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)) != greatest_lower_bound(Y,X_111)
| greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))),greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))) )],[refute_0_2816,refute_0_2817]) ).
cnf(refute_0_2819,plain,
greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)),greatest_lower_bound(Y,X_111)) )],[refute_0_2815,refute_0_2818]) ).
cnf(refute_0_2820,plain,
greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))) = greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y),
inference(subst,[],[refute_0_570:[bind(X_15,$fot(greatest_lower_bound(X_79,X_77)))]]) ).
cnf(refute_0_2821,plain,
greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79)) = greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77)),
inference(subst,[],[refute_0_1521:[bind(X,$fot(X_77)),bind(X_56,$fot(Y)),bind(X_57,$fot(X_79))]]) ).
cnf(refute_0_2822,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79)) != greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))
| greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77)) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))))]]) ).
cnf(refute_0_2823,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77)) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79)),greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))) )],[refute_0_2821,refute_0_2822]) ).
cnf(refute_0_2824,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77)) != greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))) != greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))),greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)) ),[0,1],$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79)))]]) ).
cnf(refute_0_2825,plain,
( greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))) != greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77)),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) )],[refute_0_2823,refute_0_2824]) ).
cnf(refute_0_2826,plain,
greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(Y,greatest_lower_bound(X_79,X_77))),greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)) )],[refute_0_2820,refute_0_2825]) ).
cnf(refute_0_2827,plain,
greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)) = greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57)),
inference(subst,[],[refute_0_570:[bind(Y,$fot(greatest_lower_bound(X_56,X_57)))]]) ).
cnf(refute_0_2828,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15)) = greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_2829,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15)) != greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)))]]) ).
cnf(refute_0_2830,plain,
greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15)),greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)) )],[refute_0_2828,refute_0_2829]) ).
cnf(refute_0_2831,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)) != greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57))
| greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15))
| greatest_lower_bound(X_15,greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15))) = greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)),greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57))) ),[0,1],$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15)))]]) ).
cnf(refute_0_2832,plain,
( greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)) != greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57))
| greatest_lower_bound(X_15,greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15))) = greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15))) )],[refute_0_2830,refute_0_2831]) ).
cnf(refute_0_2833,plain,
greatest_lower_bound(X_15,greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_15))) = greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,greatest_lower_bound(greatest_lower_bound(X_56,X_57),X_15)),greatest_lower_bound(X_15,greatest_lower_bound(X_56,X_57))) )],[refute_0_2827,refute_0_2832]) ).
cnf(refute_0_2834,plain,
greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)),
inference(subst,[],[refute_0_2833:[bind(X_15,$fot(X_79)),bind(X_56,$fot(Y)),bind(X_57,$fot(X_77))]]) ).
cnf(refute_0_2835,plain,
greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)) = greatest_lower_bound(X_77,X_79),
inference(subst,[],[refute_0_570:[bind(Y,$fot(X_79)),bind(X_15,$fot(X_77))]]) ).
cnf(refute_0_2836,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))) = greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))))]]) ).
cnf(refute_0_2837,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))) != greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)))
| greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)) != greatest_lower_bound(X_77,X_79)
| greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))) = greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))),greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)))) ),[1,1],$fot(greatest_lower_bound(X_77,X_79))]]) ).
cnf(refute_0_2838,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)) != greatest_lower_bound(X_77,X_79)
| greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))) = greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))),greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)))) )],[refute_0_2836,refute_0_2837]) ).
cnf(refute_0_2839,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))) = greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)),greatest_lower_bound(X_77,X_79)) )],[refute_0_2835,refute_0_2838]) ).
cnf(refute_0_2840,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))),
inference(subst,[],[refute_0_1498:[bind(X_56,$fot(Y)),bind(X_57,$fot(greatest_lower_bound(X_79,X_77))),bind(X_58,$fot(X_77))]]) ).
cnf(refute_0_2841,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))) != greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)) != greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))))]]) ).
cnf(refute_0_2842,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))) != greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)),greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77)))) )],[refute_0_2840,refute_0_2841]) ).
cnf(refute_0_2843,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_77,greatest_lower_bound(X_79,X_77))),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))) )],[refute_0_2839,refute_0_2842]) ).
cnf(refute_0_2844,plain,
greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))))]]) ).
cnf(refute_0_2845,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)) != greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))),greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)))]]) ).
cnf(refute_0_2846,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)) != greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))),greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)))) )],[refute_0_2844,refute_0_2845]) ).
cnf(refute_0_2847,plain,
greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))) )],[refute_0_2843,refute_0_2846]) ).
cnf(refute_0_2848,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))))),bind(Y0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))))),bind(Z0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))))]]) ).
cnf(refute_0_2849,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))),greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79)))) )],[refute_0_2847,refute_0_2848]) ).
cnf(refute_0_2850,plain,
greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(X_77,X_79))),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))) )],[refute_0_2834,refute_0_2849]) ).
cnf(refute_0_2851,plain,
greatest_lower_bound(X,greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))) = greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)),
inference(subst,[],[refute_0_1521:[bind(X_57,$fot(greatest_lower_bound(X_79,X_77)))]]) ).
cnf(refute_0_2852,plain,
greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79)) = greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77)),
inference(subst,[],[refute_0_1521:[bind(X,$fot(X_77)),bind(X_57,$fot(X_79))]]) ).
cnf(refute_0_2853,plain,
( greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79)) != greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))
| greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77)) = greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79)))),bind(Y0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))))]]) ).
cnf(refute_0_2854,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77)) = greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79)),greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))) )],[refute_0_2852,refute_0_2853]) ).
cnf(refute_0_2855,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))) != greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))
| greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77)) != greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))
| greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) = greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))),greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))) ),[0,1],$fot(greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79)))]]) ).
cnf(refute_0_2856,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))) != greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))
| greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) = greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77)),greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) )],[refute_0_2854,refute_0_2855]) ).
cnf(refute_0_2857,plain,
greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) = greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,greatest_lower_bound(X_79,X_77))),greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))) )],[refute_0_2851,refute_0_2856]) ).
cnf(refute_0_2858,plain,
greatest_lower_bound(greatest_lower_bound(X_79,X_77),X) = greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_79)),bind(Y,$fot(X_77)),bind(Z,$fot(X))]]) ).
cnf(refute_0_2859,plain,
greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) = greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)))]]) ).
cnf(refute_0_2860,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) != greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),X) != greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) = greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)),greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))) ),[1,1],$fot(greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)))]]) ).
cnf(refute_0_2861,plain,
( greatest_lower_bound(greatest_lower_bound(X_79,X_77),X) != greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) = greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)),greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))) )],[refute_0_2859,refute_0_2860]) ).
cnf(refute_0_2862,plain,
greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) = greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),X),greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))) )],[refute_0_2858,refute_0_2861]) ).
cnf(refute_0_2863,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) != greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))
| greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)) != greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)))
| greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) = greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))),greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)))) ),[0],$fot(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)))]]) ).
cnf(refute_0_2864,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) != greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))
| greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) = greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X)),greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)))) )],[refute_0_2862,refute_0_2863]) ).
cnf(refute_0_2865,plain,
greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) = greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))),greatest_lower_bound(X_56,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X))) )],[refute_0_2857,refute_0_2864]) ).
cnf(refute_0_2866,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) != greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)))
| greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))) = greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))))),bind(Y0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)))))]]) ).
cnf(refute_0_2867,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X))) = greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_77,greatest_lower_bound(X_56,X_79))),greatest_lower_bound(X_56,greatest_lower_bound(X_79,greatest_lower_bound(X_77,X)))) )],[refute_0_2865,refute_0_2866]) ).
cnf(refute_0_2868,plain,
greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))),
inference(subst,[],[refute_0_2867:[bind(X,$fot(X_79)),bind(X_56,$fot(greatest_lower_bound(X_79,X_77))),bind(X_77,$fot(Y)),bind(X_79,$fot(X_77))]]) ).
cnf(refute_0_2869,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)))
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))))),bind(Y0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))))),bind(Z0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))))]]) ).
cnf(refute_0_2870,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))),greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77)))) )],[refute_0_2868,refute_0_2869]) ).
cnf(refute_0_2871,plain,
greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_79,X_77),X_77))),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))) )],[refute_0_2850,refute_0_2870]) ).
cnf(refute_0_2872,plain,
( greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)
| greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) = greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))),greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)) ),[0],$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)))]]) ).
cnf(refute_0_2873,plain,
( greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)
| greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) = greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77))) )],[refute_0_2871,refute_0_2872]) ).
cnf(refute_0_2874,plain,
greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y) = greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_79)),bind(Y,$fot(X_77)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_2875,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) != greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)
| greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y) != greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) = greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)),greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y))]]) ).
cnf(refute_0_2876,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) != greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)
| greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) = greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y),greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y))) )],[refute_0_2874,refute_0_2875]) ).
cnf(refute_0_2877,plain,
( greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)
| greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) = greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)),greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)) )],[refute_0_2873,refute_0_2876]) ).
cnf(refute_0_2878,plain,
greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) = greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_79,X_77),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_79))),greatest_lower_bound(greatest_lower_bound(X_79,X_77),Y)) )],[refute_0_2826,refute_0_2877]) ).
cnf(refute_0_2879,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) != greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y))
| greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y)) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)))),bind(Y0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y))))]]) ).
cnf(refute_0_2880,plain,
greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y)) = greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_77)),greatest_lower_bound(X_79,greatest_lower_bound(X_77,Y))) )],[refute_0_2878,refute_0_2879]) ).
cnf(refute_0_2881,plain,
greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y)) = greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))),
inference(subst,[],[refute_0_2880:[bind(X_77,$fot(greatest_lower_bound(X_111,Y))),bind(X_79,$fot(X_110))]]) ).
cnf(refute_0_2882,plain,
greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_110)),bind(Y,$fot(greatest_lower_bound(X_111,Y))),bind(Z,$fot(Y))]]) ).
cnf(refute_0_2883,plain,
( greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y)) != greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) != greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y))),bind(Y0,$fot(greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y)))),bind(Z0,$fot(greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))))]]) ).
cnf(refute_0_2884,plain,
( greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y)) != greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y),greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y))) )],[refute_0_2882,refute_0_2883]) ).
cnf(refute_0_2885,plain,
greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_110,greatest_lower_bound(greatest_lower_bound(X_111,Y),Y)),greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))) )],[refute_0_2881,refute_0_2884]) ).
cnf(refute_0_2886,plain,
( greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) != greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) != greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y))),bind(Y0,$fot(greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))))),bind(Z0,$fot(greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111))))]]) ).
cnf(refute_0_2887,plain,
( greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))) != greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y),greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y)))) )],[refute_0_2885,refute_0_2886]) ).
cnf(refute_0_2888,plain,
greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_110,greatest_lower_bound(Y,greatest_lower_bound(X_111,Y))),greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111))) )],[refute_0_2819,refute_0_2887]) ).
cnf(refute_0_2889,plain,
( greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) != greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111))
| greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) != greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))
| greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) = greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y),greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))) ),[0],$fot(greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)))]]) ).
cnf(refute_0_2890,plain,
( greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y) != greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))
| greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) = greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y),greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111))) )],[refute_0_2888,refute_0_2889]) ).
cnf(refute_0_2891,plain,
greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) = greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)),Y),greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))) )],[refute_0_2814,refute_0_2890]) ).
cnf(refute_0_2892,plain,
( greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) != greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))
| greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)))),bind(Y0,$fot(greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))))]]) ).
cnf(refute_0_2893,plain,
greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y)) = greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_110,greatest_lower_bound(Y,X_111)),greatest_lower_bound(X_110,greatest_lower_bound(X_111,Y))) )],[refute_0_2891,refute_0_2892]) ).
cnf(refute_0_2894,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163)))),
inference(subst,[],[refute_0_2893:[bind(Y,$fot(inverse(X_163))),bind(X_110,$fot(identity)),bind(X_111,$fot(multiply(X_172,greatest_lower_bound(identity,X_163))))]]) ).
cnf(refute_0_2895,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(greatest_lower_bound(Y,X_79))),bind(X_56,$fot(X_78)),bind(X_57,$fot(X_79))]]) ).
cnf(refute_0_2896,plain,
greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)) = greatest_lower_bound(X_79,Y),
inference(subst,[],[refute_0_570:[bind(X_15,$fot(X_79))]]) ).
cnf(refute_0_2897,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)) != greatest_lower_bound(X_79,Y)
| greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)))
| greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)))) ),[1,1],$fot(greatest_lower_bound(X_79,Y))]]) ).
cnf(refute_0_2898,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)))
| greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) )],[refute_0_2896,refute_0_2897]) ).
cnf(refute_0_2899,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)))) )],[refute_0_2895,refute_0_2898]) ).
cnf(refute_0_2900,plain,
greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)),
inference(subst,[],[refute_0_2833:[bind(X_15,$fot(X_79)),bind(X_56,$fot(X_78)),bind(X_57,$fot(Y))]]) ).
cnf(refute_0_2901,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(greatest_lower_bound(Y,X_79))),bind(X_77,$fot(X_79))]]) ).
cnf(refute_0_2902,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79)))
| greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)))),bind(Y0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79))))),bind(Z0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y))))]]) ).
cnf(refute_0_2903,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79)))) )],[refute_0_2901,refute_0_2902]) ).
cnf(refute_0_2904,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(X_78,greatest_lower_bound(Y,X_79))),greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y))) )],[refute_0_2900,refute_0_2903]) ).
cnf(refute_0_2905,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y))
| greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y))) ),[0],$fot(greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)))]]) ).
cnf(refute_0_2906,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y))
| greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y))) )],[refute_0_2904,refute_0_2905]) ).
cnf(refute_0_2907,plain,
greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y))) )],[refute_0_2899,refute_0_2906]) ).
cnf(refute_0_2908,plain,
( greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)) != greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y))
| greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)))),bind(Y0,$fot(greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y))))]]) ).
cnf(refute_0_2909,plain,
greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y)) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(X_78,Y)),greatest_lower_bound(X_78,greatest_lower_bound(X_79,Y))) )],[refute_0_2907,refute_0_2908]) ).
cnf(refute_0_2910,plain,
greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163))),
inference(subst,[],[refute_0_2909:[bind(Y,$fot(inverse(X_163))),bind(X_78,$fot(multiply(X_172,greatest_lower_bound(identity,X_163)))),bind(X_79,$fot(identity))]]) ).
cnf(refute_0_2911,plain,
( greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163))))
| greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163))))))]]) ).
cnf(refute_0_2912,plain,
( greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163))))
| greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))),greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163)))) )],[refute_0_2910,refute_0_2911]) ).
cnf(refute_0_2913,plain,
greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),inverse(X_163))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163))))) )],[refute_0_2894,refute_0_2912]) ).
cnf(refute_0_2914,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) != greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163)))
| greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163))))
| multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163))))) ),[0],$fot(greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))))]]) ).
cnf(refute_0_2915,plain,
( multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) != greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163)))
| multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163))))) )],[refute_0_2913,refute_0_2914]) ).
cnf(refute_0_2916,plain,
multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_163),multiply(X_172,greatest_lower_bound(identity,X_163)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,inverse(X_163)),greatest_lower_bound(identity,X_163)),greatest_lower_bound(multiply(X_172,greatest_lower_bound(identity,X_163)),greatest_lower_bound(identity,inverse(X_163)))) )],[refute_0_2809,refute_0_2915]) ).
cnf(refute_0_2917,plain,
multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))))),
inference(subst,[],[refute_0_2916:[bind(X_163,$fot(least_upper_bound(a,c))),bind(X_172,$fot(least_upper_bound(b,identity)))]]) ).
cnf(refute_0_2918,plain,
multiply(least_upper_bound(X_84,identity),inverse(multiply(inverse(X_84),least_upper_bound(X_84,identity)))) = inverse(inverse(X_84)),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(inverse(X_84))),bind(X_55,$fot(least_upper_bound(X_84,identity)))]]) ).
cnf(refute_0_2919,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(identity,X_84))),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(least_upper_bound(identity,X_84)))]]) ).
cnf(refute_0_2920,plain,
multiply(inverse(X_84),least_upper_bound(identity,X_84)) = least_upper_bound(identity,inverse(X_84)),
inference(subst,[],[refute_0_74:[bind(X_86,$fot(X_84))]]) ).
cnf(refute_0_2921,plain,
( multiply(inverse(X_84),least_upper_bound(identity,X_84)) != least_upper_bound(identity,inverse(X_84))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) != least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(identity,X_84)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(identity,X_84)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_84)))]]) ).
cnf(refute_0_2922,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) != least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(identity,X_84)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(identity,X_84)),least_upper_bound(identity,inverse(X_84))) )],[refute_0_2920,refute_0_2921]) ).
cnf(refute_0_2923,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(identity,X_84)))) )],[refute_0_2919,refute_0_2922]) ).
cnf(refute_0_2924,plain,
least_upper_bound(X_84,least_upper_bound(identity,X_84)) = least_upper_bound(X_84,identity),
inference(subst,[],[refute_0_279:[bind(Y,$fot(identity)),bind(X_13,$fot(X_84))]]) ).
cnf(refute_0_2925,plain,
multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))))]]) ).
cnf(refute_0_2926,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))) != multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84)))
| least_upper_bound(X_84,least_upper_bound(identity,X_84)) != least_upper_bound(X_84,identity)
| multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))),multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84)))) ),[1,1],$fot(least_upper_bound(X_84,identity))]]) ).
cnf(refute_0_2927,plain,
( least_upper_bound(X_84,least_upper_bound(identity,X_84)) != least_upper_bound(X_84,identity)
| multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))),multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84)))) )],[refute_0_2925,refute_0_2926]) ).
cnf(refute_0_2928,plain,
multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,least_upper_bound(identity,X_84)),least_upper_bound(X_84,identity)) )],[refute_0_2924,refute_0_2927]) ).
cnf(refute_0_2929,plain,
least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(multiply(X_82,X_84))),bind(X_19,$fot(multiply(X_82,X_83)))]]) ).
cnf(refute_0_2930,plain,
multiply(X_82,least_upper_bound(X_83,X_84)) = least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_2931,plain,
( multiply(X_82,least_upper_bound(X_83,X_84)) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))
| least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)) = multiply(X_82,least_upper_bound(X_83,X_84)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_82,least_upper_bound(X_83,X_84)))),bind(Y0,$fot(least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))))]]) ).
cnf(refute_0_2932,plain,
least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)) = multiply(X_82,least_upper_bound(X_83,X_84)),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,X_84)),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) )],[refute_0_2930,refute_0_2931]) ).
cnf(refute_0_2933,plain,
( least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)) != multiply(X_82,least_upper_bound(X_83,X_84))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_83,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) ),[1],$fot(multiply(X_82,least_upper_bound(X_83,X_84)))]]) ).
cnf(refute_0_2934,plain,
( least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_83,X_84)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)),multiply(X_82,least_upper_bound(X_83,X_84))) )],[refute_0_2932,refute_0_2933]) ).
cnf(refute_0_2935,plain,
least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_83,X_84)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) )],[refute_0_2929,refute_0_2934]) ).
cnf(refute_0_2936,plain,
least_upper_bound(X_83,X_83) = X_83,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_2937,plain,
least_upper_bound(X_84,least_upper_bound(X_83,X_83)) = least_upper_bound(X_84,least_upper_bound(X_83,X_83)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_84,least_upper_bound(X_83,X_83)))]]) ).
cnf(refute_0_2938,plain,
( least_upper_bound(X_83,X_83) != X_83
| least_upper_bound(X_84,least_upper_bound(X_83,X_83)) != least_upper_bound(X_84,least_upper_bound(X_83,X_83))
| least_upper_bound(X_84,least_upper_bound(X_83,X_83)) = least_upper_bound(X_84,X_83) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_84,least_upper_bound(X_83,X_83)),least_upper_bound(X_84,least_upper_bound(X_83,X_83))) ),[1,1],$fot(X_83)]]) ).
cnf(refute_0_2939,plain,
( least_upper_bound(X_83,X_83) != X_83
| least_upper_bound(X_84,least_upper_bound(X_83,X_83)) = least_upper_bound(X_84,X_83) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,least_upper_bound(X_83,X_83)),least_upper_bound(X_84,least_upper_bound(X_83,X_83))) )],[refute_0_2937,refute_0_2938]) ).
cnf(refute_0_2940,plain,
least_upper_bound(X_84,least_upper_bound(X_83,X_83)) = least_upper_bound(X_84,X_83),
inference(resolve,[$cnf( $equal(least_upper_bound(X_83,X_83),X_83) )],[refute_0_2936,refute_0_2939]) ).
cnf(refute_0_2941,plain,
multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) = multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))),
introduced(tautology,[refl,[$fot(multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))))]]) ).
cnf(refute_0_2942,plain,
( multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) != multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))
| least_upper_bound(X_84,least_upper_bound(X_83,X_83)) != least_upper_bound(X_84,X_83)
| multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) = multiply(X_82,least_upper_bound(X_84,X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))),multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))) ),[1,1],$fot(least_upper_bound(X_84,X_83))]]) ).
cnf(refute_0_2943,plain,
( least_upper_bound(X_84,least_upper_bound(X_83,X_83)) != least_upper_bound(X_84,X_83)
| multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) = multiply(X_82,least_upper_bound(X_84,X_83)) ),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))),multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))) )],[refute_0_2941,refute_0_2942]) ).
cnf(refute_0_2944,plain,
multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) = multiply(X_82,least_upper_bound(X_84,X_83)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,least_upper_bound(X_83,X_83)),least_upper_bound(X_84,X_83)) )],[refute_0_2940,refute_0_2943]) ).
cnf(refute_0_2945,plain,
least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83))) = multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))),
inference(subst,[],[refute_0_286:[bind(X,$fot(X_82)),bind(Y,$fot(X_84)),bind(Z,$fot(least_upper_bound(X_83,X_83)))]]) ).
cnf(refute_0_2946,plain,
least_upper_bound(X,least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X)),
inference(subst,[],[refute_0_680:[bind(X_20,$fot(multiply(X_82,X_83))),bind(X_21,$fot(multiply(X_82,X_84)))]]) ).
cnf(refute_0_2947,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X))
| least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)) != multiply(X_82,least_upper_bound(X_83,X_84))
| least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))) = least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X))) ),[0,1],$fot(multiply(X_82,least_upper_bound(X_83,X_84)))]]) ).
cnf(refute_0_2948,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X))
| least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))) = least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84)),multiply(X_82,least_upper_bound(X_83,X_84))) )],[refute_0_2932,refute_0_2947]) ).
cnf(refute_0_2949,plain,
least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))) = least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X))) )],[refute_0_2946,refute_0_2948]) ).
cnf(refute_0_2950,plain,
( least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))) != least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X)) = least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))))),bind(Y0,$fot(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X))))]]) ).
cnf(refute_0_2951,plain,
least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X)) = least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X_82,least_upper_bound(X_83,X_84))),least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_84),X))) )],[refute_0_2949,refute_0_2950]) ).
cnf(refute_0_2952,plain,
least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83))),
inference(subst,[],[refute_0_2951:[bind(X,$fot(multiply(X_82,X_84))),bind(X_84,$fot(X_83))]]) ).
cnf(refute_0_2953,plain,
( least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83)))
| least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83))) != multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))))),bind(Y0,$fot(least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83))))),bind(Z0,$fot(multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))))]]) ).
cnf(refute_0_2954,plain,
( least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83))) != multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83)))) )],[refute_0_2952,refute_0_2953]) ).
cnf(refute_0_2955,plain,
least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_84),multiply(X_82,least_upper_bound(X_83,X_83))),multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))) )],[refute_0_2945,refute_0_2954]) ).
cnf(refute_0_2956,plain,
( multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) != multiply(X_82,least_upper_bound(X_84,X_83))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_84,X_83)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))))),bind(Y0,$fot(multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))))),bind(Z0,$fot(multiply(X_82,least_upper_bound(X_84,X_83))))]]) ).
cnf(refute_0_2957,plain,
( multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))) != multiply(X_82,least_upper_bound(X_84,X_83))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_84,X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83)))) )],[refute_0_2955,refute_0_2956]) ).
cnf(refute_0_2958,plain,
least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) = multiply(X_82,least_upper_bound(X_84,X_83)),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_84,least_upper_bound(X_83,X_83))),multiply(X_82,least_upper_bound(X_84,X_83))) )],[refute_0_2944,refute_0_2957]) ).
cnf(refute_0_2959,plain,
( least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != multiply(X_82,least_upper_bound(X_83,X_84))
| least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != multiply(X_82,least_upper_bound(X_84,X_83))
| multiply(X_82,least_upper_bound(X_84,X_83)) = multiply(X_82,least_upper_bound(X_83,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),multiply(X_82,least_upper_bound(X_83,X_84))) ),[0],$fot(multiply(X_82,least_upper_bound(X_84,X_83)))]]) ).
cnf(refute_0_2960,plain,
( least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))) != multiply(X_82,least_upper_bound(X_83,X_84))
| multiply(X_82,least_upper_bound(X_84,X_83)) = multiply(X_82,least_upper_bound(X_83,X_84)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),multiply(X_82,least_upper_bound(X_84,X_83))) )],[refute_0_2958,refute_0_2959]) ).
cnf(refute_0_2961,plain,
multiply(X_82,least_upper_bound(X_84,X_83)) = multiply(X_82,least_upper_bound(X_83,X_84)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),least_upper_bound(multiply(X_82,X_83),multiply(X_82,X_84))),multiply(X_82,least_upper_bound(X_83,X_84))) )],[refute_0_2935,refute_0_2960]) ).
cnf(refute_0_2962,plain,
( multiply(X_82,least_upper_bound(X_84,X_83)) != multiply(X_82,least_upper_bound(X_83,X_84))
| multiply(X_82,least_upper_bound(X_83,X_84)) = multiply(X_82,least_upper_bound(X_84,X_83)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_82,least_upper_bound(X_84,X_83)))),bind(Y0,$fot(multiply(X_82,least_upper_bound(X_83,X_84))))]]) ).
cnf(refute_0_2963,plain,
multiply(X_82,least_upper_bound(X_83,X_84)) = multiply(X_82,least_upper_bound(X_84,X_83)),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_84,X_83)),multiply(X_82,least_upper_bound(X_83,X_84))) )],[refute_0_2961,refute_0_2962]) ).
cnf(refute_0_2964,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))),
inference(subst,[],[refute_0_2963:[bind(X_82,$fot(inverse(X_84))),bind(X_83,$fot(least_upper_bound(identity,X_84)))]]) ).
cnf(refute_0_2965,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))) != multiply(inverse(X_84),least_upper_bound(X_84,identity))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) != multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,identity)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)))),bind(Y0,$fot(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))))),bind(Z0,$fot(multiply(inverse(X_84),least_upper_bound(X_84,identity))))]]) ).
cnf(refute_0_2966,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))) != multiply(inverse(X_84),least_upper_bound(X_84,identity))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)),multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84)))) )],[refute_0_2964,refute_0_2965]) ).
cnf(refute_0_2967,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(identity,X_84))),multiply(inverse(X_84),least_upper_bound(X_84,identity))) )],[refute_0_2928,refute_0_2966]) ).
cnf(refute_0_2968,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) != multiply(inverse(X_84),least_upper_bound(X_84,identity))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))
| multiply(inverse(X_84),least_upper_bound(X_84,identity)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))) ),[0],$fot(multiply(inverse(X_84),least_upper_bound(X_84,identity)))]]) ).
cnf(refute_0_2969,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))
| multiply(inverse(X_84),least_upper_bound(X_84,identity)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)),multiply(inverse(X_84),least_upper_bound(X_84,identity))) )],[refute_0_2967,refute_0_2968]) ).
cnf(refute_0_2970,plain,
least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))) = least_upper_bound(identity,inverse(X_84)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(inverse(X_84))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_2971,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,identity)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))
| least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))) != least_upper_bound(identity,inverse(X_84))
| multiply(inverse(X_84),least_upper_bound(X_84,identity)) = least_upper_bound(identity,inverse(X_84)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_84),least_upper_bound(X_84,identity)),least_upper_bound(identity,inverse(X_84))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))))]]) ).
cnf(refute_0_2972,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,identity)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))
| multiply(inverse(X_84),least_upper_bound(X_84,identity)) = least_upper_bound(identity,inverse(X_84)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,inverse(X_84))),least_upper_bound(identity,inverse(X_84))) )],[refute_0_2970,refute_0_2971]) ).
cnf(refute_0_2973,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))
| multiply(inverse(X_84),least_upper_bound(X_84,identity)) = least_upper_bound(identity,inverse(X_84)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,identity)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))) )],[refute_0_2969,refute_0_2972]) ).
cnf(refute_0_2974,plain,
multiply(inverse(X_84),least_upper_bound(X_84,identity)) = least_upper_bound(identity,inverse(X_84)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(identity,X_84),X_84)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_84)))) )],[refute_0_2923,refute_0_2973]) ).
cnf(refute_0_2975,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,identity)) != least_upper_bound(identity,inverse(X_84))
| multiply(least_upper_bound(X_84,identity),inverse(multiply(inverse(X_84),least_upper_bound(X_84,identity)))) != inverse(inverse(X_84))
| multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) = inverse(inverse(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),inverse(multiply(inverse(X_84),least_upper_bound(X_84,identity)))),inverse(inverse(X_84))) ),[0,1,0],$fot(least_upper_bound(identity,inverse(X_84)))]]) ).
cnf(refute_0_2976,plain,
( multiply(least_upper_bound(X_84,identity),inverse(multiply(inverse(X_84),least_upper_bound(X_84,identity)))) != inverse(inverse(X_84))
| multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) = inverse(inverse(X_84)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,identity)),least_upper_bound(identity,inverse(X_84))) )],[refute_0_2974,refute_0_2975]) ).
cnf(refute_0_2977,plain,
multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) = inverse(inverse(X_84)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),inverse(multiply(inverse(X_84),least_upper_bound(X_84,identity)))),inverse(inverse(X_84))) )],[refute_0_2918,refute_0_2976]) ).
cnf(refute_0_2978,plain,
( multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) != inverse(inverse(X_84))
| inverse(inverse(X_84)) != X_84
| multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) = X_84 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))),X_84) ),[0],$fot(inverse(inverse(X_84)))]]) ).
cnf(refute_0_2979,plain,
( multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) != inverse(inverse(X_84))
| multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) = X_84 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_84)),X_84) )],[refute_0_834,refute_0_2978]) ).
cnf(refute_0_2980,plain,
multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))) = X_84,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,identity),inverse(least_upper_bound(identity,inverse(X_84)))),inverse(inverse(X_84))) )],[refute_0_2977,refute_0_2979]) ).
cnf(refute_0_2981,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),
inference(subst,[],[refute_0_2980:[bind(X_84,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))]]) ).
cnf(refute_0_2982,plain,
inverse(inverse(X_103)) = multiply(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),least_upper_bound(X_103,identity)),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(least_upper_bound(X_103,identity))),bind(X_69,$fot(inverse(X_103)))]]) ).
cnf(refute_0_2983,plain,
( multiply(least_upper_bound(X_103,identity),inverse(X_103)) != least_upper_bound(identity,inverse(X_103))
| inverse(inverse(X_103)) != multiply(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),least_upper_bound(X_103,identity))
| inverse(inverse(X_103)) = multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_103)),multiply(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),least_upper_bound(X_103,identity))) ),[1,0,0],$fot(least_upper_bound(identity,inverse(X_103)))]]) ).
cnf(refute_0_2984,plain,
( inverse(inverse(X_103)) != multiply(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),least_upper_bound(X_103,identity))
| inverse(inverse(X_103)) = multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_103,identity),inverse(X_103)),least_upper_bound(identity,inverse(X_103))) )],[refute_0_381,refute_0_2983]) ).
cnf(refute_0_2985,plain,
inverse(inverse(X_103)) = multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_103)),multiply(inverse(multiply(least_upper_bound(X_103,identity),inverse(X_103))),least_upper_bound(X_103,identity))) )],[refute_0_2982,refute_0_2984]) ).
cnf(refute_0_2986,plain,
inverse(inverse(X_103)) = X_103,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_103))]]) ).
cnf(refute_0_2987,plain,
( inverse(inverse(X_103)) != X_103
| inverse(inverse(X_103)) != multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))
| X_103 = multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_103)),multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))) ),[0],$fot(X_103)]]) ).
cnf(refute_0_2988,plain,
( inverse(inverse(X_103)) != multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))
| X_103 = multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_103)),X_103) )],[refute_0_2986,refute_0_2987]) ).
cnf(refute_0_2989,plain,
X_103 = multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_103)),multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))) )],[refute_0_2985,refute_0_2988]) ).
cnf(refute_0_2990,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)),
inference(subst,[],[refute_0_2989:[bind(X_103,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_2991,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),
inference(subst,[],[refute_0_1818:[bind(X_99,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))]]) ).
cnf(refute_0_2992,plain,
least_upper_bound(X_136,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b)))) = least_upper_bound(X_136,b),
inference(subst,[],[refute_0_1229:[bind(X_11,$fot(least_upper_bound(a,c))),bind(X_20,$fot(X_136)),bind(X_21,$fot(b))]]) ).
cnf(refute_0_2993,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b)),
inference(subst,[],[refute_0_1676:[bind(Y,$fot(X_136))]]) ).
cnf(refute_0_2994,plain,
( least_upper_bound(X_136,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b)))) != least_upper_bound(X_136,b)
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))
| least_upper_bound(X_136,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))) = least_upper_bound(X_136,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_136,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b)))),least_upper_bound(X_136,b)) ),[0,1],$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b)))]]) ).
cnf(refute_0_2995,plain,
( least_upper_bound(X_136,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b)))) != least_upper_bound(X_136,b)
| least_upper_bound(X_136,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))) = least_upper_bound(X_136,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))) )],[refute_0_2993,refute_0_2994]) ).
cnf(refute_0_2996,plain,
least_upper_bound(X_136,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b))) = least_upper_bound(X_136,b),
inference(resolve,[$cnf( $equal(least_upper_bound(X_136,least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_136,b)))),least_upper_bound(X_136,b)) )],[refute_0_2992,refute_0_2995]) ).
cnf(refute_0_2997,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) = least_upper_bound(identity,b),
inference(subst,[],[refute_0_2996:[bind(X_136,$fot(identity))]]) ).
cnf(refute_0_2998,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) != least_upper_bound(identity,b)
| multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))) ),[0,0],$fot(least_upper_bound(identity,b))]]) ).
cnf(refute_0_2999,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),least_upper_bound(identity,b)) )],[refute_0_2997,refute_0_2998]) ).
cnf(refute_0_3000,plain,
multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))) )],[refute_0_2991,refute_0_2999]) ).
cnf(refute_0_3001,plain,
multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118)))),
inference(subst,[],[refute_0_1893:[bind(X_172,$fot(X_176)),bind(X_173,$fot(least_upper_bound(identity,X_118)))]]) ).
cnf(refute_0_3002,plain,
inverse(least_upper_bound(X_118,identity)) = multiply(inverse(multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))),inverse(least_upper_bound(identity,inverse(X_118)))),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(least_upper_bound(identity,inverse(X_118))))),bind(X_69,$fot(least_upper_bound(X_118,identity)))]]) ).
cnf(refute_0_3003,plain,
X_118 = multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity)),
inference(subst,[],[refute_0_2989:[bind(X_103,$fot(X_118))]]) ).
cnf(refute_0_3004,plain,
( X_118 != multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity)) = X_118 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_118)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))))]]) ).
cnf(refute_0_3005,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity)) = X_118,
inference(resolve,[$cnf( $equal(X_118,multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))) )],[refute_0_3003,refute_0_3004]) ).
cnf(refute_0_3006,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity)) != X_118
| inverse(least_upper_bound(X_118,identity)) != multiply(inverse(multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))),inverse(least_upper_bound(identity,inverse(X_118))))
| inverse(least_upper_bound(X_118,identity)) = multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_118,identity)),multiply(inverse(multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))),inverse(least_upper_bound(identity,inverse(X_118))))) ),[1,0,0],$fot(X_118)]]) ).
cnf(refute_0_3007,plain,
( inverse(least_upper_bound(X_118,identity)) != multiply(inverse(multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))),inverse(least_upper_bound(identity,inverse(X_118))))
| inverse(least_upper_bound(X_118,identity)) = multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity)),X_118) )],[refute_0_3005,refute_0_3006]) ).
cnf(refute_0_3008,plain,
inverse(least_upper_bound(X_118,identity)) = multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_118,identity)),multiply(inverse(multiply(inverse(least_upper_bound(identity,inverse(X_118))),least_upper_bound(X_118,identity))),inverse(least_upper_bound(identity,inverse(X_118))))) )],[refute_0_3002,refute_0_3007]) ).
cnf(refute_0_3009,plain,
inverse(inverse(X_118)) = X_118,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_118))]]) ).
cnf(refute_0_3010,plain,
least_upper_bound(identity,inverse(inverse(X_118))) = least_upper_bound(identity,inverse(inverse(X_118))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(inverse(X_118))))]]) ).
cnf(refute_0_3011,plain,
( inverse(inverse(X_118)) != X_118
| least_upper_bound(identity,inverse(inverse(X_118))) != least_upper_bound(identity,inverse(inverse(X_118)))
| least_upper_bound(identity,inverse(inverse(X_118))) = least_upper_bound(identity,X_118) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_118))),least_upper_bound(identity,inverse(inverse(X_118)))) ),[1,1],$fot(X_118)]]) ).
cnf(refute_0_3012,plain,
( inverse(inverse(X_118)) != X_118
| least_upper_bound(identity,inverse(inverse(X_118))) = least_upper_bound(identity,X_118) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_118))),least_upper_bound(identity,inverse(inverse(X_118)))) )],[refute_0_3010,refute_0_3011]) ).
cnf(refute_0_3013,plain,
least_upper_bound(identity,inverse(inverse(X_118))) = least_upper_bound(identity,X_118),
inference(resolve,[$cnf( $equal(inverse(inverse(X_118)),X_118) )],[refute_0_3009,refute_0_3012]) ).
cnf(refute_0_3014,plain,
multiply(identity,least_upper_bound(identity,inverse(inverse(X_118)))) = least_upper_bound(identity,inverse(inverse(X_118))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(inverse(X_118)))))]]) ).
cnf(refute_0_3015,plain,
multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)) = multiply(identity,least_upper_bound(identity,inverse(inverse(X_118)))),
inference(subst,[],[refute_0_320:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(inverse(X_118))))]]) ).
cnf(refute_0_3016,plain,
( multiply(identity,least_upper_bound(identity,inverse(inverse(X_118)))) != least_upper_bound(identity,inverse(inverse(X_118)))
| multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)) != multiply(identity,least_upper_bound(identity,inverse(inverse(X_118))))
| multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)) = least_upper_bound(identity,inverse(inverse(X_118))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(inverse(X_118)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(inverse(X_118)))))]]) ).
cnf(refute_0_3017,plain,
( multiply(identity,least_upper_bound(identity,inverse(inverse(X_118)))) != least_upper_bound(identity,inverse(inverse(X_118)))
| multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)) = least_upper_bound(identity,inverse(inverse(X_118))) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)),multiply(identity,least_upper_bound(identity,inverse(inverse(X_118))))) )],[refute_0_3015,refute_0_3016]) ).
cnf(refute_0_3018,plain,
multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)) = least_upper_bound(identity,inverse(inverse(X_118))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(inverse(X_118)))),least_upper_bound(identity,inverse(inverse(X_118)))) )],[refute_0_3014,refute_0_3017]) ).
cnf(refute_0_3019,plain,
least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) = multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)),
inference(subst,[],[refute_0_337:[bind(X_82,$fot(identity)),bind(X_83,$fot(inverse(inverse(X_118))))]]) ).
cnf(refute_0_3020,plain,
( multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)) != least_upper_bound(identity,inverse(inverse(X_118)))
| least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) != multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity))
| least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) = least_upper_bound(identity,inverse(inverse(X_118))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)))),bind(Z0,$fot(least_upper_bound(identity,inverse(inverse(X_118)))))]]) ).
cnf(refute_0_3021,plain,
( multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)) != least_upper_bound(identity,inverse(inverse(X_118)))
| least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) = least_upper_bound(identity,inverse(inverse(X_118))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))),multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity))) )],[refute_0_3019,refute_0_3020]) ).
cnf(refute_0_3022,plain,
least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) = least_upper_bound(identity,inverse(inverse(X_118))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(inverse(X_118)),identity)),least_upper_bound(identity,inverse(inverse(X_118)))) )],[refute_0_3018,refute_0_3021]) ).
cnf(refute_0_3023,plain,
( least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) != least_upper_bound(identity,inverse(inverse(X_118)))
| least_upper_bound(identity,inverse(inverse(X_118))) != least_upper_bound(identity,X_118)
| least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) = least_upper_bound(identity,X_118) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(inverse(X_118))))),bind(Z0,$fot(least_upper_bound(identity,X_118)))]]) ).
cnf(refute_0_3024,plain,
( least_upper_bound(identity,inverse(inverse(X_118))) != least_upper_bound(identity,X_118)
| least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) = least_upper_bound(identity,X_118) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))),least_upper_bound(identity,inverse(inverse(X_118)))) )],[refute_0_3022,refute_0_3023]) ).
cnf(refute_0_3025,plain,
least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) = least_upper_bound(identity,X_118),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_118))),least_upper_bound(identity,X_118)) )],[refute_0_3013,refute_0_3024]) ).
cnf(refute_0_3026,plain,
inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))) = inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))))]]) ).
cnf(refute_0_3027,plain,
( inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))) != inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))))
| least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) != least_upper_bound(identity,X_118)
| inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))) = inverse(least_upper_bound(identity,X_118)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))),inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))))) ),[1,0],$fot(least_upper_bound(identity,X_118))]]) ).
cnf(refute_0_3028,plain,
( least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))) != least_upper_bound(identity,X_118)
| inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))) = inverse(least_upper_bound(identity,X_118)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))),inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))))) )],[refute_0_3026,refute_0_3027]) ).
cnf(refute_0_3029,plain,
inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))) = inverse(least_upper_bound(identity,X_118)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))),least_upper_bound(identity,X_118)) )],[refute_0_3025,refute_0_3028]) ).
cnf(refute_0_3030,plain,
inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) = multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(least_upper_bound(X_98,X_99))),bind(X_46,$fot(inverse(X_99)))]]) ).
cnf(refute_0_3031,plain,
( multiply(least_upper_bound(X_98,X_99),inverse(X_99)) != least_upper_bound(identity,multiply(X_98,inverse(X_99)))
| inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) != multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))
| inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) = multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))),multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))) ),[0,0],$fot(least_upper_bound(identity,multiply(X_98,inverse(X_99))))]]) ).
cnf(refute_0_3032,plain,
( inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) != multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))
| inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) = multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_98,X_99),inverse(X_99)),least_upper_bound(identity,multiply(X_98,inverse(X_99)))) )],[refute_0_436,refute_0_3031]) ).
cnf(refute_0_3033,plain,
inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) = multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))),multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))) )],[refute_0_3030,refute_0_3032]) ).
cnf(refute_0_3034,plain,
multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) = inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(least_upper_bound(X_98,X_99))),bind(X_46,$fot(inverse(X_99)))]]) ).
cnf(refute_0_3035,plain,
( multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) != inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))
| inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) != multiply(X_99,inverse(least_upper_bound(X_98,X_99)))
| multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) = multiply(X_99,inverse(least_upper_bound(X_98,X_99))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))))),bind(Z0,$fot(multiply(X_99,inverse(least_upper_bound(X_98,X_99)))))]]) ).
cnf(refute_0_3036,plain,
( inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))) != multiply(X_99,inverse(least_upper_bound(X_98,X_99)))
| multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) = multiply(X_99,inverse(least_upper_bound(X_98,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))),inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))) )],[refute_0_3034,refute_0_3035]) ).
cnf(refute_0_3037,plain,
multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) = multiply(X_99,inverse(least_upper_bound(X_98,X_99))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_98,X_99),inverse(X_99))),multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) )],[refute_0_442,refute_0_3036]) ).
cnf(refute_0_3038,plain,
( multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))) != multiply(X_99,inverse(least_upper_bound(X_98,X_99)))
| inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) != multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))
| inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_98,X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))),multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))) ),[1],$fot(multiply(X_99,inverse(least_upper_bound(X_98,X_99))))]]) ).
cnf(refute_0_3039,plain,
( inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) != multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))
| inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_98,X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99))),multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) )],[refute_0_3037,refute_0_3038]) ).
cnf(refute_0_3040,plain,
inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) = multiply(X_99,inverse(least_upper_bound(X_98,X_99))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))),multiply(inverse(inverse(X_99)),inverse(least_upper_bound(X_98,X_99)))) )],[refute_0_3033,refute_0_3039]) ).
cnf(refute_0_3041,plain,
( inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) != multiply(X_99,inverse(least_upper_bound(X_98,X_99)))
| multiply(X_99,inverse(least_upper_bound(X_98,X_99))) = inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))))),bind(Y0,$fot(multiply(X_99,inverse(least_upper_bound(X_98,X_99)))))]]) ).
cnf(refute_0_3042,plain,
multiply(X_99,inverse(least_upper_bound(X_98,X_99))) = inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_98,inverse(X_99)))),multiply(X_99,inverse(least_upper_bound(X_98,X_99)))) )],[refute_0_3040,refute_0_3041]) ).
cnf(refute_0_3043,plain,
multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) = inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))),
inference(subst,[],[refute_0_3042:[bind(X_98,$fot(identity)),bind(X_99,$fot(inverse(X_118)))]]) ).
cnf(refute_0_3044,plain,
( multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) != inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))))
| inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))) != inverse(least_upper_bound(identity,X_118))
| multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) = inverse(least_upper_bound(identity,X_118)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_118))))]]) ).
cnf(refute_0_3045,plain,
( inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))) != inverse(least_upper_bound(identity,X_118))
| multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) = inverse(least_upper_bound(identity,X_118)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))),inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118)))))) )],[refute_0_3043,refute_0_3044]) ).
cnf(refute_0_3046,plain,
multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) = inverse(least_upper_bound(identity,X_118)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(identity,inverse(inverse(X_118))))),inverse(least_upper_bound(identity,X_118))) )],[refute_0_3029,refute_0_3045]) ).
cnf(refute_0_3047,plain,
( multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))) != inverse(least_upper_bound(identity,X_118))
| inverse(least_upper_bound(X_118,identity)) != multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118))))
| inverse(least_upper_bound(X_118,identity)) = inverse(least_upper_bound(identity,X_118)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_118,identity)),multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118))))) ),[1],$fot(inverse(least_upper_bound(identity,X_118)))]]) ).
cnf(refute_0_3048,plain,
( inverse(least_upper_bound(X_118,identity)) != multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118))))
| inverse(least_upper_bound(X_118,identity)) = inverse(least_upper_bound(identity,X_118)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118)))),inverse(least_upper_bound(identity,X_118))) )],[refute_0_3046,refute_0_3047]) ).
cnf(refute_0_3049,plain,
inverse(least_upper_bound(X_118,identity)) = inverse(least_upper_bound(identity,X_118)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_118,identity)),multiply(inverse(X_118),inverse(least_upper_bound(identity,inverse(X_118))))) )],[refute_0_3008,refute_0_3048]) ).
cnf(refute_0_3050,plain,
( inverse(least_upper_bound(X_118,identity)) != inverse(least_upper_bound(identity,X_118))
| inverse(least_upper_bound(identity,X_118)) = inverse(least_upper_bound(X_118,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_118,identity)))),bind(Y0,$fot(inverse(least_upper_bound(identity,X_118))))]]) ).
cnf(refute_0_3051,plain,
inverse(least_upper_bound(identity,X_118)) = inverse(least_upper_bound(X_118,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_118,identity)),inverse(least_upper_bound(identity,X_118))) )],[refute_0_3049,refute_0_3050]) ).
cnf(refute_0_3052,plain,
( multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118))))
| inverse(least_upper_bound(identity,X_118)) != inverse(least_upper_bound(X_118,identity))
| multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118))))) ),[1,1,1],$fot(inverse(least_upper_bound(X_118,identity)))]]) ).
cnf(refute_0_3053,plain,
( multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118))))
| multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_118)),inverse(least_upper_bound(X_118,identity))) )],[refute_0_3051,refute_0_3052]) ).
cnf(refute_0_3054,plain,
multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118))))) )],[refute_0_3001,refute_0_3053]) ).
cnf(refute_0_3055,plain,
( multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity))))
| multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118))))
| greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118)))) = greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity))))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118)))))]]) ).
cnf(refute_0_3056,plain,
( multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity))))
| greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118)))) = greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118))))) )],[refute_0_3001,refute_0_3055]) ).
cnf(refute_0_3057,plain,
greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(identity,X_118)))) = greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_176,least_upper_bound(identity,X_118)),inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,multiply(X_176,inverse(least_upper_bound(X_118,identity))))) )],[refute_0_3054,refute_0_3056]) ).
cnf(refute_0_3058,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))) = greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),
inference(subst,[],[refute_0_3057:[bind(X_118,$fot(b)),bind(X_176,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_3059,plain,
inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))))]]) ).
cnf(refute_0_3060,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))) != greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3061,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))) != greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))))) )],[refute_0_3059,refute_0_3060]) ).
cnf(refute_0_3062,plain,
inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) )],[refute_0_3058,refute_0_3061]) ).
cnf(refute_0_3063,plain,
inverse(greatest_lower_bound(X_166,identity)) = multiply(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),inverse(X_166)),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(X_166))),bind(X_69,$fot(greatest_lower_bound(X_166,identity)))]]) ).
cnf(refute_0_3064,plain,
multiply(inverse(X_166),greatest_lower_bound(X_166,identity)) = greatest_lower_bound(identity,inverse(X_166)),
inference(subst,[],[refute_0_794:[bind(X_157,$fot(X_166))]]) ).
cnf(refute_0_3065,plain,
( multiply(inverse(X_166),greatest_lower_bound(X_166,identity)) != greatest_lower_bound(identity,inverse(X_166))
| inverse(greatest_lower_bound(X_166,identity)) != multiply(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),inverse(X_166))
| inverse(greatest_lower_bound(X_166,identity)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_166,identity)),multiply(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),inverse(X_166))) ),[1,0,0],$fot(greatest_lower_bound(identity,inverse(X_166)))]]) ).
cnf(refute_0_3066,plain,
( inverse(greatest_lower_bound(X_166,identity)) != multiply(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),inverse(X_166))
| inverse(greatest_lower_bound(X_166,identity)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_166),greatest_lower_bound(X_166,identity)),greatest_lower_bound(identity,inverse(X_166))) )],[refute_0_3064,refute_0_3065]) ).
cnf(refute_0_3067,plain,
inverse(greatest_lower_bound(X_166,identity)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_166,identity)),multiply(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),inverse(X_166))) )],[refute_0_3063,refute_0_3066]) ).
cnf(refute_0_3068,plain,
inverse(inverse(X_166)) = X_166,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_166))]]) ).
cnf(refute_0_3069,plain,
greatest_lower_bound(identity,inverse(inverse(X_166))) = greatest_lower_bound(identity,inverse(inverse(X_166))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X_166))))]]) ).
cnf(refute_0_3070,plain,
( greatest_lower_bound(identity,inverse(inverse(X_166))) != greatest_lower_bound(identity,inverse(inverse(X_166)))
| inverse(inverse(X_166)) != X_166
| greatest_lower_bound(identity,inverse(inverse(X_166))) = greatest_lower_bound(identity,X_166) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_166))),greatest_lower_bound(identity,inverse(inverse(X_166)))) ),[1,1],$fot(X_166)]]) ).
cnf(refute_0_3071,plain,
( inverse(inverse(X_166)) != X_166
| greatest_lower_bound(identity,inverse(inverse(X_166))) = greatest_lower_bound(identity,X_166) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_166))),greatest_lower_bound(identity,inverse(inverse(X_166)))) )],[refute_0_3069,refute_0_3070]) ).
cnf(refute_0_3072,plain,
greatest_lower_bound(identity,inverse(inverse(X_166))) = greatest_lower_bound(identity,X_166),
inference(resolve,[$cnf( $equal(inverse(inverse(X_166)),X_166) )],[refute_0_3068,refute_0_3071]) ).
cnf(refute_0_3073,plain,
inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))) = inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))))]]) ).
cnf(refute_0_3074,plain,
( greatest_lower_bound(identity,inverse(inverse(X_166))) != greatest_lower_bound(identity,X_166)
| inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))) != inverse(greatest_lower_bound(identity,inverse(inverse(X_166))))
| inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))) = inverse(greatest_lower_bound(identity,X_166)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))),inverse(greatest_lower_bound(identity,inverse(inverse(X_166))))) ),[1,0],$fot(greatest_lower_bound(identity,X_166))]]) ).
cnf(refute_0_3075,plain,
( greatest_lower_bound(identity,inverse(inverse(X_166))) != greatest_lower_bound(identity,X_166)
| inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))) = inverse(greatest_lower_bound(identity,X_166)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))),inverse(greatest_lower_bound(identity,inverse(inverse(X_166))))) )],[refute_0_3073,refute_0_3074]) ).
cnf(refute_0_3076,plain,
inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))) = inverse(greatest_lower_bound(identity,X_166)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_166))),greatest_lower_bound(identity,X_166)) )],[refute_0_3072,refute_0_3075]) ).
cnf(refute_0_3077,plain,
inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(inverse(X_164))),bind(X_46,$fot(greatest_lower_bound(identity,X_164)))]]) ).
cnf(refute_0_3078,plain,
multiply(inverse(X_164),greatest_lower_bound(identity,X_164)) = greatest_lower_bound(identity,inverse(X_164)),
inference(subst,[],[refute_0_2806:[bind(X_163,$fot(X_164))]]) ).
cnf(refute_0_3079,plain,
( multiply(inverse(X_164),greatest_lower_bound(identity,X_164)) != greatest_lower_bound(identity,inverse(X_164))
| inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))
| inverse(greatest_lower_bound(identity,inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))),multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_164)))]]) ).
cnf(refute_0_3080,plain,
( inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))
| inverse(greatest_lower_bound(identity,inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_164),greatest_lower_bound(identity,X_164)),greatest_lower_bound(identity,inverse(X_164))) )],[refute_0_3078,refute_0_3079]) ).
cnf(refute_0_3081,plain,
inverse(greatest_lower_bound(identity,inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))),multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))) )],[refute_0_3077,refute_0_3080]) ).
cnf(refute_0_3082,plain,
inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),X_164),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(X_164)),bind(X_74,$fot(greatest_lower_bound(identity,X_164)))]]) ).
cnf(refute_0_3083,plain,
multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) = inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(inverse(X_164))),bind(X_46,$fot(greatest_lower_bound(identity,X_164)))]]) ).
cnf(refute_0_3084,plain,
( multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) != inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164)))
| inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)
| multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),X_164) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))))),bind(Y0,$fot(inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)))]]) ).
cnf(refute_0_3085,plain,
( inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)
| multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),X_164) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))),inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164)))) )],[refute_0_3083,refute_0_3084]) ).
cnf(refute_0_3086,plain,
multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),X_164),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_164),greatest_lower_bound(identity,X_164))),multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)) )],[refute_0_3082,refute_0_3085]) ).
cnf(refute_0_3087,plain,
( multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)
| inverse(greatest_lower_bound(identity,inverse(X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))
| inverse(greatest_lower_bound(identity,inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),X_164) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_164))),multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(identity,X_164)),X_164))]]) ).
cnf(refute_0_3088,plain,
( inverse(greatest_lower_bound(identity,inverse(X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))
| inverse(greatest_lower_bound(identity,inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),X_164) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164))),multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)) )],[refute_0_3086,refute_0_3087]) ).
cnf(refute_0_3089,plain,
inverse(greatest_lower_bound(identity,inverse(X_164))) = multiply(inverse(greatest_lower_bound(identity,X_164)),X_164),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_164))),multiply(inverse(greatest_lower_bound(identity,X_164)),inverse(inverse(X_164)))) )],[refute_0_3081,refute_0_3088]) ).
cnf(refute_0_3090,plain,
( inverse(greatest_lower_bound(identity,inverse(X_164))) != multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)
| multiply(inverse(greatest_lower_bound(identity,X_164)),X_164) = inverse(greatest_lower_bound(identity,inverse(X_164))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_164))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)))]]) ).
cnf(refute_0_3091,plain,
multiply(inverse(greatest_lower_bound(identity,X_164)),X_164) = inverse(greatest_lower_bound(identity,inverse(X_164))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_164))),multiply(inverse(greatest_lower_bound(identity,X_164)),X_164)) )],[refute_0_3089,refute_0_3090]) ).
cnf(refute_0_3092,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) = inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))),
inference(subst,[],[refute_0_3091:[bind(X_164,$fot(inverse(X_166)))]]) ).
cnf(refute_0_3093,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) != inverse(greatest_lower_bound(identity,inverse(inverse(X_166))))
| inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))) != inverse(greatest_lower_bound(identity,X_166))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) = inverse(greatest_lower_bound(identity,X_166)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_166))))]]) ).
cnf(refute_0_3094,plain,
( inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))) != inverse(greatest_lower_bound(identity,X_166))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) = inverse(greatest_lower_bound(identity,X_166)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)),inverse(greatest_lower_bound(identity,inverse(inverse(X_166))))) )],[refute_0_3092,refute_0_3093]) ).
cnf(refute_0_3095,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) = inverse(greatest_lower_bound(identity,X_166)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X_166)))),inverse(greatest_lower_bound(identity,X_166))) )],[refute_0_3076,refute_0_3094]) ).
cnf(refute_0_3096,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)) != inverse(greatest_lower_bound(identity,X_166))
| inverse(greatest_lower_bound(X_166,identity)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166))
| inverse(greatest_lower_bound(X_166,identity)) = inverse(greatest_lower_bound(identity,X_166)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_166,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166))) ),[1],$fot(inverse(greatest_lower_bound(identity,X_166)))]]) ).
cnf(refute_0_3097,plain,
( inverse(greatest_lower_bound(X_166,identity)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166))
| inverse(greatest_lower_bound(X_166,identity)) = inverse(greatest_lower_bound(identity,X_166)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166)),inverse(greatest_lower_bound(identity,X_166))) )],[refute_0_3095,refute_0_3096]) ).
cnf(refute_0_3098,plain,
inverse(greatest_lower_bound(X_166,identity)) = inverse(greatest_lower_bound(identity,X_166)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_166,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_166))),inverse(X_166))) )],[refute_0_3067,refute_0_3097]) ).
cnf(refute_0_3099,plain,
inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) = inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),
inference(subst,[],[refute_0_3098:[bind(X_166,$fot(multiply(X_172,inverse(X_173))))]]) ).
cnf(refute_0_3100,plain,
( multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) != greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))
| greatest_lower_bound(identity,multiply(X_172,inverse(X_173))) = multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))]]) ).
cnf(refute_0_3101,plain,
greatest_lower_bound(identity,multiply(X_172,inverse(X_173))) = multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)),greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) )],[refute_0_1893,refute_0_3100]) ).
cnf(refute_0_3102,plain,
( greatest_lower_bound(identity,multiply(X_172,inverse(X_173))) != multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))
| inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) != inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))
| inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) = inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)),inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) ),[1,0],$fot(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))]]) ).
cnf(refute_0_3103,plain,
( inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) != inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))
| inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) = inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))),multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))) )],[refute_0_3101,refute_0_3102]) ).
cnf(refute_0_3104,plain,
inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) = inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)),inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) )],[refute_0_3099,refute_0_3103]) ).
cnf(refute_0_3105,plain,
( inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) != inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))
| inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) != inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))
| inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)),inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))]]) ).
cnf(refute_0_3106,plain,
( inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) != inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))
| inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)),inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173))))) )],[refute_0_3099,refute_0_3105]) ).
cnf(refute_0_3107,plain,
inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),
inference(subst,[],[refute_0_388:[bind(X_50,$fot(X_173)),bind(X_73,$fot(greatest_lower_bound(X_172,X_173)))]]) ).
cnf(refute_0_3108,plain,
( inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) != inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))
| inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))) ),[1],$fot(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))))]]) ).
cnf(refute_0_3109,plain,
( inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) != inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))
| inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173))),multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) )],[refute_0_3107,refute_0_3108]) ).
cnf(refute_0_3110,plain,
( inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)) != inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))
| inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))) )],[refute_0_3106,refute_0_3109]) ).
cnf(refute_0_3111,plain,
inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) = multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(X_172,inverse(X_173)),identity)),inverse(multiply(greatest_lower_bound(X_172,X_173),inverse(X_173)))) )],[refute_0_3104,refute_0_3110]) ).
cnf(refute_0_3112,plain,
( inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) != multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))
| multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))))),bind(Y0,$fot(multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))))]]) ).
cnf(refute_0_3113,plain,
multiply(X_173,inverse(greatest_lower_bound(X_172,X_173))) = inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_172,inverse(X_173)))),multiply(X_173,inverse(greatest_lower_bound(X_172,X_173)))) )],[refute_0_3111,refute_0_3112]) ).
cnf(refute_0_3114,plain,
multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))),
inference(subst,[],[refute_0_3113:[bind(X_172,$fot(least_upper_bound(a,c))),bind(X_173,$fot(least_upper_bound(identity,b)))]]) ).
cnf(refute_0_3115,plain,
( multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3116,plain,
( inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b)))))) )],[refute_0_3114,refute_0_3115]) ).
cnf(refute_0_3117,plain,
multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(identity,b))))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3062,refute_0_3116]) ).
cnf(refute_0_3118,plain,
( multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3119,plain,
( multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3117,refute_0_3118]) ).
cnf(refute_0_3120,plain,
least_upper_bound(X_123,b) = least_upper_bound(b,X_123),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_123)),bind(Y,$fot(b))]]) ).
cnf(refute_0_3121,plain,
( least_upper_bound(X_123,b) != least_upper_bound(b,X_123)
| least_upper_bound(b,X_123) = least_upper_bound(X_123,b) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_123,b))),bind(Y0,$fot(least_upper_bound(b,X_123)))]]) ).
cnf(refute_0_3122,plain,
least_upper_bound(b,X_123) = least_upper_bound(X_123,b),
inference(resolve,[$cnf( $equal(least_upper_bound(X_123,b),least_upper_bound(b,X_123)) )],[refute_0_3120,refute_0_3121]) ).
cnf(refute_0_3123,plain,
( least_upper_bound(b,X_123) != least_upper_bound(X_123,b)
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) ),[0,1,1],$fot(least_upper_bound(X_123,b))]]) ).
cnf(refute_0_3124,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,X_123),least_upper_bound(X_123,b)) )],[refute_0_3122,refute_0_3123]) ).
cnf(refute_0_3125,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) )],[refute_0_1191,refute_0_3124]) ).
cnf(refute_0_3126,plain,
least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b)),
inference(subst,[],[refute_0_1676:[bind(Y,$fot(X_123))]]) ).
cnf(refute_0_3127,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))
| least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) ),[0],$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b)))]]) ).
cnf(refute_0_3128,plain,
( least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))
| greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))) )],[refute_0_3126,refute_0_3127]) ).
cnf(refute_0_3129,plain,
greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_123,b))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_123))) )],[refute_0_3125,refute_0_3128]) ).
cnf(refute_0_3130,plain,
greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),
inference(subst,[],[refute_0_3129:[bind(X_123,$fot(identity))]]) ).
cnf(refute_0_3131,plain,
inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) = inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))]]) ).
cnf(refute_0_3132,plain,
( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) != inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))
| inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) = inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) ),[1,0],$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))]]) ).
cnf(refute_0_3133,plain,
( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) = inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) )],[refute_0_3131,refute_0_3132]) ).
cnf(refute_0_3134,plain,
inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) = inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) )],[refute_0_3130,refute_0_3133]) ).
cnf(refute_0_3135,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))))]]) ).
cnf(refute_0_3136,plain,
( inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) != inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))) ),[1,1],$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3137,plain,
( inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))) != inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))) )],[refute_0_3135,refute_0_3136]) ).
cnf(refute_0_3138,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) )],[refute_0_3134,refute_0_3137]) ).
cnf(refute_0_3139,plain,
( inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))))]]) ).
cnf(refute_0_3140,plain,
( inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) )],[refute_0_3138,refute_0_3139]) ).
cnf(refute_0_3141,plain,
( multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))) )],[refute_0_3119,refute_0_3140]) ).
cnf(refute_0_3142,plain,
inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,b),inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(identity,b))))) )],[refute_0_3000,refute_0_3141]) ).
cnf(refute_0_3143,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))
| inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) ),[1,0,0,1],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3144,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) )],[refute_0_3142,refute_0_3143]) ).
cnf(refute_0_3145,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) )],[refute_0_2990,refute_0_3144]) ).
cnf(refute_0_3146,plain,
multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3147,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3148,plain,
multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3149,plain,
( multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != identity
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3150,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != identity
| multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) )],[refute_0_3148,refute_0_3149]) ).
cnf(refute_0_3151,plain,
multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity) )],[refute_0_3147,refute_0_3150]) ).
cnf(refute_0_3152,plain,
least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_3153,plain,
inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) = inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3154,plain,
( inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) != inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))
| least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))) ),[1,0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3155,plain,
( least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))) )],[refute_0_3153,refute_0_3154]) ).
cnf(refute_0_3156,plain,
inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) )],[refute_0_3152,refute_0_3155]) ).
cnf(refute_0_3157,plain,
multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3158,plain,
( multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))
| inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) ),[1,0],$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3159,plain,
( inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) )],[refute_0_3157,refute_0_3158]) ).
cnf(refute_0_3160,plain,
multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) )],[refute_0_3156,refute_0_3159]) ).
cnf(refute_0_3161,plain,
( multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity)
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity)))]]) ).
cnf(refute_0_3162,plain,
( multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity)
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) )],[refute_0_3160,refute_0_3161]) ).
cnf(refute_0_3163,plain,
multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity)) )],[refute_0_3151,refute_0_3162]) ).
cnf(refute_0_3164,plain,
( multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity)
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3165,plain,
( multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity)) )],[refute_0_3163,refute_0_3164]) ).
cnf(refute_0_3166,plain,
multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),identity),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) )],[refute_0_3146,refute_0_3165]) ).
cnf(refute_0_3167,plain,
multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),
inference(subst,[],[refute_0_320:[bind(X,$fot(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))))),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3168,plain,
( multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) != multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3169,plain,
( multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)),multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) )],[refute_0_3167,refute_0_3168]) ).
cnf(refute_0_3170,plain,
multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) )],[refute_0_3166,refute_0_3169]) ).
cnf(refute_0_3171,plain,
( multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) ),[1],$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3172,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) )],[refute_0_3170,refute_0_3171]) ).
cnf(refute_0_3173,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) )],[refute_0_3145,refute_0_3172]) ).
cnf(refute_0_3174,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3175,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) )],[refute_0_3173,refute_0_3174]) ).
cnf(refute_0_3176,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) ),[0,1],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3177,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) )],[refute_0_3175,refute_0_3176]) ).
cnf(refute_0_3178,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) )],[refute_0_2981,refute_0_3177]) ).
cnf(refute_0_3179,plain,
least_upper_bound(X_103,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)))),
inference(subst,[],[refute_0_417:[bind(X_46,$fot(least_upper_bound(X_103,identity))),bind(X_95,$fot(inverse(least_upper_bound(identity,inverse(X_103)))))]]) ).
cnf(refute_0_3180,plain,
( X_103 != multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)) = X_103 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_103)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))))]]) ).
cnf(refute_0_3181,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)) = X_103,
inference(resolve,[$cnf( $equal(X_103,multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))) )],[refute_0_2989,refute_0_3180]) ).
cnf(refute_0_3182,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)) != X_103
| least_upper_bound(X_103,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))))
| least_upper_bound(X_103,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_103,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))))) ),[1,1,1],$fot(X_103)]]) ).
cnf(refute_0_3183,plain,
( least_upper_bound(X_103,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))))
| least_upper_bound(X_103,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity)),X_103) )],[refute_0_3181,refute_0_3182]) ).
cnf(refute_0_3184,plain,
least_upper_bound(X_103,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_103,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_103))),least_upper_bound(X_103,identity))))) )],[refute_0_3179,refute_0_3183]) ).
cnf(refute_0_3185,plain,
( inverse(least_upper_bound(X_85,X_86)) != inverse(least_upper_bound(X_86,X_85))
| inverse(least_upper_bound(X_86,X_85)) = inverse(least_upper_bound(X_85,X_86)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_85,X_86)))),bind(Y0,$fot(inverse(least_upper_bound(X_86,X_85))))]]) ).
cnf(refute_0_3186,plain,
inverse(least_upper_bound(X_86,X_85)) = inverse(least_upper_bound(X_85,X_86)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_85,X_86)),inverse(least_upper_bound(X_86,X_85))) )],[refute_0_1787,refute_0_3185]) ).
cnf(refute_0_3187,plain,
inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))) = inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),
inference(subst,[],[refute_0_3186:[bind(X_85,$fot(inverse(least_upper_bound(X_103,identity)))),bind(X_86,$fot(inverse(least_upper_bound(identity,inverse(X_103)))))]]) ).
cnf(refute_0_3188,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)))]]) ).
cnf(refute_0_3189,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103))
| inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))) != inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103))) ),[1,0],$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))))]]) ).
cnf(refute_0_3190,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))) != inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103))) )],[refute_0_3188,refute_0_3189]) ).
cnf(refute_0_3191,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))))) )],[refute_0_3187,refute_0_3190]) ).
cnf(refute_0_3192,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))
| least_upper_bound(X_103,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103))
| least_upper_bound(X_103,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_103,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103))) ),[1],$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)))]]) ).
cnf(refute_0_3193,plain,
( least_upper_bound(X_103,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103))
| least_upper_bound(X_103,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))) )],[refute_0_3191,refute_0_3192]) ).
cnf(refute_0_3194,plain,
least_upper_bound(X_103,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_103,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_103))),inverse(least_upper_bound(X_103,identity)))),least_upper_bound(identity,X_103))) )],[refute_0_3184,refute_0_3193]) ).
cnf(refute_0_3195,plain,
multiply(identity,least_upper_bound(identity,X_103)) = least_upper_bound(identity,X_103),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,X_103)))]]) ).
cnf(refute_0_3196,plain,
multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) = least_upper_bound(inverse(least_upper_bound(X_90,identity)),multiply(X_90,inverse(least_upper_bound(X_90,identity)))),
inference(subst,[],[refute_0_149:[bind(X_89,$fot(inverse(least_upper_bound(X_90,identity))))]]) ).
cnf(refute_0_3197,plain,
inverse(least_upper_bound(identity,inverse(X_90))) = multiply(X_90,inverse(least_upper_bound(X_90,identity))),
inference(subst,[],[refute_0_398:[bind(X_103,$fot(X_90))]]) ).
cnf(refute_0_3198,plain,
( inverse(least_upper_bound(identity,inverse(X_90))) != multiply(X_90,inverse(least_upper_bound(X_90,identity)))
| multiply(X_90,inverse(least_upper_bound(X_90,identity))) = inverse(least_upper_bound(identity,inverse(X_90))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_90))))),bind(Y0,$fot(multiply(X_90,inverse(least_upper_bound(X_90,identity)))))]]) ).
cnf(refute_0_3199,plain,
multiply(X_90,inverse(least_upper_bound(X_90,identity))) = inverse(least_upper_bound(identity,inverse(X_90))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_90))),multiply(X_90,inverse(least_upper_bound(X_90,identity)))) )],[refute_0_3197,refute_0_3198]) ).
cnf(refute_0_3200,plain,
( multiply(X_90,inverse(least_upper_bound(X_90,identity))) != inverse(least_upper_bound(identity,inverse(X_90)))
| multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) != least_upper_bound(inverse(least_upper_bound(X_90,identity)),multiply(X_90,inverse(least_upper_bound(X_90,identity))))
| multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) = least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))),least_upper_bound(inverse(least_upper_bound(X_90,identity)),multiply(X_90,inverse(least_upper_bound(X_90,identity))))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(X_90))))]]) ).
cnf(refute_0_3201,plain,
( multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) != least_upper_bound(inverse(least_upper_bound(X_90,identity)),multiply(X_90,inverse(least_upper_bound(X_90,identity))))
| multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) = least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))) ),
inference(resolve,[$cnf( $equal(multiply(X_90,inverse(least_upper_bound(X_90,identity))),inverse(least_upper_bound(identity,inverse(X_90)))) )],[refute_0_3199,refute_0_3200]) ).
cnf(refute_0_3202,plain,
multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) = least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))),least_upper_bound(inverse(least_upper_bound(X_90,identity)),multiply(X_90,inverse(least_upper_bound(X_90,identity))))) )],[refute_0_3196,refute_0_3201]) ).
cnf(refute_0_3203,plain,
multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(least_upper_bound(X_90,identity)))]]) ).
cnf(refute_0_3204,plain,
( multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) != identity
| multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) != least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90))))
| identity = least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))),least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_3205,plain,
( multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))) != least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90))))
| identity = least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))),identity) )],[refute_0_3203,refute_0_3204]) ).
cnf(refute_0_3206,plain,
identity = least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),inverse(least_upper_bound(X_90,identity))),least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90))))) )],[refute_0_3202,refute_0_3205]) ).
cnf(refute_0_3207,plain,
( identity != least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90))))
| least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90))))))]]) ).
cnf(refute_0_3208,plain,
least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(inverse(least_upper_bound(X_90,identity)),inverse(least_upper_bound(identity,inverse(X_90))))) )],[refute_0_3206,refute_0_3207]) ).
cnf(refute_0_3209,plain,
least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))) = identity,
inference(subst,[],[refute_0_3208:[bind(X_90,$fot(X_103))]]) ).
cnf(refute_0_3210,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) = inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))))]]) ).
cnf(refute_0_3211,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) != inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))))
| least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))) != identity
| inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_3212,plain,
( least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))) != identity
| inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))))) )],[refute_0_3210,refute_0_3211]) ).
cnf(refute_0_3213,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) = inverse(identity),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103)))),identity) )],[refute_0_3209,refute_0_3212]) ).
cnf(refute_0_3214,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) != inverse(identity)
| inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) = identity ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_3215,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) = identity ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),inverse(identity)) )],[refute_0_3213,refute_0_3214]) ).
cnf(refute_0_3216,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_3215]) ).
cnf(refute_0_3217,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)))]]) ).
cnf(refute_0_3218,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))
| inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) != identity
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) = multiply(identity,least_upper_bound(identity,X_103)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_3219,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))) != identity
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) = multiply(identity,least_upper_bound(identity,X_103)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))) )],[refute_0_3217,refute_0_3218]) ).
cnf(refute_0_3220,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) = multiply(identity,least_upper_bound(identity,X_103)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),identity) )],[refute_0_3216,refute_0_3219]) ).
cnf(refute_0_3221,plain,
( multiply(identity,least_upper_bound(identity,X_103)) != least_upper_bound(identity,X_103)
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) != multiply(identity,least_upper_bound(identity,X_103))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) = least_upper_bound(identity,X_103) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,X_103)))),bind(Z0,$fot(least_upper_bound(identity,X_103)))]]) ).
cnf(refute_0_3222,plain,
( multiply(identity,least_upper_bound(identity,X_103)) != least_upper_bound(identity,X_103)
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) = least_upper_bound(identity,X_103) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)),multiply(identity,least_upper_bound(identity,X_103))) )],[refute_0_3220,refute_0_3221]) ).
cnf(refute_0_3223,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) = least_upper_bound(identity,X_103),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,X_103)),least_upper_bound(identity,X_103)) )],[refute_0_3195,refute_0_3222]) ).
cnf(refute_0_3224,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)) != least_upper_bound(identity,X_103)
| least_upper_bound(X_103,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))
| least_upper_bound(X_103,identity) = least_upper_bound(identity,X_103) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_103,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))) ),[1],$fot(least_upper_bound(identity,X_103))]]) ).
cnf(refute_0_3225,plain,
( least_upper_bound(X_103,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))
| least_upper_bound(X_103,identity) = least_upper_bound(identity,X_103) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103)),least_upper_bound(identity,X_103)) )],[refute_0_3223,refute_0_3224]) ).
cnf(refute_0_3226,plain,
least_upper_bound(X_103,identity) = least_upper_bound(identity,X_103),
inference(resolve,[$cnf( $equal(least_upper_bound(X_103,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_103,identity)),inverse(least_upper_bound(identity,inverse(X_103))))),least_upper_bound(identity,X_103))) )],[refute_0_3194,refute_0_3225]) ).
cnf(refute_0_3227,plain,
( least_upper_bound(X_103,identity) != least_upper_bound(identity,X_103)
| least_upper_bound(identity,X_103) = least_upper_bound(X_103,identity) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_103,identity))),bind(Y0,$fot(least_upper_bound(identity,X_103)))]]) ).
cnf(refute_0_3228,plain,
least_upper_bound(identity,X_103) = least_upper_bound(X_103,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(X_103,identity),least_upper_bound(identity,X_103)) )],[refute_0_3226,refute_0_3227]) ).
cnf(refute_0_3229,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(subst,[],[refute_0_3228:[bind(X_103,$fot(b))]]) ).
cnf(refute_0_3230,plain,
least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_227,b))) = least_upper_bound(X_227,b),
inference(subst,[],[refute_0_2996:[bind(X_136,$fot(X_227))]]) ).
cnf(refute_0_3231,plain,
least_upper_bound(b,X_227) = least_upper_bound(X_227,b),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(b)),bind(Y,$fot(X_227))]]) ).
cnf(refute_0_3232,plain,
( least_upper_bound(b,X_227) != least_upper_bound(X_227,b)
| least_upper_bound(X_227,b) = least_upper_bound(b,X_227) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(b,X_227))),bind(Y0,$fot(least_upper_bound(X_227,b)))]]) ).
cnf(refute_0_3233,plain,
least_upper_bound(X_227,b) = least_upper_bound(b,X_227),
inference(resolve,[$cnf( $equal(least_upper_bound(b,X_227),least_upper_bound(X_227,b)) )],[refute_0_3231,refute_0_3232]) ).
cnf(refute_0_3234,plain,
( least_upper_bound(X_227,b) != least_upper_bound(b,X_227)
| least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_227,b))) != least_upper_bound(X_227,b)
| least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_227))) = least_upper_bound(X_227,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_227,b))),least_upper_bound(X_227,b)) ),[0,1,1],$fot(least_upper_bound(b,X_227))]]) ).
cnf(refute_0_3235,plain,
( least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_227,b))) != least_upper_bound(X_227,b)
| least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_227))) = least_upper_bound(X_227,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_227,b),least_upper_bound(b,X_227)) )],[refute_0_3233,refute_0_3234]) ).
cnf(refute_0_3236,plain,
least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X_227))) = least_upper_bound(X_227,b),
inference(resolve,[$cnf( $equal(least_upper_bound(X_227,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(X_227,b))),least_upper_bound(X_227,b)) )],[refute_0_3230,refute_0_3235]) ).
cnf(refute_0_3237,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = least_upper_bound(identity,b),
inference(subst,[],[refute_0_3236:[bind(X_227,$fot(identity))]]) ).
cnf(refute_0_3238,plain,
( least_upper_bound(identity,b) != least_upper_bound(b,identity)
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) != least_upper_bound(identity,b)
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = least_upper_bound(b,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),bind(Y0,$fot(least_upper_bound(identity,b))),bind(Z0,$fot(least_upper_bound(b,identity)))]]) ).
cnf(refute_0_3239,plain,
( least_upper_bound(identity,b) != least_upper_bound(b,identity)
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = least_upper_bound(b,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),least_upper_bound(identity,b)) )],[refute_0_3237,refute_0_3238]) ).
cnf(refute_0_3240,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = least_upper_bound(b,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),least_upper_bound(b,identity)) )],[refute_0_3229,refute_0_3239]) ).
cnf(refute_0_3241,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3242,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) != least_upper_bound(b,identity)
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) ),[1,0],$fot(least_upper_bound(b,identity))]]) ).
cnf(refute_0_3243,plain,
( least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) != least_upper_bound(b,identity)
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3241,refute_0_3242]) ).
cnf(refute_0_3244,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),least_upper_bound(b,identity)) )],[refute_0_3240,refute_0_3243]) ).
cnf(refute_0_3245,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(subst,[],[refute_0_2387:[bind(X,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3246,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),bind(Z0,$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3247,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3245,refute_0_3246]) ).
cnf(refute_0_3248,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3244,refute_0_3247]) ).
cnf(refute_0_3249,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) ),[0],$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3250,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3248,refute_0_3249]) ).
cnf(refute_0_3251,plain,
multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) )],[refute_0_3178,refute_0_3250]) ).
cnf(refute_0_3252,plain,
inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) = greatest_lower_bound(identity,least_upper_bound(a,c)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3253,plain,
greatest_lower_bound(least_upper_bound(a,c),identity) = greatest_lower_bound(identity,least_upper_bound(a,c)),
inference(subst,[],[refute_0_1670:[bind(X_58,$fot(identity))]]) ).
cnf(refute_0_3254,plain,
greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,greatest_lower_bound(X_79,least_upper_bound(Y,X_79))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(least_upper_bound(Y,X_79))),bind(X_56,$fot(X_78)),bind(X_57,$fot(X_79))]]) ).
cnf(refute_0_3255,plain,
greatest_lower_bound(X_79,least_upper_bound(Y,X_79)) = X_79,
inference(subst,[],[refute_0_262:[bind(X,$fot(X_79))]]) ).
cnf(refute_0_3256,plain,
( greatest_lower_bound(X_79,least_upper_bound(Y,X_79)) != X_79
| greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,greatest_lower_bound(X_79,least_upper_bound(Y,X_79)))
| greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,greatest_lower_bound(X_79,least_upper_bound(Y,X_79)))) ),[1,1],$fot(X_79)]]) ).
cnf(refute_0_3257,plain,
( greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,greatest_lower_bound(X_79,least_upper_bound(Y,X_79)))
| greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,X_79) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,least_upper_bound(Y,X_79)),X_79) )],[refute_0_3255,refute_0_3256]) ).
cnf(refute_0_3258,plain,
greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_78,X_79),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,greatest_lower_bound(X_79,least_upper_bound(Y,X_79)))) )],[refute_0_3254,refute_0_3257]) ).
cnf(refute_0_3259,plain,
greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) = greatest_lower_bound(X_79,greatest_lower_bound(X_78,least_upper_bound(Y,X_79))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(least_upper_bound(Y,X_79))),bind(X_77,$fot(X_79))]]) ).
cnf(refute_0_3260,plain,
( greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,X_79)
| greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_79,greatest_lower_bound(X_78,least_upper_bound(Y,X_79)))
| greatest_lower_bound(X_79,greatest_lower_bound(X_78,least_upper_bound(Y,X_79))) = greatest_lower_bound(X_78,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,X_79)) ),[0],$fot(greatest_lower_bound(X_79,greatest_lower_bound(X_78,least_upper_bound(Y,X_79))))]]) ).
cnf(refute_0_3261,plain,
( greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)) != greatest_lower_bound(X_78,X_79)
| greatest_lower_bound(X_79,greatest_lower_bound(X_78,least_upper_bound(Y,X_79))) = greatest_lower_bound(X_78,X_79) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(X_78,least_upper_bound(Y,X_79)))) )],[refute_0_3259,refute_0_3260]) ).
cnf(refute_0_3262,plain,
greatest_lower_bound(X_79,greatest_lower_bound(X_78,least_upper_bound(Y,X_79))) = greatest_lower_bound(X_78,X_79),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_79),greatest_lower_bound(X_78,X_79)),greatest_lower_bound(X_78,X_79)) )],[refute_0_3258,refute_0_3261]) ).
cnf(refute_0_3263,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = greatest_lower_bound(least_upper_bound(a,c),identity),
inference(subst,[],[refute_0_3262:[bind(Y,$fot(b)),bind(X_78,$fot(least_upper_bound(a,c))),bind(X_79,$fot(identity))]]) ).
cnf(refute_0_3264,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) != greatest_lower_bound(least_upper_bound(a,c),identity)
| greatest_lower_bound(least_upper_bound(a,c),identity) != greatest_lower_bound(identity,least_upper_bound(a,c))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),identity))),bind(Z0,$fot(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3265,plain,
( greatest_lower_bound(least_upper_bound(a,c),identity) != greatest_lower_bound(identity,least_upper_bound(a,c))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(least_upper_bound(a,c),identity)) )],[refute_0_3263,refute_0_3264]) ).
cnf(refute_0_3266,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) = greatest_lower_bound(identity,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3253,refute_0_3265]) ).
cnf(refute_0_3267,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3268,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) ),[1,0],$fot(greatest_lower_bound(identity,least_upper_bound(a,c)))]]) ).
cnf(refute_0_3269,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) )],[refute_0_3267,refute_0_3268]) ).
cnf(refute_0_3270,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3266,refute_0_3269]) ).
cnf(refute_0_3271,plain,
inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),
inference(subst,[],[refute_0_608:[bind(X_199,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),bind(X_200,$fot(identity))]]) ).
cnf(refute_0_3272,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3273,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3274,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity))) )],[refute_0_3272,refute_0_3273]) ).
cnf(refute_0_3275,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),identity)),inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) )],[refute_0_3271,refute_0_3274]) ).
cnf(refute_0_3276,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_3277,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) )],[refute_0_3275,refute_0_3276]) ).
cnf(refute_0_3278,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_3270,refute_0_3277]) ).
cnf(refute_0_3279,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3280,plain,
( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3281,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) )],[refute_0_3279,refute_0_3280]) ).
cnf(refute_0_3282,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_3278,refute_0_3281]) ).
cnf(refute_0_3283,plain,
( inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) != inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))),bind(Z0,$fot(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3284,plain,
( inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))) )],[refute_0_3282,refute_0_3283]) ).
cnf(refute_0_3285,plain,
inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3252,refute_0_3284]) ).
cnf(refute_0_3286,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),greatest_lower_bound(identity,least_upper_bound(a,c))) ),[0],$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3287,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3285,refute_0_3286]) ).
cnf(refute_0_3288,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = greatest_lower_bound(identity,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))) )],[refute_0_3173,refute_0_3287]) ).
cnf(refute_0_3289,plain,
multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3290,plain,
( multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) ),[1,1],$fot(greatest_lower_bound(identity,least_upper_bound(a,c)))]]) ).
cnf(refute_0_3291,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3289,refute_0_3290]) ).
cnf(refute_0_3292,plain,
multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3288,refute_0_3291]) ).
cnf(refute_0_3293,plain,
( multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c)))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) ),[0],$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3294,plain,
( multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_3292,refute_0_3293]) ).
cnf(refute_0_3295,plain,
multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) )],[refute_0_3251,refute_0_3294]) ).
cnf(refute_0_3296,plain,
( multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c)))))
| multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))
| multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c)))))) ),[1,1,1],$fot(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))]]) ).
cnf(refute_0_3297,plain,
( multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c)))))
| multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))) )],[refute_0_3295,refute_0_3296]) ).
cnf(refute_0_3298,plain,
multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(identity,least_upper_bound(a,c)))))) )],[refute_0_2917,refute_0_3297]) ).
cnf(refute_0_3299,plain,
greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)),
inference(subst,[],[refute_0_1521:[bind(X_56,$fot(identity)),bind(X_57,$fot(multiply(b,inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_3300,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_98,inverse(X_99)))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_98,inverse(X_99))))]]) ).
cnf(refute_0_3301,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_98,inverse(X_99)))) != identity
| least_upper_bound(identity,multiply(X_98,inverse(X_99))) != multiply(least_upper_bound(X_98,X_99),inverse(X_99))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_98,X_99),inverse(X_99))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_98,inverse(X_99)))),identity) ),[0,1],$fot(multiply(least_upper_bound(X_98,X_99),inverse(X_99)))]]) ).
cnf(refute_0_3302,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_98,inverse(X_99)))) != identity
| greatest_lower_bound(identity,multiply(least_upper_bound(X_98,X_99),inverse(X_99))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_98,inverse(X_99))),multiply(least_upper_bound(X_98,X_99),inverse(X_99))) )],[refute_0_438,refute_0_3301]) ).
cnf(refute_0_3303,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_98,X_99),inverse(X_99))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_98,inverse(X_99)))),identity) )],[refute_0_3300,refute_0_3302]) ).
cnf(refute_0_3304,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c)))) = identity,
inference(subst,[],[refute_0_3303:[bind(X_98,$fot(b)),bind(X_99,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_3305,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c)))) != identity
| least_upper_bound(b,greatest_lower_bound(a,c)) != b
| greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c)))),identity) ),[0,1,0],$fot(b)]]) ).
cnf(refute_0_3306,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c)))) != identity
| greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_179,refute_0_3305]) ).
cnf(refute_0_3307,plain,
greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c)))),identity) )],[refute_0_3304,refute_0_3306]) ).
cnf(refute_0_3308,plain,
( greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))
| greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) != identity
| greatest_lower_bound(X,identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_3309,plain,
( greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))
| greatest_lower_bound(X,identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),identity) )],[refute_0_3307,refute_0_3308]) ).
cnf(refute_0_3310,plain,
greatest_lower_bound(X,identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) )],[refute_0_3299,refute_0_3309]) ).
cnf(refute_0_3311,plain,
greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406))),
inference(subst,[],[refute_0_3310:[bind(X,$fot(greatest_lower_bound(X_405,X_406)))]]) ).
cnf(refute_0_3312,plain,
greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406)) = greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)),
inference(subst,[],[refute_0_1548:[bind(Y,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(X_56,$fot(X_405)),bind(X_58,$fot(X_406))]]) ).
cnf(refute_0_3313,plain,
( greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406)) != greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))
| greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406)))
| greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) = greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406)))) ),[1,1],$fot(greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))]]) ).
cnf(refute_0_3314,plain,
( greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406)))
| greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) = greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406)),greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))) )],[refute_0_3312,refute_0_3313]) ).
cnf(refute_0_3315,plain,
greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) = greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_405,X_406)))) )],[refute_0_3311,refute_0_3314]) ).
cnf(refute_0_3316,plain,
greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) = greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)),
inference(subst,[],[refute_0_2134:[bind(X_154,$fot(greatest_lower_bound(X_405,X_406)))]]) ).
cnf(refute_0_3317,plain,
( greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) != greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406))
| greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) != greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))
| greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) = greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity),greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)))]]) ).
cnf(refute_0_3318,plain,
( greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) != greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))
| greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) = greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity),greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406))) )],[refute_0_3316,refute_0_3317]) ).
cnf(refute_0_3319,plain,
greatest_lower_bound(X,greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))))) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)),
inference(subst,[],[refute_0_1521:[bind(X_56,$fot(identity)),bind(X_57,$fot(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_3320,plain,
greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(X_57,$fot(identity))]]) ).
cnf(refute_0_3321,plain,
( greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))
| greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) != identity
| greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3322,plain,
( greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))
| greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),identity) )],[refute_0_3307,refute_0_3321]) ).
cnf(refute_0_3323,plain,
greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_56,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_3320,refute_0_3322]) ).
cnf(refute_0_3324,plain,
greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(greatest_lower_bound(a,c))))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(X_77,$fot(identity)),bind(X_78,$fot(X_56))]]) ).
cnf(refute_0_3325,plain,
( greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,identity)
| greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(greatest_lower_bound(a,c)))))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(X_56,identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,identity)) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_3326,plain,
( greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_56,identity)
| greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(X_56,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_3324,refute_0_3325]) ).
cnf(refute_0_3327,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(b,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(X_56,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_56,identity)) )],[refute_0_3323,refute_0_3326]) ).
cnf(refute_0_3328,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(X_397,identity),
inference(subst,[],[refute_0_3327:[bind(X_56,$fot(X_397))]]) ).
cnf(refute_0_3329,plain,
( greatest_lower_bound(X,greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))))) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))
| greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(X_397,identity)
| greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))) ),[0,1],$fot(greatest_lower_bound(X_397,identity))]]) ).
cnf(refute_0_3330,plain,
( greatest_lower_bound(X,greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))))) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))
| greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(X_397,identity)) )],[refute_0_3328,refute_0_3329]) ).
cnf(refute_0_3331,plain,
greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))) )],[refute_0_3319,refute_0_3330]) ).
cnf(refute_0_3332,plain,
greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X) = greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_397)),bind(Y,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(Z,$fot(X))]]) ).
cnf(refute_0_3333,plain,
greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)))]]) ).
cnf(refute_0_3334,plain,
( greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X) != greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) = greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))) ),[1,1],$fot(greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)))]]) ).
cnf(refute_0_3335,plain,
( greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X) != greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) = greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))) )],[refute_0_3333,refute_0_3334]) ).
cnf(refute_0_3336,plain,
greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) = greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X),greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) )],[refute_0_3332,refute_0_3335]) ).
cnf(refute_0_3337,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)) != greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)))
| greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_397,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)))]]) ).
cnf(refute_0_3338,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))
| greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X)),greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)))) )],[refute_0_3336,refute_0_3337]) ).
cnf(refute_0_3339,plain,
greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_397,identity)),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_397,multiply(b,inverse(greatest_lower_bound(a,c)))),X))) )],[refute_0_3331,refute_0_3338]) ).
cnf(refute_0_3340,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)))
| greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) = greatest_lower_bound(X,greatest_lower_bound(X_397,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_397,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)))))]]) ).
cnf(refute_0_3341,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X))) = greatest_lower_bound(X,greatest_lower_bound(X_397,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_397,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_397,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X)))) )],[refute_0_3339,refute_0_3340]) ).
cnf(refute_0_3342,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))) = greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity)),
inference(subst,[],[refute_0_3341:[bind(X,$fot(X_406)),bind(X_397,$fot(X_405))]]) ).
cnf(refute_0_3343,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) != greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))
| greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))) != greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) = greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)),greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))))]]) ).
cnf(refute_0_3344,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) != greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))
| greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) = greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406))),greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity))) )],[refute_0_3342,refute_0_3343]) ).
cnf(refute_0_3345,plain,
( greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity) != greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))
| greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) = greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)),greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))) )],[refute_0_3318,refute_0_3344]) ).
cnf(refute_0_3346,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_405,X_406)) = greatest_lower_bound(X_406,greatest_lower_bound(X_405,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_405,X_406),identity),greatest_lower_bound(identity,greatest_lower_bound(X_405,greatest_lower_bound(multiply(b,inverse(greatest_lower_bound(a,c))),X_406)))) )],[refute_0_3315,refute_0_3345]) ).
cnf(refute_0_3347,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) = greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)),
inference(subst,[],[refute_0_3346:[bind(X_405,$fot(identity)),bind(X_406,$fot(greatest_lower_bound(X_407,X_408)))]]) ).
cnf(refute_0_3348,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) = greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),
inference(subst,[],[refute_0_3346:[bind(X_405,$fot(X_407)),bind(X_406,$fot(X_408))]]) ).
cnf(refute_0_3349,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) != greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))
| greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) != greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) = greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))) ),[0,1],$fot(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)))]]) ).
cnf(refute_0_3350,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) != greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) = greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) )],[refute_0_3348,refute_0_3349]) ).
cnf(refute_0_3351,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) = greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))) )],[refute_0_3347,refute_0_3350]) ).
cnf(refute_0_3352,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) = greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)),
inference(subst,[],[refute_0_2833:[bind(X_15,$fot(identity)),bind(X_56,$fot(X_408)),bind(X_57,$fot(X_407))]]) ).
cnf(refute_0_3353,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) != greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) != greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) = greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))),greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)))]]) ).
cnf(refute_0_3354,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) != greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) = greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))),greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407))) )],[refute_0_3352,refute_0_3353]) ).
cnf(refute_0_3355,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(greatest_lower_bound(X_407,X_408))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_3356,plain,
greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,X)),
inference(subst,[],[refute_0_1548:[bind(Y,$fot(X_56)),bind(X_56,$fot(X_57)),bind(X_58,$fot(X))]]) ).
cnf(refute_0_3357,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))
| greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,X))
| greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,X))) ),[0],$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)))]]) ).
cnf(refute_0_3358,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))
| greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(X_57,X)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,X))) )],[refute_0_3356,refute_0_3357]) ).
cnf(refute_0_3359,plain,
greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X))) )],[refute_0_1521,refute_0_3358]) ).
cnf(refute_0_3360,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,X))
| greatest_lower_bound(X_57,greatest_lower_bound(X_56,X)) = greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)))),bind(Y0,$fot(greatest_lower_bound(X_57,greatest_lower_bound(X_56,X))))]]) ).
cnf(refute_0_3361,plain,
greatest_lower_bound(X_57,greatest_lower_bound(X_56,X)) = greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,X))) )],[refute_0_3359,refute_0_3360]) ).
cnf(refute_0_3362,plain,
greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) = greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),
inference(subst,[],[refute_0_3361:[bind(X,$fot(identity)),bind(X_56,$fot(identity)),bind(X_57,$fot(greatest_lower_bound(X_407,X_408)))]]) ).
cnf(refute_0_3363,plain,
( greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) != greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))))]]) ).
cnf(refute_0_3364,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)),greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)))) )],[refute_0_3362,refute_0_3363]) ).
cnf(refute_0_3365,plain,
greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) )],[refute_0_3355,refute_0_3364]) ).
cnf(refute_0_3366,plain,
( greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) != greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))) ),[1],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)))]]) ).
cnf(refute_0_3367,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) != greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) )],[refute_0_3365,refute_0_3366]) ).
cnf(refute_0_3368,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) != greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))
| greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))) )],[refute_0_3354,refute_0_3367]) ).
cnf(refute_0_3369,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))),greatest_lower_bound(greatest_lower_bound(X_407,X_408),greatest_lower_bound(identity,identity))) )],[refute_0_3351,refute_0_3368]) ).
cnf(refute_0_3370,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) = greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))))]]) ).
cnf(refute_0_3371,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) = greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_408,X_407)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) )],[refute_0_3369,refute_0_3370]) ).
cnf(refute_0_3372,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_3371:[bind(X_407,$fot(inverse(least_upper_bound(a,c)))),bind(X_408,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_3373,plain,
least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),
inference(subst,[],[refute_0_1609:[bind(X_11,$fot(greatest_lower_bound(X_407,X_408))),bind(X_16,$fot(identity))]]) ).
cnf(refute_0_3374,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) != greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))
| least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) ),[0,0],$fot(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)))]]) ).
cnf(refute_0_3375,plain,
( least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))) )],[refute_0_3348,refute_0_3374]) ).
cnf(refute_0_3376,plain,
least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) )],[refute_0_3373,refute_0_3375]) ).
cnf(refute_0_3377,plain,
least_upper_bound(X_355,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))) = least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(greatest_lower_bound(X_11,X_16))),bind(X_30,$fot(X_355)),bind(X_31,$fot(greatest_lower_bound(X_16,X_11)))]]) ).
cnf(refute_0_3378,plain,
( least_upper_bound(X_355,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))) != least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355))
| least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)) != greatest_lower_bound(X_16,X_11)
| least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) = least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))),least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355))) ),[0,1],$fot(greatest_lower_bound(X_16,X_11))]]) ).
cnf(refute_0_3379,plain,
( least_upper_bound(X_355,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))) != least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355))
| least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) = least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16)),greatest_lower_bound(X_16,X_11)) )],[refute_0_1609,refute_0_3378]) ).
cnf(refute_0_3380,plain,
least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) = least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(greatest_lower_bound(X_16,X_11),greatest_lower_bound(X_11,X_16))),least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355))) )],[refute_0_3377,refute_0_3379]) ).
cnf(refute_0_3381,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192))) = least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X)),
inference(subst,[],[refute_0_680:[bind(X_20,$fot(greatest_lower_bound(X_192,X_191))),bind(X_21,$fot(greatest_lower_bound(X_191,X_192)))]]) ).
cnf(refute_0_3382,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192))) != least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X))
| least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)) != greatest_lower_bound(X_192,X_191)
| least_upper_bound(X,greatest_lower_bound(X_192,X_191)) = least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192))),least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X))) ),[0,1],$fot(greatest_lower_bound(X_192,X_191))]]) ).
cnf(refute_0_3383,plain,
( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192))) != least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X))
| least_upper_bound(X,greatest_lower_bound(X_192,X_191)) = least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192)),greatest_lower_bound(X_192,X_191)) )],[refute_0_1610,refute_0_3382]) ).
cnf(refute_0_3384,plain,
least_upper_bound(X,greatest_lower_bound(X_192,X_191)) = least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_192,X_191),greatest_lower_bound(X_191,X_192))),least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X))) )],[refute_0_3381,refute_0_3383]) ).
cnf(refute_0_3385,plain,
( least_upper_bound(X,greatest_lower_bound(X_192,X_191)) != least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X))
| least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X)) = least_upper_bound(X,greatest_lower_bound(X_192,X_191)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,greatest_lower_bound(X_192,X_191)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X))))]]) ).
cnf(refute_0_3386,plain,
least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X)) = least_upper_bound(X,greatest_lower_bound(X_192,X_191)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X_192,X_191)),least_upper_bound(greatest_lower_bound(X_192,X_191),least_upper_bound(greatest_lower_bound(X_191,X_192),X))) )],[refute_0_3384,refute_0_3385]) ).
cnf(refute_0_3387,plain,
least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)) = least_upper_bound(X_355,greatest_lower_bound(X_11,X_16)),
inference(subst,[],[refute_0_3386:[bind(X,$fot(X_355)),bind(X_191,$fot(X_16)),bind(X_192,$fot(X_11))]]) ).
cnf(refute_0_3388,plain,
( least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) != least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355))
| least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)) != least_upper_bound(X_355,greatest_lower_bound(X_11,X_16))
| least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) = least_upper_bound(X_355,greatest_lower_bound(X_11,X_16)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)),least_upper_bound(X_355,greatest_lower_bound(X_11,X_16))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)))]]) ).
cnf(refute_0_3389,plain,
( least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) != least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355))
| least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) = least_upper_bound(X_355,greatest_lower_bound(X_11,X_16)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355)),least_upper_bound(X_355,greatest_lower_bound(X_11,X_16))) )],[refute_0_3387,refute_0_3388]) ).
cnf(refute_0_3390,plain,
least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) = least_upper_bound(X_355,greatest_lower_bound(X_11,X_16)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)),least_upper_bound(greatest_lower_bound(X_11,X_16),least_upper_bound(greatest_lower_bound(X_16,X_11),X_355))) )],[refute_0_3380,refute_0_3389]) ).
cnf(refute_0_3391,plain,
( least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) != least_upper_bound(X_355,greatest_lower_bound(X_11,X_16))
| least_upper_bound(X_355,greatest_lower_bound(X_11,X_16)) = least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)))),bind(Y0,$fot(least_upper_bound(X_355,greatest_lower_bound(X_11,X_16))))]]) ).
cnf(refute_0_3392,plain,
least_upper_bound(X_355,greatest_lower_bound(X_11,X_16)) = least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,greatest_lower_bound(X_16,X_11)),least_upper_bound(X_355,greatest_lower_bound(X_11,X_16))) )],[refute_0_3390,refute_0_3391]) ).
cnf(refute_0_3393,plain,
least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) = least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),
inference(subst,[],[refute_0_3392:[bind(X_11,$fot(greatest_lower_bound(X_407,X_408))),bind(X_16,$fot(identity)),bind(X_355,$fot(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity))))]]) ).
cnf(refute_0_3394,plain,
( least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) != least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)))
| least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))))]]) ).
cnf(refute_0_3395,plain,
( least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)),least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)))) )],[refute_0_3393,refute_0_3394]) ).
cnf(refute_0_3396,plain,
least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(greatest_lower_bound(X_407,X_408),identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) )],[refute_0_3376,refute_0_3395]) ).
cnf(refute_0_3397,plain,
least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),
inference(subst,[],[refute_0_1609:[bind(X_11,$fot(greatest_lower_bound(X_438,X_440)))]]) ).
cnf(refute_0_3398,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)) = greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),
inference(subst,[],[refute_0_2891:[bind(Y,$fot(X_438)),bind(X_110,$fot(X_16)),bind(X_111,$fot(X_440))]]) ).
cnf(refute_0_3399,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)) != greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) != greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))) ),[0,0],$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)))]]) ).
cnf(refute_0_3400,plain,
( least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) != greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438))) )],[refute_0_3398,refute_0_3399]) ).
cnf(refute_0_3401,plain,
least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))) )],[refute_0_3397,refute_0_3400]) ).
cnf(refute_0_3402,plain,
greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16) = greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16)),
inference(subst,[],[refute_0_566:[bind(X,$fot(X_438)),bind(Y,$fot(X_440)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_3403,plain,
least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)))]]) ).
cnf(refute_0_3404,plain,
( greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16) != greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) != least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16))) ),[1,1],$fot(greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16)))]]) ).
cnf(refute_0_3405,plain,
( greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16) != greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16))) )],[refute_0_3403,refute_0_3404]) ).
cnf(refute_0_3406,plain,
least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) = least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))) )],[refute_0_3402,refute_0_3405]) ).
cnf(refute_0_3407,plain,
( least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) != greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) != least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16)))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))) = greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))))]]) ).
cnf(refute_0_3408,plain,
( least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)) != greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))
| least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))) = greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16)))) )],[refute_0_3406,refute_0_3407]) ).
cnf(refute_0_3409,plain,
least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X_438,greatest_lower_bound(X_440,X_16))) = greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_16,greatest_lower_bound(X_440,X_438)),greatest_lower_bound(greatest_lower_bound(X_438,X_440),X_16)),greatest_lower_bound(X_16,greatest_lower_bound(X_438,X_440))) )],[refute_0_3401,refute_0_3408]) ).
cnf(refute_0_3410,plain,
least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) = greatest_lower_bound(X_408,greatest_lower_bound(identity,X_407)),
inference(subst,[],[refute_0_3409:[bind(X_16,$fot(X_408)),bind(X_438,$fot(identity)),bind(X_440,$fot(X_407))]]) ).
cnf(refute_0_3411,plain,
( least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) != greatest_lower_bound(X_408,greatest_lower_bound(identity,X_407))
| least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| greatest_lower_bound(X_408,greatest_lower_bound(identity,X_407)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) ),[0],$fot(greatest_lower_bound(X_408,greatest_lower_bound(identity,X_407)))]]) ).
cnf(refute_0_3412,plain,
( least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) != greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))
| greatest_lower_bound(X_408,greatest_lower_bound(identity,X_407)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),greatest_lower_bound(X_408,greatest_lower_bound(identity,X_407))) )],[refute_0_3410,refute_0_3411]) ).
cnf(refute_0_3413,plain,
greatest_lower_bound(X_408,greatest_lower_bound(identity,X_407)) = greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_408,greatest_lower_bound(X_407,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))),greatest_lower_bound(identity,greatest_lower_bound(X_407,X_408))) )],[refute_0_3396,refute_0_3412]) ).
cnf(refute_0_3414,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),
inference(subst,[],[refute_0_3413:[bind(X_407,$fot(inverse(least_upper_bound(a,c)))),bind(X_408,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_3415,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_3416,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)))) )],[refute_0_3414,refute_0_3415]) ).
cnf(refute_0_3417,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) )],[refute_0_3372,refute_0_3416]) ).
cnf(refute_0_3418,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))) = greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))),
inference(subst,[],[refute_0_1548:[bind(X_58,$fot(greatest_lower_bound(least_upper_bound(X_409,Y),X_411)))]]) ).
cnf(refute_0_3419,plain,
greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)) = greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(Y,X_56)),X_58),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_56)),bind(Y,$fot(least_upper_bound(Y,X_56))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_3420,plain,
greatest_lower_bound(X_56,least_upper_bound(Y,X_56)) = X_56,
inference(subst,[],[refute_0_262:[bind(X,$fot(X_56))]]) ).
cnf(refute_0_3421,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(Y,X_56)),X_58)
| greatest_lower_bound(X_56,least_upper_bound(Y,X_56)) != X_56
| greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)) = greatest_lower_bound(X_56,X_58) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(Y,X_56)),X_58)) ),[1,0],$fot(X_56)]]) ).
cnf(refute_0_3422,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)) != greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(Y,X_56)),X_58)
| greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)) = greatest_lower_bound(X_56,X_58) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,least_upper_bound(Y,X_56)),X_56) )],[refute_0_3420,refute_0_3421]) ).
cnf(refute_0_3423,plain,
greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)) = greatest_lower_bound(X_56,X_58),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(Y,X_56),X_58)),greatest_lower_bound(greatest_lower_bound(X_56,least_upper_bound(Y,X_56)),X_58)) )],[refute_0_3419,refute_0_3422]) ).
cnf(refute_0_3424,plain,
greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411)) = greatest_lower_bound(Y,X_411),
inference(subst,[],[refute_0_3423:[bind(Y,$fot(X_409)),bind(X_56,$fot(Y)),bind(X_58,$fot(X_411))]]) ).
cnf(refute_0_3425,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))) != greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411)))
| greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411)) != greatest_lower_bound(Y,X_411)
| greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_411)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))),greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411)))) ),[1,1],$fot(greatest_lower_bound(Y,X_411))]]) ).
cnf(refute_0_3426,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))) != greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411)))
| greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_411)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411)),greatest_lower_bound(Y,X_411)) )],[refute_0_3424,refute_0_3425]) ).
cnf(refute_0_3427,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))) = greatest_lower_bound(X_56,greatest_lower_bound(Y,X_411)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_409,Y),X_411))),greatest_lower_bound(X_56,greatest_lower_bound(Y,greatest_lower_bound(least_upper_bound(X_409,Y),X_411)))) )],[refute_0_3418,refute_0_3426]) ).
cnf(refute_0_3428,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_3427:[bind(Y,$fot(identity)),bind(X_409,$fot(b)),bind(X_411,$fot(inverse(least_upper_bound(a,c)))),bind(X_56,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_3429,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_3430,plain,
( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) )],[refute_0_3428,refute_0_3429]) ).
cnf(refute_0_3431,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) )],[refute_0_3417,refute_0_3430]) ).
cnf(refute_0_3432,plain,
greatest_lower_bound(X_439,greatest_lower_bound(greatest_lower_bound(X,Y),X_440)) = greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y))),
inference(subst,[],[refute_0_2891:[bind(Y,$fot(greatest_lower_bound(X,Y))),bind(X_110,$fot(X_439)),bind(X_111,$fot(X_440))]]) ).
cnf(refute_0_3433,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_440)) = greatest_lower_bound(greatest_lower_bound(X,Y),X_440),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(X_440))]]) ).
cnf(refute_0_3434,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_440)) != greatest_lower_bound(greatest_lower_bound(X,Y),X_440)
| greatest_lower_bound(greatest_lower_bound(X,Y),X_440) = greatest_lower_bound(X,greatest_lower_bound(Y,X_440)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_440)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),X_440)))]]) ).
cnf(refute_0_3435,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_440) = greatest_lower_bound(X,greatest_lower_bound(Y,X_440)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_440)),greatest_lower_bound(greatest_lower_bound(X,Y),X_440)) )],[refute_0_3433,refute_0_3434]) ).
cnf(refute_0_3436,plain,
( greatest_lower_bound(X_439,greatest_lower_bound(greatest_lower_bound(X,Y),X_440)) != greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y)))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_440) != greatest_lower_bound(X,greatest_lower_bound(Y,X_440))
| greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))) = greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_439,greatest_lower_bound(greatest_lower_bound(X,Y),X_440)),greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y)))) ),[0,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_440)))]]) ).
cnf(refute_0_3437,plain,
( greatest_lower_bound(X_439,greatest_lower_bound(greatest_lower_bound(X,Y),X_440)) != greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y)))
| greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))) = greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_440),greatest_lower_bound(X,greatest_lower_bound(Y,X_440))) )],[refute_0_3435,refute_0_3436]) ).
cnf(refute_0_3438,plain,
greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))) = greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_439,greatest_lower_bound(greatest_lower_bound(X,Y),X_440)),greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y)))) )],[refute_0_3432,refute_0_3437]) ).
cnf(refute_0_3439,plain,
( greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))) != greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y)))
| greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y))) = greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))))),bind(Y0,$fot(greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y)))))]]) ).
cnf(refute_0_3440,plain,
greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y))) = greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_439,greatest_lower_bound(X,greatest_lower_bound(Y,X_440))),greatest_lower_bound(X_439,greatest_lower_bound(X_440,greatest_lower_bound(X,Y)))) )],[refute_0_3438,refute_0_3439]) ).
cnf(refute_0_3441,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_3440:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(least_upper_bound(b,identity))),bind(X_439,$fot(identity)),bind(X_440,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_3442,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_3443,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))) )],[refute_0_3441,refute_0_3442]) ).
cnf(refute_0_3444,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) )],[refute_0_3431,refute_0_3443]) ).
cnf(refute_0_3445,plain,
( multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3446,plain,
( multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))
| multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity)))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) )],[refute_0_3444,refute_0_3445]) ).
cnf(refute_0_3447,plain,
multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,identity))))) )],[refute_0_3298,refute_0_3446]) ).
cnf(refute_0_3448,plain,
( multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))),least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))))) ),[1,1],$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_3449,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) )],[refute_0_3447,refute_0_3448]) ).
cnf(refute_0_3450,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))),least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))))) )],[refute_0_2798,refute_0_3449]) ).
cnf(refute_0_3451,plain,
multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))),
inference(subst,[],[refute_0_2389:[bind(X,$fot(greatest_lower_bound(identity,least_upper_bound(a,c)))),bind(Y,$fot(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_3452,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) != multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c)))
| multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))),least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))) ),[0],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3453,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_3451,refute_0_3452]) ).
cnf(refute_0_3454,plain,
least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) = greatest_lower_bound(X_56,X_57),
inference(subst,[],[lub_absorbtion:[bind(X,$fot(greatest_lower_bound(X_56,X_57)))]]) ).
cnf(refute_0_3455,plain,
( greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))
| least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) != greatest_lower_bound(X_56,X_57)
| least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) = greatest_lower_bound(X_56,X_57) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)),greatest_lower_bound(X_56,X_57)) ),[0,1],$fot(greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y)))]]) ).
cnf(refute_0_3456,plain,
( least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)) != greatest_lower_bound(X_56,X_57)
| least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) = greatest_lower_bound(X_56,X_57) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y),greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) )],[refute_0_1510,refute_0_3455]) ).
cnf(refute_0_3457,plain,
least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(X_56,greatest_lower_bound(X_57,Y))) = greatest_lower_bound(X_56,X_57),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_56,X_57),greatest_lower_bound(greatest_lower_bound(X_56,X_57),Y)),greatest_lower_bound(X_56,X_57)) )],[refute_0_3454,refute_0_3456]) ).
cnf(refute_0_3458,plain,
least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(identity,least_upper_bound(a,c)),
inference(subst,[],[refute_0_3457:[bind(Y,$fot(inverse(least_upper_bound(a,c)))),bind(X_56,$fot(identity)),bind(X_57,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_3459,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))
| least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_3460,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3458,refute_0_3459]) ).
cnf(refute_0_3461,plain,
( multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))),least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))) )],[refute_0_3453,refute_0_3460]) ).
cnf(refute_0_3462,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(identity,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,least_upper_bound(a,c))),least_upper_bound(greatest_lower_bound(identity,least_upper_bound(a,c)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))) )],[refute_0_3450,refute_0_3461]) ).
cnf(refute_0_3463,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))))) != inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) = inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))) ),[0,1,0],$fot(greatest_lower_bound(identity,least_upper_bound(a,c)))]]) ).
cnf(refute_0_3464,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))))) != inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) = inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3462,refute_0_3463]) ).
cnf(refute_0_3465,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) = inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,least_upper_bound(a,c))))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))) )],[refute_0_2797,refute_0_3464]) ).
cnf(refute_0_3466,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3467,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) != identity
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) != inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))
| identity = inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_3468,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) != inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))
| identity = inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),identity) )],[refute_0_3466,refute_0_3467]) ).
cnf(refute_0_3469,plain,
identity = inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))) )],[refute_0_3465,refute_0_3468]) ).
cnf(refute_0_3470,plain,
( identity != inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))
| inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_3471,plain,
inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))) )],[refute_0_3469,refute_0_3470]) ).
cnf(refute_0_3472,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))
| inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) != identity
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3473,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),identity) )],[refute_0_3471,refute_0_3472]) ).
cnf(refute_0_3474,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))) )],[refute_0_2796,refute_0_3473]) ).
cnf(refute_0_3475,plain,
inverse(least_upper_bound(X_375,least_upper_bound(Y,X_22))) = inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)),
inference(subst,[],[refute_0_1787:[bind(X_85,$fot(X_375)),bind(X_86,$fot(least_upper_bound(Y,X_22)))]]) ).
cnf(refute_0_3476,plain,
least_upper_bound(Y,least_upper_bound(X_375,X_22)) = least_upper_bound(X_375,least_upper_bound(Y,X_22)),
inference(subst,[],[refute_0_747:[bind(X_20,$fot(X_375))]]) ).
cnf(refute_0_3477,plain,
( least_upper_bound(Y,least_upper_bound(X_375,X_22)) != least_upper_bound(X_375,least_upper_bound(Y,X_22))
| least_upper_bound(X_375,least_upper_bound(Y,X_22)) = least_upper_bound(Y,least_upper_bound(X_375,X_22)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_375,X_22)))),bind(Y0,$fot(least_upper_bound(X_375,least_upper_bound(Y,X_22))))]]) ).
cnf(refute_0_3478,plain,
least_upper_bound(X_375,least_upper_bound(Y,X_22)) = least_upper_bound(Y,least_upper_bound(X_375,X_22)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_375,X_22)),least_upper_bound(X_375,least_upper_bound(Y,X_22))) )],[refute_0_3476,refute_0_3477]) ).
cnf(refute_0_3479,plain,
( inverse(least_upper_bound(X_375,least_upper_bound(Y,X_22))) != inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))
| least_upper_bound(X_375,least_upper_bound(Y,X_22)) != least_upper_bound(Y,least_upper_bound(X_375,X_22))
| inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) = inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_375,least_upper_bound(Y,X_22))),inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))) ),[0,0],$fot(least_upper_bound(Y,least_upper_bound(X_375,X_22)))]]) ).
cnf(refute_0_3480,plain,
( inverse(least_upper_bound(X_375,least_upper_bound(Y,X_22))) != inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))
| inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) = inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_375,least_upper_bound(Y,X_22)),least_upper_bound(Y,least_upper_bound(X_375,X_22))) )],[refute_0_3478,refute_0_3479]) ).
cnf(refute_0_3481,plain,
inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) = inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_375,least_upper_bound(Y,X_22))),inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))) )],[refute_0_3475,refute_0_3480]) ).
cnf(refute_0_3482,plain,
least_upper_bound(least_upper_bound(Y,X_22),X_375) = least_upper_bound(Y,least_upper_bound(X_22,X_375)),
inference(subst,[],[refute_0_131:[bind(X,$fot(Y)),bind(Y,$fot(X_22)),bind(Z,$fot(X_375))]]) ).
cnf(refute_0_3483,plain,
inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) = inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)))]]) ).
cnf(refute_0_3484,plain,
( inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) != inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))
| least_upper_bound(least_upper_bound(Y,X_22),X_375) != least_upper_bound(Y,least_upper_bound(X_22,X_375))
| inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) = inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)),inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))) ),[1,0],$fot(least_upper_bound(Y,least_upper_bound(X_22,X_375)))]]) ).
cnf(refute_0_3485,plain,
( least_upper_bound(least_upper_bound(Y,X_22),X_375) != least_upper_bound(Y,least_upper_bound(X_22,X_375))
| inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) = inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)),inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))) )],[refute_0_3483,refute_0_3484]) ).
cnf(refute_0_3486,plain,
inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) = inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),X_375),least_upper_bound(Y,least_upper_bound(X_22,X_375))) )],[refute_0_3482,refute_0_3485]) ).
cnf(refute_0_3487,plain,
( inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) != inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))
| inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)) != inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375)))
| inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) = inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))),inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375)))) ),[0],$fot(inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)))]]) ).
cnf(refute_0_3488,plain,
( inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) != inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))
| inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) = inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375)),inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375)))) )],[refute_0_3486,refute_0_3487]) ).
cnf(refute_0_3489,plain,
inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) = inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))),inverse(least_upper_bound(least_upper_bound(Y,X_22),X_375))) )],[refute_0_3481,refute_0_3488]) ).
cnf(refute_0_3490,plain,
( inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) != inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375)))
| inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))) = inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))))),bind(Y0,$fot(inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375)))))]]) ).
cnf(refute_0_3491,plain,
inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375))) = inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(Y,least_upper_bound(X_375,X_22))),inverse(least_upper_bound(Y,least_upper_bound(X_22,X_375)))) )],[refute_0_3489,refute_0_3490]) ).
cnf(refute_0_3492,plain,
inverse(least_upper_bound(a,least_upper_bound(identity,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))),
inference(subst,[],[refute_0_3491:[bind(Y,$fot(a)),bind(X_22,$fot(identity)),bind(X_375,$fot(c))]]) ).
cnf(refute_0_3493,plain,
inverse(least_upper_bound(X_449,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_417:[bind(X_46,$fot(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),bind(X_95,$fot(least_upper_bound(a,least_upper_bound(c,X_449))))]]) ).
cnf(refute_0_3494,plain,
multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(a,least_upper_bound(c,X_257)))) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(least_upper_bound(a,least_upper_bound(c,X_257))))]]) ).
cnf(refute_0_3495,plain,
multiply(inverse(a),inverse(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)))) = inverse(least_upper_bound(a,least_upper_bound(c,X_33))),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(least_upper_bound(a,least_upper_bound(c,X_33)))),bind(X_55,$fot(inverse(a)))]]) ).
cnf(refute_0_3496,plain,
multiply(least_upper_bound(a,least_upper_bound(X_33,c)),inverse(a)) = least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))),
inference(subst,[],[refute_0_1873:[bind(X_90,$fot(a)),bind(X_91,$fot(least_upper_bound(X_33,c)))]]) ).
cnf(refute_0_3497,plain,
least_upper_bound(X_33,c) = least_upper_bound(c,X_33),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_33)),bind(Y,$fot(c))]]) ).
cnf(refute_0_3498,plain,
( least_upper_bound(X_33,c) != least_upper_bound(c,X_33)
| least_upper_bound(c,X_33) = least_upper_bound(X_33,c) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_33,c))),bind(Y0,$fot(least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_3499,plain,
least_upper_bound(c,X_33) = least_upper_bound(X_33,c),
inference(resolve,[$cnf( $equal(least_upper_bound(X_33,c),least_upper_bound(c,X_33)) )],[refute_0_3497,refute_0_3498]) ).
cnf(refute_0_3500,plain,
( least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(c,X_33))
| least_upper_bound(c,X_33) != least_upper_bound(X_33,c)
| least_upper_bound(b,least_upper_bound(c,X_33)) = least_upper_bound(a,least_upper_bound(X_33,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(c,X_33))) ),[1,1],$fot(least_upper_bound(X_33,c))]]) ).
cnf(refute_0_3501,plain,
( least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(c,X_33))
| least_upper_bound(b,least_upper_bound(c,X_33)) = least_upper_bound(a,least_upper_bound(X_33,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,X_33),least_upper_bound(X_33,c)) )],[refute_0_3499,refute_0_3500]) ).
cnf(refute_0_3502,plain,
least_upper_bound(b,least_upper_bound(c,X_33)) = least_upper_bound(a,least_upper_bound(X_33,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(c,X_33))) )],[refute_0_136,refute_0_3501]) ).
cnf(refute_0_3503,plain,
( least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(X_33,c))
| least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(c,X_33))
| least_upper_bound(a,least_upper_bound(c,X_33)) = least_upper_bound(a,least_upper_bound(X_33,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(X_33,c))) ),[0],$fot(least_upper_bound(a,least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_3504,plain,
( least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(X_33,c))
| least_upper_bound(a,least_upper_bound(c,X_33)) = least_upper_bound(a,least_upper_bound(X_33,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(c,X_33))) )],[refute_0_136,refute_0_3503]) ).
cnf(refute_0_3505,plain,
least_upper_bound(a,least_upper_bound(c,X_33)) = least_upper_bound(a,least_upper_bound(X_33,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(X_33,c))) )],[refute_0_3502,refute_0_3504]) ).
cnf(refute_0_3506,plain,
( least_upper_bound(a,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(X_33,c))
| least_upper_bound(a,least_upper_bound(X_33,c)) = least_upper_bound(a,least_upper_bound(c,X_33)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(c,X_33)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_33,c))))]]) ).
cnf(refute_0_3507,plain,
least_upper_bound(a,least_upper_bound(X_33,c)) = least_upper_bound(a,least_upper_bound(c,X_33)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(X_33,c))) )],[refute_0_3505,refute_0_3506]) ).
cnf(refute_0_3508,plain,
( multiply(least_upper_bound(a,least_upper_bound(X_33,c)),inverse(a)) != least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a)))
| least_upper_bound(a,least_upper_bound(X_33,c)) != least_upper_bound(a,least_upper_bound(c,X_33))
| multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) = least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(X_33,c)),inverse(a)),least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a)))) ),[0,0],$fot(least_upper_bound(a,least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_3509,plain,
( multiply(least_upper_bound(a,least_upper_bound(X_33,c)),inverse(a)) != least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a)))
| multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) = least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_33,c)),least_upper_bound(a,least_upper_bound(c,X_33))) )],[refute_0_3507,refute_0_3508]) ).
cnf(refute_0_3510,plain,
multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) = least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(X_33,c)),inverse(a)),least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a)))) )],[refute_0_3496,refute_0_3509]) ).
cnf(refute_0_3511,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) = least_upper_bound(multiply(Y,inverse(X_100)),multiply(least_upper_bound(X_100,X_101),inverse(X_100))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_100))),bind(Z,$fot(least_upper_bound(X_100,X_101)))]]) ).
cnf(refute_0_3512,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) != least_upper_bound(multiply(Y,inverse(X_100)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))
| multiply(least_upper_bound(X_100,X_101),inverse(X_100)) != least_upper_bound(identity,multiply(X_101,inverse(X_100)))
| multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) = least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)),least_upper_bound(multiply(Y,inverse(X_100)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_101,inverse(X_100))))]]) ).
cnf(refute_0_3513,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) != least_upper_bound(multiply(Y,inverse(X_100)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))
| multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) = least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_100,X_101),inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) )],[refute_0_2502,refute_0_3512]) ).
cnf(refute_0_3514,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) = least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)),least_upper_bound(multiply(Y,inverse(X_100)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))) )],[refute_0_3511,refute_0_3513]) ).
cnf(refute_0_3515,plain,
least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100))),
inference(subst,[],[refute_0_2375:[bind(X_20,$fot(identity)),bind(X_89,$fot(inverse(X_100))),bind(X_90,$fot(Y)),bind(X_91,$fot(X_101))]]) ).
cnf(refute_0_3516,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) != least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100))))
| least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100)))
| multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)),least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100)))) ),[0],$fot(least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))))]]) ).
cnf(refute_0_3517,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) != least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100))))
| multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100)))) )],[refute_0_3515,refute_0_3516]) ).
cnf(refute_0_3518,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)),least_upper_bound(multiply(Y,inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100))))) )],[refute_0_3514,refute_0_3517]) ).
cnf(refute_0_3519,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100)))
| least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100))) = multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100)))))]]) ).
cnf(refute_0_3520,plain,
least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100))) = multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_100,X_101)),inverse(X_100)),least_upper_bound(identity,multiply(least_upper_bound(Y,X_101),inverse(X_100)))) )],[refute_0_3518,refute_0_3519]) ).
cnf(refute_0_3521,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),
inference(subst,[],[refute_0_3520:[bind(Y,$fot(X_33)),bind(X_100,$fot(a)),bind(X_101,$fot(c))]]) ).
cnf(refute_0_3522,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) != least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a)))
| least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))) != multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a))
| multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)),multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))))]]) ).
cnf(refute_0_3523,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) != least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a)))
| multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a))),multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a))) )],[refute_0_3521,refute_0_3522]) ).
cnf(refute_0_3524,plain,
multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)),least_upper_bound(identity,multiply(least_upper_bound(X_33,c),inverse(a)))) )],[refute_0_3510,refute_0_3523]) ).
cnf(refute_0_3525,plain,
( multiply(inverse(a),inverse(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)))) != inverse(least_upper_bound(a,least_upper_bound(c,X_33)))
| multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)) != multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a))
| multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) = inverse(least_upper_bound(a,least_upper_bound(c,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),inverse(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)))),inverse(least_upper_bound(a,least_upper_bound(c,X_33)))) ),[0,1,0],$fot(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))]]) ).
cnf(refute_0_3526,plain,
( multiply(inverse(a),inverse(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)))) != inverse(least_upper_bound(a,least_upper_bound(c,X_33)))
| multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) = inverse(least_upper_bound(a,least_upper_bound(c,X_33))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)),multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a))) )],[refute_0_3524,refute_0_3525]) ).
cnf(refute_0_3527,plain,
multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) = inverse(least_upper_bound(a,least_upper_bound(c,X_33))),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),inverse(a)))),inverse(least_upper_bound(a,least_upper_bound(c,X_33)))) )],[refute_0_3495,refute_0_3526]) ).
cnf(refute_0_3528,plain,
multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity) = least_upper_bound(X_33,least_upper_bound(a,c)),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(least_upper_bound(X_33,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3529,plain,
multiply(inverse(a),a) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_3530,plain,
multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)))]]) ).
cnf(refute_0_3531,plain,
( multiply(inverse(a),a) != identity
| multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) != multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a))
| multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)),multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3532,plain,
( multiply(inverse(a),a) != identity
| multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)),multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a))) )],[refute_0_3530,refute_0_3531]) ).
cnf(refute_0_3533,plain,
multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_3529,refute_0_3532]) ).
cnf(refute_0_3534,plain,
( multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) != multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity)
| multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity) != least_upper_bound(X_33,least_upper_bound(a,c))
| multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) = least_upper_bound(X_33,least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)))),bind(Y0,$fot(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity))),bind(Z0,$fot(least_upper_bound(X_33,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3535,plain,
( multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity) != least_upper_bound(X_33,least_upper_bound(a,c))
| multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) = least_upper_bound(X_33,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)),multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity)) )],[refute_0_3533,refute_0_3534]) ).
cnf(refute_0_3536,plain,
multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) = least_upper_bound(X_33,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),identity),least_upper_bound(X_33,least_upper_bound(a,c))) )],[refute_0_3528,refute_0_3535]) ).
cnf(refute_0_3537,plain,
multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a) = multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_33,least_upper_bound(a,c)))),bind(Y,$fot(inverse(a))),bind(Z,$fot(a))]]) ).
cnf(refute_0_3538,plain,
( multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a) != multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a))
| multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) != least_upper_bound(X_33,least_upper_bound(a,c))
| multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a) = least_upper_bound(X_33,least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a))),bind(Y0,$fot(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)))),bind(Z0,$fot(least_upper_bound(X_33,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3539,plain,
( multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)) != least_upper_bound(X_33,least_upper_bound(a,c))
| multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a) = least_upper_bound(X_33,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a),multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a))) )],[refute_0_3537,refute_0_3538]) ).
cnf(refute_0_3540,plain,
multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a) = least_upper_bound(X_33,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),multiply(inverse(a),a)),least_upper_bound(X_33,least_upper_bound(a,c))) )],[refute_0_3536,refute_0_3539]) ).
cnf(refute_0_3541,plain,
inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)) = inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)))]]) ).
cnf(refute_0_3542,plain,
( multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a) != least_upper_bound(X_33,least_upper_bound(a,c))
| inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)) != inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a))
| inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)) = inverse(least_upper_bound(X_33,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)),inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a))) ),[1,0],$fot(least_upper_bound(X_33,least_upper_bound(a,c)))]]) ).
cnf(refute_0_3543,plain,
( multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a) != least_upper_bound(X_33,least_upper_bound(a,c))
| inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)) = inverse(least_upper_bound(X_33,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)),inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a))) )],[refute_0_3541,refute_0_3542]) ).
cnf(refute_0_3544,plain,
inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)) = inverse(least_upper_bound(X_33,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a),least_upper_bound(X_33,least_upper_bound(a,c))) )],[refute_0_3540,refute_0_3543]) ).
cnf(refute_0_3545,plain,
multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) = inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))),bind(X_46,$fot(a))]]) ).
cnf(refute_0_3546,plain,
( multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) != inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a))
| inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)) != inverse(least_upper_bound(X_33,least_upper_bound(a,c)))
| multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) = inverse(least_upper_bound(X_33,least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))))),bind(Y0,$fot(inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)))),bind(Z0,$fot(inverse(least_upper_bound(X_33,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_3547,plain,
( inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)) != inverse(least_upper_bound(X_33,least_upper_bound(a,c)))
| multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) = inverse(least_upper_bound(X_33,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))),inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a))) )],[refute_0_3545,refute_0_3546]) ).
cnf(refute_0_3548,plain,
multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) = inverse(least_upper_bound(X_33,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)),a)),inverse(least_upper_bound(X_33,least_upper_bound(a,c)))) )],[refute_0_3544,refute_0_3547]) ).
cnf(refute_0_3549,plain,
( multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) != inverse(least_upper_bound(X_33,least_upper_bound(a,c)))
| multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) != inverse(least_upper_bound(a,least_upper_bound(c,X_33)))
| inverse(least_upper_bound(X_33,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))),inverse(least_upper_bound(a,least_upper_bound(c,X_33)))) ),[0],$fot(inverse(least_upper_bound(X_33,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3550,plain,
( multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))) != inverse(least_upper_bound(a,least_upper_bound(c,X_33)))
| inverse(least_upper_bound(X_33,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,X_33))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))),inverse(least_upper_bound(X_33,least_upper_bound(a,c)))) )],[refute_0_3548,refute_0_3549]) ).
cnf(refute_0_3551,plain,
inverse(least_upper_bound(X_33,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,X_33))),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(multiply(least_upper_bound(X_33,least_upper_bound(a,c)),inverse(a)))),inverse(least_upper_bound(a,least_upper_bound(c,X_33)))) )],[refute_0_3527,refute_0_3550]) ).
cnf(refute_0_3552,plain,
inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,X_257))),
inference(subst,[],[refute_0_3551:[bind(X_33,$fot(X_257))]]) ).
cnf(refute_0_3553,plain,
( inverse(least_upper_bound(X_257,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,X_257)))
| inverse(least_upper_bound(a,least_upper_bound(c,X_257))) = inverse(least_upper_bound(X_257,least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_257,least_upper_bound(a,c))))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,X_257)))))]]) ).
cnf(refute_0_3554,plain,
inverse(least_upper_bound(a,least_upper_bound(c,X_257))) = inverse(least_upper_bound(X_257,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_257,least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(c,X_257)))) )],[refute_0_3552,refute_0_3553]) ).
cnf(refute_0_3555,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(a,least_upper_bound(c,X_257)))) != identity
| inverse(least_upper_bound(a,least_upper_bound(c,X_257))) != inverse(least_upper_bound(X_257,least_upper_bound(a,c)))
| multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(a,least_upper_bound(c,X_257)))),identity) ),[0,1],$fot(inverse(least_upper_bound(X_257,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3556,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(a,least_upper_bound(c,X_257)))) != identity
| multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,X_257))),inverse(least_upper_bound(X_257,least_upper_bound(a,c)))) )],[refute_0_3554,refute_0_3555]) ).
cnf(refute_0_3557,plain,
multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c)))) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(a,least_upper_bound(c,X_257)))),identity) )],[refute_0_3494,refute_0_3556]) ).
cnf(refute_0_3558,plain,
multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c)))) = identity,
inference(subst,[],[refute_0_3557:[bind(X_257,$fot(X_449))]]) ).
cnf(refute_0_3559,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c)))) != identity
| inverse(least_upper_bound(X_449,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))
| inverse(least_upper_bound(X_449,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_449,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_3560,plain,
( inverse(least_upper_bound(X_449,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))
| inverse(least_upper_bound(X_449,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c)))),identity) )],[refute_0_3558,refute_0_3559]) ).
cnf(refute_0_3561,plain,
inverse(least_upper_bound(X_449,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_449,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) )],[refute_0_3493,refute_0_3560]) ).
cnf(refute_0_3562,plain,
multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(least_upper_bound(a,least_upper_bound(X_449,c)))))]]) ).
cnf(refute_0_3563,plain,
least_upper_bound(identity,identity) = identity,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(identity))]]) ).
cnf(refute_0_3564,plain,
multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_3565,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity))
| least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3566,plain,
( least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity))) )],[refute_0_3564,refute_0_3565]) ).
cnf(refute_0_3567,plain,
multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_3563,refute_0_3566]) ).
cnf(refute_0_3568,plain,
least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))) = least_upper_bound(a,least_upper_bound(X_449,c)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(least_upper_bound(X_449,c))),bind(X_19,$fot(a))]]) ).
cnf(refute_0_3569,plain,
least_upper_bound(c,c) = c,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(c))]]) ).
cnf(refute_0_3570,plain,
least_upper_bound(X_449,least_upper_bound(c,c)) = least_upper_bound(X_449,least_upper_bound(c,c)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_449,least_upper_bound(c,c)))]]) ).
cnf(refute_0_3571,plain,
( least_upper_bound(X_449,least_upper_bound(c,c)) != least_upper_bound(X_449,least_upper_bound(c,c))
| least_upper_bound(c,c) != c
| least_upper_bound(X_449,least_upper_bound(c,c)) = least_upper_bound(X_449,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_449,least_upper_bound(c,c)),least_upper_bound(X_449,least_upper_bound(c,c))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_3572,plain,
( least_upper_bound(c,c) != c
| least_upper_bound(X_449,least_upper_bound(c,c)) = least_upper_bound(X_449,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_449,least_upper_bound(c,c)),least_upper_bound(X_449,least_upper_bound(c,c))) )],[refute_0_3570,refute_0_3571]) ).
cnf(refute_0_3573,plain,
least_upper_bound(X_449,least_upper_bound(c,c)) = least_upper_bound(X_449,c),
inference(resolve,[$cnf( $equal(least_upper_bound(c,c),c) )],[refute_0_3569,refute_0_3572]) ).
cnf(refute_0_3574,plain,
least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))) = least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))))]]) ).
cnf(refute_0_3575,plain,
( least_upper_bound(X_449,least_upper_bound(c,c)) != least_upper_bound(X_449,c)
| least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))) != least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c)))
| least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))),least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c)))) ),[1,1],$fot(least_upper_bound(X_449,c))]]) ).
cnf(refute_0_3576,plain,
( least_upper_bound(X_449,least_upper_bound(c,c)) != least_upper_bound(X_449,c)
| least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))),least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c)))) )],[refute_0_3574,refute_0_3575]) ).
cnf(refute_0_3577,plain,
least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))) = least_upper_bound(a,least_upper_bound(X_449,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_449,least_upper_bound(c,c)),least_upper_bound(X_449,c)) )],[refute_0_3573,refute_0_3576]) ).
cnf(refute_0_3578,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) = least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(least_upper_bound(X_356,X_354)))]]) ).
cnf(refute_0_3579,plain,
least_upper_bound(X_21,least_upper_bound(X_356,X_354)) = least_upper_bound(X_354,least_upper_bound(X_356,X_21)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(X_354)),bind(X_30,$fot(X_21)),bind(X_31,$fot(X_356))]]) ).
cnf(refute_0_3580,plain,
( least_upper_bound(X_21,least_upper_bound(X_356,X_354)) != least_upper_bound(X_354,least_upper_bound(X_356,X_21))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) != least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))),least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))) ),[0,1,1],$fot(least_upper_bound(X_354,least_upper_bound(X_356,X_21)))]]) ).
cnf(refute_0_3581,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) != least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_356,X_354)),least_upper_bound(X_354,least_upper_bound(X_356,X_21))) )],[refute_0_3579,refute_0_3580]) ).
cnf(refute_0_3582,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))),least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))) )],[refute_0_3578,refute_0_3581]) ).
cnf(refute_0_3583,plain,
least_upper_bound(X_356,least_upper_bound(X_356,X_21)) = least_upper_bound(X_356,X_21),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(X_21)),bind(X_19,$fot(X_356))]]) ).
cnf(refute_0_3584,plain,
least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))) = least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))]]) ).
cnf(refute_0_3585,plain,
( least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))) != least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))
| least_upper_bound(X_356,least_upper_bound(X_356,X_21)) != least_upper_bound(X_356,X_21)
| least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))) = least_upper_bound(X_354,least_upper_bound(X_356,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))),least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) ),[1,1],$fot(least_upper_bound(X_356,X_21))]]) ).
cnf(refute_0_3586,plain,
( least_upper_bound(X_356,least_upper_bound(X_356,X_21)) != least_upper_bound(X_356,X_21)
| least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))) = least_upper_bound(X_354,least_upper_bound(X_356,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))),least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) )],[refute_0_3584,refute_0_3585]) ).
cnf(refute_0_3587,plain,
least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))) = least_upper_bound(X_354,least_upper_bound(X_356,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(X_356,X_21)),least_upper_bound(X_356,X_21)) )],[refute_0_3583,refute_0_3586]) ).
cnf(refute_0_3588,plain,
least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))))]]) ).
cnf(refute_0_3589,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))
| least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))) != least_upper_bound(X_354,least_upper_bound(X_356,X_21))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))) ),[1,1],$fot(least_upper_bound(X_354,least_upper_bound(X_356,X_21)))]]) ).
cnf(refute_0_3590,plain,
( least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))) != least_upper_bound(X_354,least_upper_bound(X_356,X_21))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))) )],[refute_0_3588,refute_0_3589]) ).
cnf(refute_0_3591,plain,
least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))),least_upper_bound(X_354,least_upper_bound(X_356,X_21))) )],[refute_0_3587,refute_0_3590]) ).
cnf(refute_0_3592,plain,
least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))),
inference(subst,[],[refute_0_729:[bind(Y,$fot(least_upper_bound(X_356,X_354)))]]) ).
cnf(refute_0_3593,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))
| least_upper_bound(X_21,least_upper_bound(X_356,X_354)) != least_upper_bound(X_354,least_upper_bound(X_356,X_21))
| least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))) ),[1,1,1],$fot(least_upper_bound(X_354,least_upper_bound(X_356,X_21)))]]) ).
cnf(refute_0_3594,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))
| least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_356,X_354)),least_upper_bound(X_354,least_upper_bound(X_356,X_21))) )],[refute_0_3579,refute_0_3593]) ).
cnf(refute_0_3595,plain,
least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))) )],[refute_0_3592,refute_0_3594]) ).
cnf(refute_0_3596,plain,
least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y)))),
inference(subst,[],[refute_0_747:[bind(X_22,$fot(least_upper_bound(X_139,least_upper_bound(X_140,Y))))]]) ).
cnf(refute_0_3597,plain,
( least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))) != least_upper_bound(Y,least_upper_bound(X_139,X_140))
| least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) != least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))))
| least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,X_140))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))),least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_139,X_140)))]]) ).
cnf(refute_0_3598,plain,
( least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) != least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))))
| least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,X_140))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))),least_upper_bound(Y,least_upper_bound(X_139,X_140))) )],[refute_0_1245,refute_0_3597]) ).
cnf(refute_0_3599,plain,
least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))) = least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,X_140))),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_20,least_upper_bound(X_139,least_upper_bound(X_140,Y)))),least_upper_bound(X_20,least_upper_bound(Y,least_upper_bound(X_139,least_upper_bound(X_140,Y))))) )],[refute_0_3596,refute_0_3598]) ).
cnf(refute_0_3600,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356))),
inference(subst,[],[refute_0_3599:[bind(Y,$fot(X_21)),bind(X_139,$fot(X_354)),bind(X_140,$fot(X_356))]]) ).
cnf(refute_0_3601,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) != least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356)))
| least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356)))) ),[0],$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))))]]) ).
cnf(refute_0_3602,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))))
| least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356)))) )],[refute_0_3600,refute_0_3601]) ).
cnf(refute_0_3603,plain,
least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))))) )],[refute_0_3595,refute_0_3602]) ).
cnf(refute_0_3604,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) != least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356)))
| least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356)))))]]) ).
cnf(refute_0_3605,plain,
least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_354,X_356)))) )],[refute_0_3603,refute_0_3604]) ).
cnf(refute_0_3606,plain,
least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))),
inference(subst,[],[refute_0_3605:[bind(X_21,$fot(X_354)),bind(X_354,$fot(least_upper_bound(X_356,X_21)))]]) ).
cnf(refute_0_3607,plain,
least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356))),
inference(subst,[],[refute_0_3599:[bind(Y,$fot(X_354)),bind(X_139,$fot(least_upper_bound(X_356,X_21))),bind(X_140,$fot(X_356))]]) ).
cnf(refute_0_3608,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))
| least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356)))
| least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))))]]) ).
cnf(refute_0_3609,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))
| least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356)))) )],[refute_0_3607,refute_0_3608]) ).
cnf(refute_0_3610,plain,
least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(least_upper_bound(X_356,X_21),X_356))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))) )],[refute_0_3606,refute_0_3609]) ).
cnf(refute_0_3611,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) = least_upper_bound(Y,least_upper_bound(X_31,least_upper_bound(X_356,X_354))),
inference(subst,[],[refute_0_927:[bind(X_30,$fot(least_upper_bound(X_356,X_354)))]]) ).
cnf(refute_0_3612,plain,
least_upper_bound(X_31,least_upper_bound(X_356,X_354)) = least_upper_bound(X_354,least_upper_bound(X_356,X_31)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(X_354)),bind(X_30,$fot(X_31)),bind(X_31,$fot(X_356))]]) ).
cnf(refute_0_3613,plain,
( least_upper_bound(X_31,least_upper_bound(X_356,X_354)) != least_upper_bound(X_354,least_upper_bound(X_356,X_31))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) != least_upper_bound(Y,least_upper_bound(X_31,least_upper_bound(X_356,X_354)))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) = least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)),least_upper_bound(Y,least_upper_bound(X_31,least_upper_bound(X_356,X_354)))) ),[1,1],$fot(least_upper_bound(X_354,least_upper_bound(X_356,X_31)))]]) ).
cnf(refute_0_3614,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) != least_upper_bound(Y,least_upper_bound(X_31,least_upper_bound(X_356,X_354)))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) = least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_356,X_354)),least_upper_bound(X_354,least_upper_bound(X_356,X_31))) )],[refute_0_3612,refute_0_3613]) ).
cnf(refute_0_3615,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) = least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)),least_upper_bound(Y,least_upper_bound(X_31,least_upper_bound(X_356,X_354)))) )],[refute_0_3611,refute_0_3614]) ).
cnf(refute_0_3616,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_356)),bind(Y,$fot(X_354)),bind(Z,$fot(least_upper_bound(X_31,Y)))]]) ).
cnf(refute_0_3617,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) != least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31)))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) != least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y)))
| least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))) = least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)),least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31)))) ),[0],$fot(least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))))]]) ).
cnf(refute_0_3618,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)) != least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31)))
| least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))) = least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)),least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y)))) )],[refute_0_3616,refute_0_3617]) ).
cnf(refute_0_3619,plain,
least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))) = least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_31,Y)),least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31)))) )],[refute_0_3615,refute_0_3618]) ).
cnf(refute_0_3620,plain,
( least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))) != least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31)))
| least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31)))))]]) ).
cnf(refute_0_3621,plain,
least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31))) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_31,Y))),least_upper_bound(Y,least_upper_bound(X_354,least_upper_bound(X_356,X_31)))) )],[refute_0_3619,refute_0_3620]) ).
cnf(refute_0_3622,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))),
inference(subst,[],[refute_0_3621:[bind(Y,$fot(least_upper_bound(X_356,X_354))),bind(X_31,$fot(least_upper_bound(X_356,X_21))),bind(X_354,$fot(X_20)),bind(X_356,$fot(X_354))]]) ).
cnf(refute_0_3623,plain,
( least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) != least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354))))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))))),bind(Y0,$fot(least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))))]]) ).
cnf(refute_0_3624,plain,
( least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))),least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354))))) )],[refute_0_3622,refute_0_3623]) ).
cnf(refute_0_3625,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_354,least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_21),least_upper_bound(X_356,X_354)))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))) )],[refute_0_3610,refute_0_3624]) ).
cnf(refute_0_3626,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))))]]) ).
cnf(refute_0_3627,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21))))) )],[refute_0_3625,refute_0_3626]) ).
cnf(refute_0_3628,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,least_upper_bound(X_356,X_21)))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) )],[refute_0_3591,refute_0_3627]) ).
cnf(refute_0_3629,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) != least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) != least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))),least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))))]]) ).
cnf(refute_0_3630,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) != least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) )],[refute_0_3628,refute_0_3629]) ).
cnf(refute_0_3631,plain,
least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21))),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_356)),bind(Y,$fot(X_354)),bind(Z,$fot(least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_3632,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) != least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))
| least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)) != least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21)))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_3633,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) != least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21)),least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21)))) )],[refute_0_3631,refute_0_3632]) ).
cnf(refute_0_3634,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))) != least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))) )],[refute_0_3630,refute_0_3633]) ).
cnf(refute_0_3635,plain,
least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21)))),least_upper_bound(least_upper_bound(X_356,X_354),least_upper_bound(X_20,X_21))) )],[refute_0_3582,refute_0_3634]) ).
cnf(refute_0_3636,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) != least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21)))
| least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))))),bind(Y0,$fot(least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21)))))]]) ).
cnf(refute_0_3637,plain,
least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),least_upper_bound(X_356,least_upper_bound(X_354,least_upper_bound(X_20,X_21)))) )],[refute_0_3635,refute_0_3636]) ).
cnf(refute_0_3638,plain,
least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) = least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))),
inference(subst,[],[refute_0_3637:[bind(X_20,$fot(a)),bind(X_21,$fot(c)),bind(X_354,$fot(X_449)),bind(X_356,$fot(c))]]) ).
cnf(refute_0_3639,plain,
( least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) != least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c)))
| least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_449,c))))]]) ).
cnf(refute_0_3640,plain,
( least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))),least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c)))) )],[refute_0_3638,refute_0_3639]) ).
cnf(refute_0_3641,plain,
least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) = least_upper_bound(a,least_upper_bound(X_449,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_449,least_upper_bound(c,c))),least_upper_bound(a,least_upper_bound(X_449,c))) )],[refute_0_3577,refute_0_3640]) ).
cnf(refute_0_3642,plain,
least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))) = least_upper_bound(X_449,least_upper_bound(a,c)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(least_upper_bound(a,c))),bind(X_19,$fot(X_449))]]) ).
cnf(refute_0_3643,plain,
inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))) = least_upper_bound(X_449,least_upper_bound(a,c)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(least_upper_bound(X_449,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3644,plain,
least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_3645,plain,
( inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))) != least_upper_bound(X_449,least_upper_bound(a,c))
| least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))
| least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) ),[1,1],$fot(least_upper_bound(X_449,least_upper_bound(a,c)))]]) ).
cnf(refute_0_3646,plain,
( inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))) != least_upper_bound(X_449,least_upper_bound(a,c))
| least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) )],[refute_0_3644,refute_0_3645]) ).
cnf(refute_0_3647,plain,
least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))),least_upper_bound(X_449,least_upper_bound(a,c))) )],[refute_0_3643,refute_0_3646]) ).
cnf(refute_0_3648,plain,
( least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c)))
| least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))) != least_upper_bound(X_449,least_upper_bound(a,c))
| least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(X_449,least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))),bind(Y0,$fot(least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))))),bind(Z0,$fot(least_upper_bound(X_449,least_upper_bound(a,c))))]]) ).
cnf(refute_0_3649,plain,
( least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))) != least_upper_bound(X_449,least_upper_bound(a,c))
| least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(X_449,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c)))) )],[refute_0_3647,refute_0_3648]) ).
cnf(refute_0_3650,plain,
least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(X_449,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_449,least_upper_bound(X_449,least_upper_bound(a,c))),least_upper_bound(X_449,least_upper_bound(a,c))) )],[refute_0_3642,refute_0_3649]) ).
cnf(refute_0_3651,plain,
least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_3652,plain,
( least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(X_449,least_upper_bound(a,c))
| least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))
| least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) ),[1,1],$fot(least_upper_bound(X_449,least_upper_bound(a,c)))]]) ).
cnf(refute_0_3653,plain,
( least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(X_449,least_upper_bound(a,c))
| least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) )],[refute_0_3651,refute_0_3652]) ).
cnf(refute_0_3654,plain,
least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(X_449,least_upper_bound(a,c))) )],[refute_0_3650,refute_0_3653]) ).
cnf(refute_0_3655,plain,
( least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c)))
| least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_449,c))))]]) ).
cnf(refute_0_3656,plain,
( least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c)))) )],[refute_0_3654,refute_0_3655]) ).
cnf(refute_0_3657,plain,
least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(X_449,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_449,least_upper_bound(a,c))),least_upper_bound(a,least_upper_bound(X_449,c))) )],[refute_0_3641,refute_0_3656]) ).
cnf(refute_0_3658,plain,
least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_131:[bind(X,$fot(c)),bind(Y,$fot(X_449)),bind(Z,$fot(inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_3659,plain,
( least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))
| least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_449,c))))]]) ).
cnf(refute_0_3660,plain,
( least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) )],[refute_0_3658,refute_0_3659]) ).
cnf(refute_0_3661,plain,
least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_449,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_449,inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(X_449,c))) )],[refute_0_3657,refute_0_3660]) ).
cnf(refute_0_3662,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_3663,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))
| least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) ),[1,1],$fot(least_upper_bound(a,least_upper_bound(X_449,c)))]]) ).
cnf(refute_0_3664,plain,
( least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) )],[refute_0_3662,refute_0_3663]) ).
cnf(refute_0_3665,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(X_449,c))) )],[refute_0_3661,refute_0_3664]) ).
cnf(refute_0_3666,plain,
( least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c)))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_449,c))))]]) ).
cnf(refute_0_3667,plain,
( least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c)))) )],[refute_0_3665,refute_0_3666]) ).
cnf(refute_0_3668,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = least_upper_bound(a,least_upper_bound(X_449,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(a,least_upper_bound(X_449,c))) )],[refute_0_3568,refute_0_3667]) ).
cnf(refute_0_3669,plain,
least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_131:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(c,X_449))),bind(Z,$fot(inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_3670,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))
| least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_449,c))))]]) ).
cnf(refute_0_3671,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_449,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) )],[refute_0_3669,refute_0_3670]) ).
cnf(refute_0_3672,plain,
least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_449,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_449),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(X_449,c))) )],[refute_0_3668,refute_0_3671]) ).
cnf(refute_0_3673,plain,
inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_3674,plain,
( inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))
| least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) ),[1,0],$fot(least_upper_bound(a,least_upper_bound(X_449,c)))]]) ).
cnf(refute_0_3675,plain,
( least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(X_449,c))
| inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))))) )],[refute_0_3673,refute_0_3674]) ).
cnf(refute_0_3676,plain,
inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(X_449,c))) )],[refute_0_3672,refute_0_3675]) ).
cnf(refute_0_3677,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_3678,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != inverse(least_upper_bound(a,least_upper_bound(X_449,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity))) ),[1,0],$fot(inverse(least_upper_bound(a,least_upper_bound(X_449,c))))]]) ).
cnf(refute_0_3679,plain,
( inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))) != inverse(least_upper_bound(a,least_upper_bound(X_449,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity))) )],[refute_0_3677,refute_0_3678]) ).
cnf(refute_0_3680,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),inverse(least_upper_bound(a,least_upper_bound(X_449,c)))) )],[refute_0_3676,refute_0_3679]) ).
cnf(refute_0_3681,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity))
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity)))]]) ).
cnf(refute_0_3682,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity))) )],[refute_0_3680,refute_0_3681]) ).
cnf(refute_0_3683,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity)) )],[refute_0_3567,refute_0_3682]) ).
cnf(refute_0_3684,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity) != inverse(least_upper_bound(a,least_upper_bound(X_449,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(X_449,c)))))]]) ).
cnf(refute_0_3685,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity) != inverse(least_upper_bound(a,least_upper_bound(X_449,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity)) )],[refute_0_3683,refute_0_3684]) ).
cnf(refute_0_3686,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_449,c))),identity),inverse(least_upper_bound(a,least_upper_bound(X_449,c)))) )],[refute_0_3562,refute_0_3685]) ).
cnf(refute_0_3687,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)) != inverse(least_upper_bound(a,least_upper_bound(X_449,c)))
| inverse(least_upper_bound(X_449,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_449,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_449,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity))) ),[1],$fot(inverse(least_upper_bound(a,least_upper_bound(X_449,c))))]]) ).
cnf(refute_0_3688,plain,
( inverse(least_upper_bound(X_449,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_449,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity)),inverse(least_upper_bound(a,least_upper_bound(X_449,c)))) )],[refute_0_3686,refute_0_3687]) ).
cnf(refute_0_3689,plain,
inverse(least_upper_bound(X_449,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(X_449,c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_449,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(a,least_upper_bound(c,X_449)),inverse(inverse(least_upper_bound(X_449,least_upper_bound(a,c)))))),least_upper_bound(identity,identity))) )],[refute_0_3561,refute_0_3688]) ).
cnf(refute_0_3690,plain,
inverse(least_upper_bound(identity,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(identity,c))),
inference(subst,[],[refute_0_3689:[bind(X_449,$fot(identity))]]) ).
cnf(refute_0_3691,plain,
( inverse(least_upper_bound(a,least_upper_bound(identity,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| inverse(least_upper_bound(identity,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(identity,c)))
| inverse(least_upper_bound(identity,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,least_upper_bound(a,c))))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(identity,c))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity)))))]]) ).
cnf(refute_0_3692,plain,
( inverse(least_upper_bound(a,least_upper_bound(identity,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| inverse(least_upper_bound(identity,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(identity,c)))) )],[refute_0_3690,refute_0_3691]) ).
cnf(refute_0_3693,plain,
inverse(least_upper_bound(identity,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(identity,c))),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_3492,refute_0_3692]) ).
cnf(refute_0_3694,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)),
inference(subst,[],[refute_0_2039:[bind(X_213,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3695,plain,
least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(greatest_lower_bound(identity,least_upper_bound(a,c)))),bind(X_46,$fot(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3696,plain,
multiply(greatest_lower_bound(X_154,X_155),inverse(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)))) = inverse(inverse(X_155)),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(inverse(X_155))),bind(X_55,$fot(greatest_lower_bound(X_154,X_155)))]]) ).
cnf(refute_0_3697,plain,
( multiply(greatest_lower_bound(X_154,X_155),inverse(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)))) != inverse(inverse(X_155))
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(identity,multiply(inverse(X_155),X_154))
| multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) = inverse(inverse(X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_154,X_155),inverse(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)))),inverse(inverse(X_155))) ),[0,1,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))]]) ).
cnf(refute_0_3698,plain,
( multiply(greatest_lower_bound(X_154,X_155),inverse(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)))) != inverse(inverse(X_155))
| multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) = inverse(inverse(X_155)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)),greatest_lower_bound(identity,multiply(inverse(X_155),X_154))) )],[refute_0_110,refute_0_3697]) ).
cnf(refute_0_3699,plain,
multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) = inverse(inverse(X_155)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_154,X_155),inverse(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)))),inverse(inverse(X_155))) )],[refute_0_3696,refute_0_3698]) ).
cnf(refute_0_3700,plain,
inverse(inverse(X_155)) = X_155,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_155))]]) ).
cnf(refute_0_3701,plain,
( multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) != inverse(inverse(X_155))
| inverse(inverse(X_155)) != X_155
| multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) = X_155 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))),X_155) ),[0],$fot(inverse(inverse(X_155)))]]) ).
cnf(refute_0_3702,plain,
( multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) != inverse(inverse(X_155))
| multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) = X_155 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_155)),X_155) )],[refute_0_3700,refute_0_3701]) ).
cnf(refute_0_3703,plain,
multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))) = X_155,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_154,X_155),inverse(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))),inverse(inverse(X_155))) )],[refute_0_3699,refute_0_3702]) ).
cnf(refute_0_3704,plain,
multiply(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))),
inference(subst,[],[refute_0_3703:[bind(X_154,$fot(identity)),bind(X_155,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3705,plain,
( multiply(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != greatest_lower_bound(identity,least_upper_bound(a,c))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) ),[0,0],$fot(greatest_lower_bound(identity,least_upper_bound(a,c)))]]) ).
cnf(refute_0_3706,plain,
( multiply(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),greatest_lower_bound(identity,least_upper_bound(a,c))) )],[refute_0_3288,refute_0_3705]) ).
cnf(refute_0_3707,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) )],[refute_0_3704,refute_0_3706]) ).
cnf(refute_0_3708,plain,
inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) = least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3709,plain,
multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity) = inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3710,plain,
inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(inverse(X_87))),bind(X_46,$fot(least_upper_bound(identity,X_87)))]]) ).
cnf(refute_0_3711,plain,
multiply(inverse(X_87),least_upper_bound(identity,X_87)) = least_upper_bound(identity,inverse(X_87)),
inference(subst,[],[refute_0_74:[bind(X_86,$fot(X_87))]]) ).
cnf(refute_0_3712,plain,
( multiply(inverse(X_87),least_upper_bound(identity,X_87)) != least_upper_bound(identity,inverse(X_87))
| inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))
| inverse(least_upper_bound(identity,inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))),multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_87)))]]) ).
cnf(refute_0_3713,plain,
( inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))
| inverse(least_upper_bound(identity,inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),least_upper_bound(identity,X_87)),least_upper_bound(identity,inverse(X_87))) )],[refute_0_3711,refute_0_3712]) ).
cnf(refute_0_3714,plain,
inverse(least_upper_bound(identity,inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))),multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))) )],[refute_0_3710,refute_0_3713]) ).
cnf(refute_0_3715,plain,
inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),X_87),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(X_87)),bind(X_74,$fot(least_upper_bound(identity,X_87)))]]) ).
cnf(refute_0_3716,plain,
multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) = inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(inverse(X_87))),bind(X_46,$fot(least_upper_bound(identity,X_87)))]]) ).
cnf(refute_0_3717,plain,
( multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) != inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87)))
| inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),X_87)
| multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),X_87) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))))),bind(Y0,$fot(inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,X_87)),X_87)))]]) ).
cnf(refute_0_3718,plain,
( inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),X_87)
| multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),X_87) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))),inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87)))) )],[refute_0_3716,refute_0_3717]) ).
cnf(refute_0_3719,plain,
multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),X_87),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_87),least_upper_bound(identity,X_87))),multiply(inverse(least_upper_bound(identity,X_87)),X_87)) )],[refute_0_3715,refute_0_3718]) ).
cnf(refute_0_3720,plain,
( multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),X_87)
| inverse(least_upper_bound(identity,inverse(X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))
| inverse(least_upper_bound(identity,inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),X_87) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))) ),[1],$fot(multiply(inverse(least_upper_bound(identity,X_87)),X_87))]]) ).
cnf(refute_0_3721,plain,
( inverse(least_upper_bound(identity,inverse(X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))
| inverse(least_upper_bound(identity,inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),X_87) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87))),multiply(inverse(least_upper_bound(identity,X_87)),X_87)) )],[refute_0_3719,refute_0_3720]) ).
cnf(refute_0_3722,plain,
inverse(least_upper_bound(identity,inverse(X_87))) = multiply(inverse(least_upper_bound(identity,X_87)),X_87),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),multiply(inverse(least_upper_bound(identity,X_87)),inverse(inverse(X_87)))) )],[refute_0_3714,refute_0_3721]) ).
cnf(refute_0_3723,plain,
inverse(inverse(greatest_lower_bound(X_87,identity))) = greatest_lower_bound(X_87,identity),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(X_87,identity)))]]) ).
cnf(refute_0_3724,plain,
least_upper_bound(identity,inverse(X_87)) = inverse(greatest_lower_bound(X_87,identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(X_87))]]) ).
cnf(refute_0_3725,plain,
inverse(least_upper_bound(identity,inverse(X_87))) = inverse(least_upper_bound(identity,inverse(X_87))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(X_87))))]]) ).
cnf(refute_0_3726,plain,
( inverse(least_upper_bound(identity,inverse(X_87))) != inverse(least_upper_bound(identity,inverse(X_87)))
| least_upper_bound(identity,inverse(X_87)) != inverse(greatest_lower_bound(X_87,identity))
| inverse(least_upper_bound(identity,inverse(X_87))) = inverse(inverse(greatest_lower_bound(X_87,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),inverse(least_upper_bound(identity,inverse(X_87)))) ),[1,0],$fot(inverse(greatest_lower_bound(X_87,identity)))]]) ).
cnf(refute_0_3727,plain,
( least_upper_bound(identity,inverse(X_87)) != inverse(greatest_lower_bound(X_87,identity))
| inverse(least_upper_bound(identity,inverse(X_87))) = inverse(inverse(greatest_lower_bound(X_87,identity))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),inverse(least_upper_bound(identity,inverse(X_87)))) )],[refute_0_3725,refute_0_3726]) ).
cnf(refute_0_3728,plain,
inverse(least_upper_bound(identity,inverse(X_87))) = inverse(inverse(greatest_lower_bound(X_87,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_87)),inverse(greatest_lower_bound(X_87,identity))) )],[refute_0_3724,refute_0_3727]) ).
cnf(refute_0_3729,plain,
( inverse(inverse(greatest_lower_bound(X_87,identity))) != greatest_lower_bound(X_87,identity)
| inverse(least_upper_bound(identity,inverse(X_87))) != inverse(inverse(greatest_lower_bound(X_87,identity)))
| inverse(least_upper_bound(identity,inverse(X_87))) = greatest_lower_bound(X_87,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_87))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(X_87,identity))))),bind(Z0,$fot(greatest_lower_bound(X_87,identity)))]]) ).
cnf(refute_0_3730,plain,
( inverse(inverse(greatest_lower_bound(X_87,identity))) != greatest_lower_bound(X_87,identity)
| inverse(least_upper_bound(identity,inverse(X_87))) = greatest_lower_bound(X_87,identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),inverse(inverse(greatest_lower_bound(X_87,identity)))) )],[refute_0_3728,refute_0_3729]) ).
cnf(refute_0_3731,plain,
inverse(least_upper_bound(identity,inverse(X_87))) = greatest_lower_bound(X_87,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_87,identity))),greatest_lower_bound(X_87,identity)) )],[refute_0_3723,refute_0_3730]) ).
cnf(refute_0_3732,plain,
( inverse(least_upper_bound(identity,inverse(X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),X_87)
| inverse(least_upper_bound(identity,inverse(X_87))) != greatest_lower_bound(X_87,identity)
| greatest_lower_bound(X_87,identity) = multiply(inverse(least_upper_bound(identity,X_87)),X_87) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),multiply(inverse(least_upper_bound(identity,X_87)),X_87)) ),[0],$fot(greatest_lower_bound(X_87,identity))]]) ).
cnf(refute_0_3733,plain,
( inverse(least_upper_bound(identity,inverse(X_87))) != multiply(inverse(least_upper_bound(identity,X_87)),X_87)
| greatest_lower_bound(X_87,identity) = multiply(inverse(least_upper_bound(identity,X_87)),X_87) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),greatest_lower_bound(X_87,identity)) )],[refute_0_3731,refute_0_3732]) ).
cnf(refute_0_3734,plain,
greatest_lower_bound(X_87,identity) = multiply(inverse(least_upper_bound(identity,X_87)),X_87),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_87))),multiply(inverse(least_upper_bound(identity,X_87)),X_87)) )],[refute_0_3722,refute_0_3733]) ).
cnf(refute_0_3735,plain,
greatest_lower_bound(multiply(inverse(X_84),X_83),identity) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(X_84),X_83)),
inference(subst,[],[refute_0_3734:[bind(X_87,$fot(multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_3736,plain,
( greatest_lower_bound(multiply(inverse(X_84),X_83),identity) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(X_84),X_83))
| least_upper_bound(identity,multiply(inverse(X_84),X_83)) != multiply(inverse(X_84),least_upper_bound(X_83,X_84))
| greatest_lower_bound(multiply(inverse(X_84),X_83),identity) = multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_84),X_83),identity),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(X_84),X_83))) ),[1,0,0],$fot(multiply(inverse(X_84),least_upper_bound(X_83,X_84)))]]) ).
cnf(refute_0_3737,plain,
( greatest_lower_bound(multiply(inverse(X_84),X_83),identity) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(X_84),X_83))
| greatest_lower_bound(multiply(inverse(X_84),X_83),identity) = multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_84),X_83)),multiply(inverse(X_84),least_upper_bound(X_83,X_84))) )],[refute_0_2042,refute_0_3736]) ).
cnf(refute_0_3738,plain,
greatest_lower_bound(multiply(inverse(X_84),X_83),identity) = multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_84),X_83),identity),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_84),X_83))),multiply(inverse(X_84),X_83))) )],[refute_0_3735,refute_0_3737]) ).
cnf(refute_0_3739,plain,
greatest_lower_bound(multiply(inverse(X_84),X_83),identity) = greatest_lower_bound(identity,multiply(inverse(X_84),X_83)),
inference(subst,[],[refute_0_2134:[bind(X_154,$fot(multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_3740,plain,
( greatest_lower_bound(multiply(inverse(X_84),X_83),identity) != multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))
| greatest_lower_bound(multiply(inverse(X_84),X_83),identity) != greatest_lower_bound(identity,multiply(inverse(X_84),X_83))
| greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_84),X_83),identity),multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_3741,plain,
( greatest_lower_bound(multiply(inverse(X_84),X_83),identity) != multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))
| greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_84),X_83),identity),greatest_lower_bound(identity,multiply(inverse(X_84),X_83))) )],[refute_0_3739,refute_0_3740]) ).
cnf(refute_0_3742,plain,
( X_46 != multiply(X_50,multiply(inverse(X_50),X_46))
| multiply(X_50,multiply(inverse(X_50),X_46)) = X_46 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(X_50,multiply(inverse(X_50),X_46))))]]) ).
cnf(refute_0_3743,plain,
multiply(X_50,multiply(inverse(X_50),X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(X_50,multiply(inverse(X_50),X_46))) )],[refute_0_823,refute_0_3742]) ).
cnf(refute_0_3744,plain,
multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84))) = least_upper_bound(X_83,X_84),
inference(subst,[],[refute_0_3743:[bind(X_46,$fot(least_upper_bound(X_83,X_84))),bind(X_50,$fot(X_84))]]) ).
cnf(refute_0_3745,plain,
inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) = inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))))]]) ).
cnf(refute_0_3746,plain,
( multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84))) != least_upper_bound(X_83,X_84)
| inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) != inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84))))
| inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) = inverse(least_upper_bound(X_83,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84))))) ),[1,0],$fot(least_upper_bound(X_83,X_84))]]) ).
cnf(refute_0_3747,plain,
( multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84))) != least_upper_bound(X_83,X_84)
| inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) = inverse(least_upper_bound(X_83,X_84)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84))))) )],[refute_0_3745,refute_0_3746]) ).
cnf(refute_0_3748,plain,
inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) = inverse(least_upper_bound(X_83,X_84)),
inference(resolve,[$cnf( $equal(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84))),least_upper_bound(X_83,X_84)) )],[refute_0_3744,refute_0_3747]) ).
cnf(refute_0_3749,plain,
multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83) = multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83))]]) ).
cnf(refute_0_3750,plain,
( multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83) != multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83)
| inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) != inverse(least_upper_bound(X_83,X_84))
| multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83),multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83)) ),[1,0],$fot(inverse(least_upper_bound(X_83,X_84)))]]) ).
cnf(refute_0_3751,plain,
( inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))) != inverse(least_upper_bound(X_83,X_84))
| multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83),multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83)) )],[refute_0_3749,refute_0_3750]) ).
cnf(refute_0_3752,plain,
multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83),
inference(resolve,[$cnf( $equal(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),inverse(least_upper_bound(X_83,X_84))) )],[refute_0_3748,refute_0_3751]) ).
cnf(refute_0_3753,plain,
multiply(multiply(inverse(X_74),inverse(X_73)),Z) = multiply(inverse(X_74),multiply(inverse(X_73),Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_74))),bind(Y,$fot(inverse(X_73)))]]) ).
cnf(refute_0_3754,plain,
inverse(multiply(X_73,X_74)) = multiply(inverse(X_74),inverse(X_73)),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(X_73)),bind(X_46,$fot(X_74))]]) ).
cnf(refute_0_3755,plain,
( inverse(multiply(X_73,X_74)) != multiply(inverse(X_74),inverse(X_73))
| multiply(inverse(X_74),inverse(X_73)) = inverse(multiply(X_73,X_74)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(multiply(X_73,X_74)))),bind(Y0,$fot(multiply(inverse(X_74),inverse(X_73))))]]) ).
cnf(refute_0_3756,plain,
multiply(inverse(X_74),inverse(X_73)) = inverse(multiply(X_73,X_74)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_73,X_74)),multiply(inverse(X_74),inverse(X_73))) )],[refute_0_3754,refute_0_3755]) ).
cnf(refute_0_3757,plain,
( multiply(multiply(inverse(X_74),inverse(X_73)),Z) != multiply(inverse(X_74),multiply(inverse(X_73),Z))
| multiply(inverse(X_74),inverse(X_73)) != inverse(multiply(X_73,X_74))
| multiply(inverse(multiply(X_73,X_74)),Z) = multiply(inverse(X_74),multiply(inverse(X_73),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_74),inverse(X_73)),Z),multiply(inverse(X_74),multiply(inverse(X_73),Z))) ),[0,0],$fot(inverse(multiply(X_73,X_74)))]]) ).
cnf(refute_0_3758,plain,
( multiply(multiply(inverse(X_74),inverse(X_73)),Z) != multiply(inverse(X_74),multiply(inverse(X_73),Z))
| multiply(inverse(multiply(X_73,X_74)),Z) = multiply(inverse(X_74),multiply(inverse(X_73),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_74),inverse(X_73)),inverse(multiply(X_73,X_74))) )],[refute_0_3756,refute_0_3757]) ).
cnf(refute_0_3759,plain,
multiply(inverse(multiply(X_73,X_74)),Z) = multiply(inverse(X_74),multiply(inverse(X_73),Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_74),inverse(X_73)),Z),multiply(inverse(X_74),multiply(inverse(X_73),Z))) )],[refute_0_3753,refute_0_3758]) ).
cnf(refute_0_3760,plain,
( multiply(inverse(multiply(X_73,X_74)),Z) != multiply(inverse(X_74),multiply(inverse(X_73),Z))
| multiply(inverse(X_74),multiply(inverse(X_73),Z)) = multiply(inverse(multiply(X_73,X_74)),Z) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(multiply(X_73,X_74)),Z))),bind(Y0,$fot(multiply(inverse(X_74),multiply(inverse(X_73),Z))))]]) ).
cnf(refute_0_3761,plain,
multiply(inverse(X_74),multiply(inverse(X_73),Z)) = multiply(inverse(multiply(X_73,X_74)),Z),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_73,X_74)),Z),multiply(inverse(X_74),multiply(inverse(X_73),Z))) )],[refute_0_3759,refute_0_3760]) ).
cnf(refute_0_3762,plain,
multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) = multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83),
inference(subst,[],[refute_0_3761:[bind(Z,$fot(X_83)),bind(X_73,$fot(X_84)),bind(X_74,$fot(multiply(inverse(X_84),least_upper_bound(X_83,X_84))))]]) ).
cnf(refute_0_3763,plain,
( multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83) != multiply(inverse(least_upper_bound(X_83,X_84)),X_83)
| multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) != multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83)
| multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)))),bind(Y0,$fot(multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_83,X_84)),X_83)))]]) ).
cnf(refute_0_3764,plain,
( multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83) != multiply(inverse(least_upper_bound(X_83,X_84)),X_83)
| multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)),multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83)) )],[refute_0_3762,refute_0_3763]) ).
cnf(refute_0_3765,plain,
multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_84,multiply(inverse(X_84),least_upper_bound(X_83,X_84)))),X_83),multiply(inverse(least_upper_bound(X_83,X_84)),X_83)) )],[refute_0_3752,refute_0_3764]) ).
cnf(refute_0_3766,plain,
( multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)) != multiply(inverse(least_upper_bound(X_83,X_84)),X_83)
| greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) != multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))
| greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_84),X_83)),multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))) ),[1],$fot(multiply(inverse(least_upper_bound(X_83,X_84)),X_83))]]) ).
cnf(refute_0_3767,plain,
( greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) != multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))
| greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83)),multiply(inverse(least_upper_bound(X_83,X_84)),X_83)) )],[refute_0_3765,refute_0_3766]) ).
cnf(refute_0_3768,plain,
( greatest_lower_bound(multiply(inverse(X_84),X_83),identity) != multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))
| greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_84),X_83)),multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))) )],[refute_0_3741,refute_0_3767]) ).
cnf(refute_0_3769,plain,
greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) = multiply(inverse(least_upper_bound(X_83,X_84)),X_83),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_84),X_83),identity),multiply(inverse(multiply(inverse(X_84),least_upper_bound(X_83,X_84))),multiply(inverse(X_84),X_83))) )],[refute_0_3738,refute_0_3768]) ).
cnf(refute_0_3770,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity),
inference(subst,[],[refute_0_3769:[bind(X_83,$fot(identity)),bind(X_84,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3771,plain,
( multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity) != inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) != multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity)
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))]]) ).
cnf(refute_0_3772,plain,
( multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity) != inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)),multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity)) )],[refute_0_3770,refute_0_3771]) ).
cnf(refute_0_3773,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) = inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3709,refute_0_3772]) ).
cnf(refute_0_3774,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) = inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))))]]) ).
cnf(refute_0_3775,plain,
( greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) != inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) != inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) = inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) ),[1,0],$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3776,plain,
( greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)) != inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) = inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) )],[refute_0_3774,refute_0_3775]) ).
cnf(refute_0_3777,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) = inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)),inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3773,refute_0_3776]) ).
cnf(refute_0_3778,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) != inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))
| inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) = least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3779,plain,
( inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) != least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) = least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))),inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) )],[refute_0_3777,refute_0_3778]) ).
cnf(refute_0_3780,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) = least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) )],[refute_0_3708,refute_0_3779]) ).
cnf(refute_0_3781,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))))]]) ).
cnf(refute_0_3782,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) != multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))))
| inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) != least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))))) ),[1,1],$fot(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3783,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))) != least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))))) )],[refute_0_3781,refute_0_3782]) ).
cnf(refute_0_3784,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) = multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) )],[refute_0_3780,refute_0_3783]) ).
cnf(refute_0_3785,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) != multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) ),[0],$fot(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))]]) ).
cnf(refute_0_3786,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
| multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3784,refute_0_3785]) ).
cnf(refute_0_3787,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),identity)))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) )],[refute_0_3707,refute_0_3786]) ).
cnf(refute_0_3788,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) ),[1,1],$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3789,plain,
( least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) )],[refute_0_3787,refute_0_3788]) ).
cnf(refute_0_3790,plain,
least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))) )],[refute_0_3695,refute_0_3789]) ).
cnf(refute_0_3791,plain,
multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89) = least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_89)),bind(Y,$fot(a)),bind(Z,$fot(least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_3792,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89) != least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89))
| least_upper_bound(a,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(X_33,c))
| multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) = least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89),least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89))) ),[0,0],$fot(least_upper_bound(a,least_upper_bound(X_33,c)))]]) ).
cnf(refute_0_3793,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89) != least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89))
| multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) = least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(X_33,c))) )],[refute_0_3505,refute_0_3792]) ).
cnf(refute_0_3794,plain,
multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) = least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89),least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89))) )],[refute_0_3791,refute_0_3793]) ).
cnf(refute_0_3795,plain,
least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)) = multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89),
inference(subst,[],[refute_0_630:[bind(X,$fot(X_89)),bind(Y,$fot(a)),bind(Z,$fot(least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_3796,plain,
( multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) != least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89))
| least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)) != multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89)
| multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) = multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89),multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89)) ),[0],$fot(least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)))]]) ).
cnf(refute_0_3797,plain,
( multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) != least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89))
| multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) = multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89)),multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89)) )],[refute_0_3795,refute_0_3796]) ).
cnf(refute_0_3798,plain,
multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89) = multiply(least_upper_bound(a,least_upper_bound(c,X_33)),X_89),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(X_33,c)),X_89),least_upper_bound(multiply(a,X_89),multiply(least_upper_bound(c,X_33),X_89))) )],[refute_0_3794,refute_0_3797]) ).
cnf(refute_0_3799,plain,
multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),
inference(subst,[],[refute_0_3798:[bind(X_33,$fot(identity)),bind(X_89,$fot(inverse(least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3800,plain,
multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89) = least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_89)),bind(Y,$fot(X_90)),bind(Z,$fot(least_upper_bound(X_21,X)))]]) ).
cnf(refute_0_3801,plain,
least_upper_bound(X,least_upper_bound(X_90,X_21)) = least_upper_bound(X_90,least_upper_bound(X_21,X)),
inference(subst,[],[refute_0_680:[bind(X_20,$fot(X_90))]]) ).
cnf(refute_0_3802,plain,
( least_upper_bound(X,least_upper_bound(X_90,X_21)) != least_upper_bound(X_90,least_upper_bound(X_21,X))
| least_upper_bound(X_90,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(X_90,X_21)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_90,X_21)))),bind(Y0,$fot(least_upper_bound(X_90,least_upper_bound(X_21,X))))]]) ).
cnf(refute_0_3803,plain,
least_upper_bound(X_90,least_upper_bound(X_21,X)) = least_upper_bound(X,least_upper_bound(X_90,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_90,X_21)),least_upper_bound(X_90,least_upper_bound(X_21,X))) )],[refute_0_3801,refute_0_3802]) ).
cnf(refute_0_3804,plain,
( multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89))
| least_upper_bound(X_90,least_upper_bound(X_21,X)) != least_upper_bound(X,least_upper_bound(X_90,X_21))
| multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) = least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89),least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89))) ),[0,0],$fot(least_upper_bound(X,least_upper_bound(X_90,X_21)))]]) ).
cnf(refute_0_3805,plain,
( multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89))
| multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) = least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_90,least_upper_bound(X_21,X)),least_upper_bound(X,least_upper_bound(X_90,X_21))) )],[refute_0_3803,refute_0_3804]) ).
cnf(refute_0_3806,plain,
multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) = least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89),least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89))) )],[refute_0_3800,refute_0_3805]) ).
cnf(refute_0_3807,plain,
least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)) = multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89),
inference(subst,[],[refute_0_630:[bind(X,$fot(X_89)),bind(Y,$fot(X_90)),bind(Z,$fot(least_upper_bound(X_21,X)))]]) ).
cnf(refute_0_3808,plain,
( multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89))
| least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)) != multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89)
| multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) = multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89),multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89)) ),[0],$fot(least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)))]]) ).
cnf(refute_0_3809,plain,
( multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) != least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89))
| multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) = multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89)),multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89)) )],[refute_0_3807,refute_0_3808]) ).
cnf(refute_0_3810,plain,
multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89) = multiply(least_upper_bound(X_90,least_upper_bound(X_21,X)),X_89),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X,least_upper_bound(X_90,X_21)),X_89),least_upper_bound(multiply(X_90,X_89),multiply(least_upper_bound(X_21,X),X_89))) )],[refute_0_3806,refute_0_3809]) ).
cnf(refute_0_3811,plain,
multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity))),
inference(subst,[],[refute_0_3810:[bind(X,$fot(c)),bind(X_21,$fot(identity)),bind(X_89,$fot(inverse(least_upper_bound(b,identity)))),bind(X_90,$fot(a))]]) ).
cnf(refute_0_3812,plain,
( multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))))),bind(Y0,$fot(multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity))))),bind(Z0,$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3813,plain,
( multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))),multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3811,refute_0_3812]) ).
cnf(refute_0_3814,plain,
multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(identity,c)),inverse(least_upper_bound(b,identity))),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3799,refute_0_3813]) ).
cnf(refute_0_3815,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)),
inference(subst,[],[monotony_lub2:[bind(Z,$fot(least_upper_bound(X_356,X_354)))]]) ).
cnf(refute_0_3816,plain,
least_upper_bound(Y,least_upper_bound(X_356,X_354)) = least_upper_bound(X_354,least_upper_bound(X_356,Y)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(X_354)),bind(X_30,$fot(Y)),bind(X_31,$fot(X_356))]]) ).
cnf(refute_0_3817,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X))
| least_upper_bound(Y,least_upper_bound(X_356,X_354)) != least_upper_bound(X_354,least_upper_bound(X_356,Y))
| multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X))) ),[0,0],$fot(least_upper_bound(X_354,least_upper_bound(X_356,Y)))]]) ).
cnf(refute_0_3818,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X))
| multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_356,X_354)),least_upper_bound(X_354,least_upper_bound(X_356,Y))) )],[refute_0_3816,refute_0_3817]) ).
cnf(refute_0_3819,plain,
multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X))) )],[refute_0_3815,refute_0_3818]) ).
cnf(refute_0_3820,plain,
least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)) = multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X),
inference(subst,[],[refute_0_630:[bind(Z,$fot(least_upper_bound(X_356,X_354)))]]) ).
cnf(refute_0_3821,plain,
( multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X))
| least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)) != multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X)
| multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X),multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X)) ),[0],$fot(least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)))]]) ).
cnf(refute_0_3822,plain,
( multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X))
| multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X)),multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X)) )],[refute_0_3820,refute_0_3821]) ).
cnf(refute_0_3823,plain,
multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_356,X_354),X))) )],[refute_0_3819,refute_0_3822]) ).
cnf(refute_0_3824,plain,
( multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) != multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X)
| multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X) = multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X))),bind(Y0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X)))]]) ).
cnf(refute_0_3825,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X) = multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_354,least_upper_bound(X_356,Y)),X),multiply(least_upper_bound(Y,least_upper_bound(X_356,X_354)),X)) )],[refute_0_3823,refute_0_3824]) ).
cnf(refute_0_3826,plain,
multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))),
inference(subst,[],[refute_0_3825:[bind(X,$fot(inverse(least_upper_bound(b,identity)))),bind(Y,$fot(identity)),bind(X_354,$fot(c)),bind(X_356,$fot(a))]]) ).
cnf(refute_0_3827,plain,
( multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))))),bind(Y0,$fot(multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))))),bind(Z0,$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3828,plain,
( multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))),multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3826,refute_0_3827]) ).
cnf(refute_0_3829,plain,
multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(c,least_upper_bound(a,identity)),inverse(least_upper_bound(b,identity))),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3814,refute_0_3828]) ).
cnf(refute_0_3830,plain,
multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))),
inference(subst,[],[refute_0_2389:[bind(X,$fot(inverse(least_upper_bound(b,identity)))),bind(Y,$fot(least_upper_bound(a,c))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_3831,plain,
( multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))))),bind(Z0,$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3832,plain,
( multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))),multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3830,refute_0_3831]) ).
cnf(refute_0_3833,plain,
multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(a,c)),inverse(least_upper_bound(b,identity))),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3829,refute_0_3832]) ).
cnf(refute_0_3834,plain,
multiply(multiply(inverse(greatest_lower_bound(identity,Y)),Y),Z) = multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_3835,plain,
inverse(greatest_lower_bound(identity,inverse(Y))) = multiply(inverse(greatest_lower_bound(identity,Y)),Y),
inference(subst,[],[refute_0_3089:[bind(X_164,$fot(Y))]]) ).
cnf(refute_0_3836,plain,
( inverse(greatest_lower_bound(identity,inverse(Y))) != multiply(inverse(greatest_lower_bound(identity,Y)),Y)
| multiply(inverse(greatest_lower_bound(identity,Y)),Y) = inverse(greatest_lower_bound(identity,inverse(Y))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(Y))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,Y)),Y)))]]) ).
cnf(refute_0_3837,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),Y) = inverse(greatest_lower_bound(identity,inverse(Y))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(Y))),multiply(inverse(greatest_lower_bound(identity,Y)),Y)) )],[refute_0_3835,refute_0_3836]) ).
cnf(refute_0_3838,plain,
( multiply(multiply(inverse(greatest_lower_bound(identity,Y)),Y),Z) != multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))
| multiply(inverse(greatest_lower_bound(identity,Y)),Y) != inverse(greatest_lower_bound(identity,inverse(Y)))
| multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) = multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(identity,Y)),Y),Z),multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))) ),[0,0],$fot(inverse(greatest_lower_bound(identity,inverse(Y))))]]) ).
cnf(refute_0_3839,plain,
( multiply(multiply(inverse(greatest_lower_bound(identity,Y)),Y),Z) != multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) = multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),Y),inverse(greatest_lower_bound(identity,inverse(Y)))) )],[refute_0_3837,refute_0_3838]) ).
cnf(refute_0_3840,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) = multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(identity,Y)),Y),Z),multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))) )],[refute_0_3834,refute_0_3839]) ).
cnf(refute_0_3841,plain,
multiply(least_upper_bound(identity,inverse(X_89)),X_89) = least_upper_bound(identity,multiply(identity,X_89)),
inference(subst,[],[refute_0_413:[bind(X_90,$fot(identity))]]) ).
cnf(refute_0_3842,plain,
inverse(greatest_lower_bound(X_89,identity)) = least_upper_bound(identity,inverse(X_89)),
inference(subst,[],[refute_0_1137:[bind(X_364,$fot(X_89))]]) ).
cnf(refute_0_3843,plain,
( inverse(greatest_lower_bound(X_89,identity)) != least_upper_bound(identity,inverse(X_89))
| least_upper_bound(identity,inverse(X_89)) = inverse(greatest_lower_bound(X_89,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(X_89,identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_3844,plain,
least_upper_bound(identity,inverse(X_89)) = inverse(greatest_lower_bound(X_89,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_89,identity)),least_upper_bound(identity,inverse(X_89))) )],[refute_0_3842,refute_0_3843]) ).
cnf(refute_0_3845,plain,
( multiply(least_upper_bound(identity,inverse(X_89)),X_89) != least_upper_bound(identity,multiply(identity,X_89))
| least_upper_bound(identity,inverse(X_89)) != inverse(greatest_lower_bound(X_89,identity))
| multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) = least_upper_bound(identity,multiply(identity,X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_89)),X_89),least_upper_bound(identity,multiply(identity,X_89))) ),[0,0],$fot(inverse(greatest_lower_bound(X_89,identity)))]]) ).
cnf(refute_0_3846,plain,
( multiply(least_upper_bound(identity,inverse(X_89)),X_89) != least_upper_bound(identity,multiply(identity,X_89))
| multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) = least_upper_bound(identity,multiply(identity,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_89)),inverse(greatest_lower_bound(X_89,identity))) )],[refute_0_3844,refute_0_3845]) ).
cnf(refute_0_3847,plain,
multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) = least_upper_bound(identity,multiply(identity,X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_89)),X_89),least_upper_bound(identity,multiply(identity,X_89))) )],[refute_0_3841,refute_0_3846]) ).
cnf(refute_0_3848,plain,
inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))) = multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(inverse(X_166))),bind(X_46,$fot(greatest_lower_bound(X_166,identity)))]]) ).
cnf(refute_0_3849,plain,
( multiply(inverse(X_166),greatest_lower_bound(X_166,identity)) != greatest_lower_bound(identity,inverse(X_166))
| inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))) != multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))
| inverse(greatest_lower_bound(identity,inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_166)))]]) ).
cnf(refute_0_3850,plain,
( inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))) != multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))
| inverse(greatest_lower_bound(identity,inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_166),greatest_lower_bound(X_166,identity)),greatest_lower_bound(identity,inverse(X_166))) )],[refute_0_3064,refute_0_3849]) ).
cnf(refute_0_3851,plain,
inverse(greatest_lower_bound(identity,inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))) )],[refute_0_3848,refute_0_3850]) ).
cnf(refute_0_3852,plain,
inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))) = multiply(inverse(greatest_lower_bound(X_166,identity)),X_166),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(X_166)),bind(X_74,$fot(greatest_lower_bound(X_166,identity)))]]) ).
cnf(refute_0_3853,plain,
multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) = inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(inverse(X_166))),bind(X_46,$fot(greatest_lower_bound(X_166,identity)))]]) ).
cnf(refute_0_3854,plain,
( multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) != inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity)))
| inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))) != multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)
| multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),X_166) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))))),bind(Y0,$fot(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)))]]) ).
cnf(refute_0_3855,plain,
( inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))) != multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)
| multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),X_166) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))),inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity)))) )],[refute_0_3853,refute_0_3854]) ).
cnf(refute_0_3856,plain,
multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),X_166),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_166),greatest_lower_bound(X_166,identity))),multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)) )],[refute_0_3852,refute_0_3855]) ).
cnf(refute_0_3857,plain,
( multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))) != multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)
| inverse(greatest_lower_bound(identity,inverse(X_166))) != multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))
| inverse(greatest_lower_bound(identity,inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),X_166) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_166))),multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_166,identity)),X_166))]]) ).
cnf(refute_0_3858,plain,
( inverse(greatest_lower_bound(identity,inverse(X_166))) != multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))
| inverse(greatest_lower_bound(identity,inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),X_166) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166))),multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)) )],[refute_0_3856,refute_0_3857]) ).
cnf(refute_0_3859,plain,
inverse(greatest_lower_bound(identity,inverse(X_166))) = multiply(inverse(greatest_lower_bound(X_166,identity)),X_166),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_166))),multiply(inverse(greatest_lower_bound(X_166,identity)),inverse(inverse(X_166)))) )],[refute_0_3851,refute_0_3858]) ).
cnf(refute_0_3860,plain,
( inverse(greatest_lower_bound(identity,inverse(X_166))) != multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)
| multiply(inverse(greatest_lower_bound(X_166,identity)),X_166) = inverse(greatest_lower_bound(identity,inverse(X_166))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_166))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)))]]) ).
cnf(refute_0_3861,plain,
multiply(inverse(greatest_lower_bound(X_166,identity)),X_166) = inverse(greatest_lower_bound(identity,inverse(X_166))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_166))),multiply(inverse(greatest_lower_bound(X_166,identity)),X_166)) )],[refute_0_3859,refute_0_3860]) ).
cnf(refute_0_3862,plain,
multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) = inverse(greatest_lower_bound(identity,inverse(X_89))),
inference(subst,[],[refute_0_3861:[bind(X_166,$fot(X_89))]]) ).
cnf(refute_0_3863,plain,
( multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) != inverse(greatest_lower_bound(identity,inverse(X_89)))
| multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) != least_upper_bound(identity,multiply(identity,X_89))
| inverse(greatest_lower_bound(identity,inverse(X_89))) = least_upper_bound(identity,multiply(identity,X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_89,identity)),X_89),least_upper_bound(identity,multiply(identity,X_89))) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_3864,plain,
( multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) != least_upper_bound(identity,multiply(identity,X_89))
| inverse(greatest_lower_bound(identity,inverse(X_89))) = least_upper_bound(identity,multiply(identity,X_89)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_89,identity)),X_89),inverse(greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_3862,refute_0_3863]) ).
cnf(refute_0_3865,plain,
multiply(identity,least_upper_bound(X_89,identity)) = least_upper_bound(X_89,identity),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_89,identity)))]]) ).
cnf(refute_0_3866,plain,
least_upper_bound(identity,multiply(identity,X_89)) = multiply(identity,least_upper_bound(X_89,identity)),
inference(subst,[],[refute_0_337:[bind(X_82,$fot(identity)),bind(X_83,$fot(X_89))]]) ).
cnf(refute_0_3867,plain,
( multiply(identity,least_upper_bound(X_89,identity)) != least_upper_bound(X_89,identity)
| least_upper_bound(identity,multiply(identity,X_89)) != multiply(identity,least_upper_bound(X_89,identity))
| least_upper_bound(identity,multiply(identity,X_89)) = least_upper_bound(X_89,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,X_89)))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_89,identity)))),bind(Z0,$fot(least_upper_bound(X_89,identity)))]]) ).
cnf(refute_0_3868,plain,
( multiply(identity,least_upper_bound(X_89,identity)) != least_upper_bound(X_89,identity)
| least_upper_bound(identity,multiply(identity,X_89)) = least_upper_bound(X_89,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_89)),multiply(identity,least_upper_bound(X_89,identity))) )],[refute_0_3866,refute_0_3867]) ).
cnf(refute_0_3869,plain,
least_upper_bound(identity,multiply(identity,X_89)) = least_upper_bound(X_89,identity),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_89,identity)),least_upper_bound(X_89,identity)) )],[refute_0_3865,refute_0_3868]) ).
cnf(refute_0_3870,plain,
( inverse(greatest_lower_bound(identity,inverse(X_89))) != least_upper_bound(identity,multiply(identity,X_89))
| least_upper_bound(identity,multiply(identity,X_89)) != least_upper_bound(X_89,identity)
| inverse(greatest_lower_bound(identity,inverse(X_89))) = least_upper_bound(X_89,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,inverse(X_89))),least_upper_bound(X_89,identity)) ),[0],$fot(least_upper_bound(identity,multiply(identity,X_89)))]]) ).
cnf(refute_0_3871,plain,
( inverse(greatest_lower_bound(identity,inverse(X_89))) != least_upper_bound(identity,multiply(identity,X_89))
| inverse(greatest_lower_bound(identity,inverse(X_89))) = least_upper_bound(X_89,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_89)),least_upper_bound(X_89,identity)) )],[refute_0_3869,refute_0_3870]) ).
cnf(refute_0_3872,plain,
( multiply(inverse(greatest_lower_bound(X_89,identity)),X_89) != least_upper_bound(identity,multiply(identity,X_89))
| inverse(greatest_lower_bound(identity,inverse(X_89))) = least_upper_bound(X_89,identity) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_89))),least_upper_bound(identity,multiply(identity,X_89))) )],[refute_0_3864,refute_0_3871]) ).
cnf(refute_0_3873,plain,
inverse(greatest_lower_bound(identity,inverse(X_89))) = least_upper_bound(X_89,identity),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_89,identity)),X_89),least_upper_bound(identity,multiply(identity,X_89))) )],[refute_0_3847,refute_0_3872]) ).
cnf(refute_0_3874,plain,
inverse(greatest_lower_bound(identity,inverse(Y))) = least_upper_bound(Y,identity),
inference(subst,[],[refute_0_3873:[bind(X_89,$fot(Y))]]) ).
cnf(refute_0_3875,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) = multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z))]]) ).
cnf(refute_0_3876,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) != multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z)
| inverse(greatest_lower_bound(identity,inverse(Y))) != least_upper_bound(Y,identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) = multiply(least_upper_bound(Y,identity),Z) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z),multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z)) ),[1,0],$fot(least_upper_bound(Y,identity))]]) ).
cnf(refute_0_3877,plain,
( inverse(greatest_lower_bound(identity,inverse(Y))) != least_upper_bound(Y,identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) = multiply(least_upper_bound(Y,identity),Z) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z),multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z)) )],[refute_0_3875,refute_0_3876]) ).
cnf(refute_0_3878,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) = multiply(least_upper_bound(Y,identity),Z),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(Y))),least_upper_bound(Y,identity)) )],[refute_0_3874,refute_0_3877]) ).
cnf(refute_0_3879,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) != multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))
| multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) != multiply(least_upper_bound(Y,identity),Z)
| multiply(least_upper_bound(Y,identity),Z) = multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z),multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))) ),[0],$fot(multiply(least_upper_bound(Y,identity),Z))]]) ).
cnf(refute_0_3880,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z) != multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))
| multiply(least_upper_bound(Y,identity),Z) = multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z),multiply(least_upper_bound(Y,identity),Z)) )],[refute_0_3878,refute_0_3879]) ).
cnf(refute_0_3881,plain,
multiply(least_upper_bound(Y,identity),Z) = multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(Y))),Z),multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))) )],[refute_0_3840,refute_0_3880]) ).
cnf(refute_0_3882,plain,
( multiply(least_upper_bound(Y,identity),Z) != multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))
| multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)) = multiply(least_upper_bound(Y,identity),Z) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(Y,identity),Z))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))))]]) ).
cnf(refute_0_3883,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z)) = multiply(least_upper_bound(Y,identity),Z),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,identity),Z),multiply(inverse(greatest_lower_bound(identity,Y)),multiply(Y,Z))) )],[refute_0_3881,refute_0_3882]) ).
cnf(refute_0_3884,plain,
multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))),
inference(subst,[],[refute_0_3883:[bind(Y,$fot(least_upper_bound(a,c))),bind(Z,$fot(inverse(least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3885,plain,
( multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity)))
| multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))))),bind(Z0,$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3886,plain,
( multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity)))) )],[refute_0_3884,refute_0_3885]) ).
cnf(refute_0_3887,plain,
multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(a,c),identity),inverse(least_upper_bound(b,identity))),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3833,refute_0_3886]) ).
cnf(refute_0_3888,plain,
( multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) ),[1],$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3889,plain,
( least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3887,refute_0_3888]) ).
cnf(refute_0_3890,plain,
least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) )],[refute_0_3790,refute_0_3889]) ).
cnf(refute_0_3891,plain,
( greatest_lower_bound(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,X_88))) != inverse(least_upper_bound(identity,X_88))
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,X_88))),inverse(least_upper_bound(identity,X_88))) ),[0,0],$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3892,plain,
( greatest_lower_bound(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,X_88))) != inverse(least_upper_bound(identity,X_88))
| greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3890,refute_0_3891]) ).
cnf(refute_0_3893,plain,
greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,X_88))),inverse(least_upper_bound(identity,X_88))) )],[refute_0_3694,refute_0_3892]) ).
cnf(refute_0_3894,plain,
inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45)),
inference(subst,[],[refute_0_238:[bind(X_46,$fot(least_upper_bound(identity,inverse(X_45))))]]) ).
cnf(refute_0_3895,plain,
greatest_lower_bound(inverse(X_45),identity) = multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45)),
inference(subst,[],[refute_0_3734:[bind(X_87,$fot(inverse(X_45)))]]) ).
cnf(refute_0_3896,plain,
( greatest_lower_bound(inverse(X_45),identity) != multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45))
| multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45)) = greatest_lower_bound(inverse(X_45),identity) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(inverse(X_45),identity))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45))))]]) ).
cnf(refute_0_3897,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45)) = greatest_lower_bound(inverse(X_45),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_45),identity),multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45))) )],[refute_0_3895,refute_0_3896]) ).
cnf(refute_0_3898,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45)) != greatest_lower_bound(inverse(X_45),identity)
| inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) != multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45))
| inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = greatest_lower_bound(inverse(X_45),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45))) ),[1],$fot(greatest_lower_bound(inverse(X_45),identity))]]) ).
cnf(refute_0_3899,plain,
( inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) != multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45))
| inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = greatest_lower_bound(inverse(X_45),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45)),greatest_lower_bound(inverse(X_45),identity)) )],[refute_0_3897,refute_0_3898]) ).
cnf(refute_0_3900,plain,
inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = greatest_lower_bound(inverse(X_45),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),multiply(inverse(least_upper_bound(identity,inverse(X_45))),inverse(X_45))) )],[refute_0_3894,refute_0_3899]) ).
cnf(refute_0_3901,plain,
multiply(least_upper_bound(X_45,identity),identity) = least_upper_bound(X_45,identity),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(least_upper_bound(X_45,identity)))]]) ).
cnf(refute_0_3902,plain,
least_upper_bound(identity,multiply(X_45,identity)) = multiply(least_upper_bound(X_45,identity),identity),
inference(subst,[],[refute_0_701:[bind(X_89,$fot(identity)),bind(X_90,$fot(X_45))]]) ).
cnf(refute_0_3903,plain,
( multiply(least_upper_bound(X_45,identity),identity) != least_upper_bound(X_45,identity)
| least_upper_bound(identity,multiply(X_45,identity)) != multiply(least_upper_bound(X_45,identity),identity)
| least_upper_bound(identity,multiply(X_45,identity)) = least_upper_bound(X_45,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(X_45,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_45,identity),identity))),bind(Z0,$fot(least_upper_bound(X_45,identity)))]]) ).
cnf(refute_0_3904,plain,
( multiply(least_upper_bound(X_45,identity),identity) != least_upper_bound(X_45,identity)
| least_upper_bound(identity,multiply(X_45,identity)) = least_upper_bound(X_45,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_45,identity)),multiply(least_upper_bound(X_45,identity),identity)) )],[refute_0_3902,refute_0_3903]) ).
cnf(refute_0_3905,plain,
least_upper_bound(identity,multiply(X_45,identity)) = least_upper_bound(X_45,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_45,identity),identity),least_upper_bound(X_45,identity)) )],[refute_0_3901,refute_0_3904]) ).
cnf(refute_0_3906,plain,
multiply(X_82,least_upper_bound(X_83,inverse(X_82))) = least_upper_bound(multiply(X_82,X_83),multiply(X_82,inverse(X_82))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(inverse(X_82)))]]) ).
cnf(refute_0_3907,plain,
multiply(X_82,inverse(X_82)) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(X_82))]]) ).
cnf(refute_0_3908,plain,
( multiply(X_82,inverse(X_82)) != identity
| multiply(X_82,least_upper_bound(X_83,inverse(X_82))) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,inverse(X_82)))
| multiply(X_82,least_upper_bound(X_83,inverse(X_82))) = least_upper_bound(multiply(X_82,X_83),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,inverse(X_82))),least_upper_bound(multiply(X_82,X_83),multiply(X_82,inverse(X_82)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3909,plain,
( multiply(X_82,least_upper_bound(X_83,inverse(X_82))) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,inverse(X_82)))
| multiply(X_82,least_upper_bound(X_83,inverse(X_82))) = least_upper_bound(multiply(X_82,X_83),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_82,inverse(X_82)),identity) )],[refute_0_3907,refute_0_3908]) ).
cnf(refute_0_3910,plain,
multiply(X_82,least_upper_bound(X_83,inverse(X_82))) = least_upper_bound(multiply(X_82,X_83),identity),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,inverse(X_82))),least_upper_bound(multiply(X_82,X_83),multiply(X_82,inverse(X_82)))) )],[refute_0_3906,refute_0_3909]) ).
cnf(refute_0_3911,plain,
least_upper_bound(multiply(X_82,X_83),identity) = least_upper_bound(identity,multiply(X_82,X_83)),
inference(subst,[],[refute_0_63:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_82,X_83)))]]) ).
cnf(refute_0_3912,plain,
( multiply(X_82,least_upper_bound(X_83,inverse(X_82))) != least_upper_bound(multiply(X_82,X_83),identity)
| least_upper_bound(multiply(X_82,X_83),identity) != least_upper_bound(identity,multiply(X_82,X_83))
| multiply(X_82,least_upper_bound(X_83,inverse(X_82))) = least_upper_bound(identity,multiply(X_82,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_82,least_upper_bound(X_83,inverse(X_82))),least_upper_bound(identity,multiply(X_82,X_83))) ),[0],$fot(least_upper_bound(multiply(X_82,X_83),identity))]]) ).
cnf(refute_0_3913,plain,
( multiply(X_82,least_upper_bound(X_83,inverse(X_82))) != least_upper_bound(multiply(X_82,X_83),identity)
| multiply(X_82,least_upper_bound(X_83,inverse(X_82))) = least_upper_bound(identity,multiply(X_82,X_83)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),identity),least_upper_bound(identity,multiply(X_82,X_83))) )],[refute_0_3911,refute_0_3912]) ).
cnf(refute_0_3914,plain,
multiply(X_82,least_upper_bound(X_83,inverse(X_82))) = least_upper_bound(identity,multiply(X_82,X_83)),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,inverse(X_82))),least_upper_bound(multiply(X_82,X_83),identity)) )],[refute_0_3910,refute_0_3913]) ).
cnf(refute_0_3915,plain,
multiply(X_45,least_upper_bound(identity,inverse(X_45))) = least_upper_bound(identity,multiply(X_45,identity)),
inference(subst,[],[refute_0_3914:[bind(X_82,$fot(X_45)),bind(X_83,$fot(identity))]]) ).
cnf(refute_0_3916,plain,
( multiply(X_45,least_upper_bound(identity,inverse(X_45))) != least_upper_bound(identity,multiply(X_45,identity))
| least_upper_bound(identity,multiply(X_45,identity)) != least_upper_bound(X_45,identity)
| multiply(X_45,least_upper_bound(identity,inverse(X_45))) = least_upper_bound(X_45,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(X_45,least_upper_bound(identity,inverse(X_45))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_45,identity)))),bind(Z0,$fot(least_upper_bound(X_45,identity)))]]) ).
cnf(refute_0_3917,plain,
( least_upper_bound(identity,multiply(X_45,identity)) != least_upper_bound(X_45,identity)
| multiply(X_45,least_upper_bound(identity,inverse(X_45))) = least_upper_bound(X_45,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_45,least_upper_bound(identity,inverse(X_45))),least_upper_bound(identity,multiply(X_45,identity))) )],[refute_0_3915,refute_0_3916]) ).
cnf(refute_0_3918,plain,
multiply(X_45,least_upper_bound(identity,inverse(X_45))) = least_upper_bound(X_45,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_45,identity)),least_upper_bound(X_45,identity)) )],[refute_0_3905,refute_0_3917]) ).
cnf(refute_0_3919,plain,
inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))))]]) ).
cnf(refute_0_3920,plain,
( multiply(X_45,least_upper_bound(identity,inverse(X_45))) != least_upper_bound(X_45,identity)
| inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) != inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45))))
| inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = inverse(least_upper_bound(X_45,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45))))) ),[1,0],$fot(least_upper_bound(X_45,identity))]]) ).
cnf(refute_0_3921,plain,
( multiply(X_45,least_upper_bound(identity,inverse(X_45))) != least_upper_bound(X_45,identity)
| inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = inverse(least_upper_bound(X_45,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45))))) )],[refute_0_3919,refute_0_3920]) ).
cnf(refute_0_3922,plain,
inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) = inverse(least_upper_bound(X_45,identity)),
inference(resolve,[$cnf( $equal(multiply(X_45,least_upper_bound(identity,inverse(X_45))),least_upper_bound(X_45,identity)) )],[refute_0_3918,refute_0_3921]) ).
cnf(refute_0_3923,plain,
( inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) != greatest_lower_bound(inverse(X_45),identity)
| inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) != inverse(least_upper_bound(X_45,identity))
| inverse(least_upper_bound(X_45,identity)) = greatest_lower_bound(inverse(X_45),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),greatest_lower_bound(inverse(X_45),identity)) ),[0],$fot(inverse(least_upper_bound(X_45,identity)))]]) ).
cnf(refute_0_3924,plain,
( inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) != greatest_lower_bound(inverse(X_45),identity)
| inverse(least_upper_bound(X_45,identity)) = greatest_lower_bound(inverse(X_45),identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),inverse(least_upper_bound(X_45,identity))) )],[refute_0_3922,refute_0_3923]) ).
cnf(refute_0_3925,plain,
greatest_lower_bound(inverse(X_45),identity) = greatest_lower_bound(identity,inverse(X_45)),
inference(subst,[],[refute_0_2134:[bind(X_154,$fot(inverse(X_45)))]]) ).
cnf(refute_0_3926,plain,
( greatest_lower_bound(inverse(X_45),identity) != greatest_lower_bound(identity,inverse(X_45))
| inverse(least_upper_bound(X_45,identity)) != greatest_lower_bound(inverse(X_45),identity)
| inverse(least_upper_bound(X_45,identity)) = greatest_lower_bound(identity,inverse(X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(inverse(X_45),identity)) ),[1],$fot(greatest_lower_bound(identity,inverse(X_45)))]]) ).
cnf(refute_0_3927,plain,
( inverse(least_upper_bound(X_45,identity)) != greatest_lower_bound(inverse(X_45),identity)
| inverse(least_upper_bound(X_45,identity)) = greatest_lower_bound(identity,inverse(X_45)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_45),identity),greatest_lower_bound(identity,inverse(X_45))) )],[refute_0_3925,refute_0_3926]) ).
cnf(refute_0_3928,plain,
( inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))) != greatest_lower_bound(inverse(X_45),identity)
| inverse(least_upper_bound(X_45,identity)) = greatest_lower_bound(identity,inverse(X_45)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(inverse(X_45),identity)) )],[refute_0_3924,refute_0_3927]) ).
cnf(refute_0_3929,plain,
inverse(least_upper_bound(X_45,identity)) = greatest_lower_bound(identity,inverse(X_45)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_45,least_upper_bound(identity,inverse(X_45)))),greatest_lower_bound(inverse(X_45),identity)) )],[refute_0_3900,refute_0_3928]) ).
cnf(refute_0_3930,plain,
( inverse(least_upper_bound(X_45,identity)) != greatest_lower_bound(identity,inverse(X_45))
| greatest_lower_bound(identity,inverse(X_45)) = inverse(least_upper_bound(X_45,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_45,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_45))))]]) ).
cnf(refute_0_3931,plain,
greatest_lower_bound(identity,inverse(X_45)) = inverse(least_upper_bound(X_45,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,inverse(X_45))) )],[refute_0_3929,refute_0_3930]) ).
cnf(refute_0_3932,plain,
greatest_lower_bound(identity,inverse(X_88)) = inverse(least_upper_bound(X_88,identity)),
inference(subst,[],[refute_0_3931:[bind(X_45,$fot(X_88))]]) ).
cnf(refute_0_3933,plain,
greatest_lower_bound(inverse(X_88),identity) = greatest_lower_bound(identity,inverse(X_88)),
inference(subst,[],[refute_0_2134:[bind(X_154,$fot(inverse(X_88)))]]) ).
cnf(refute_0_3934,plain,
( greatest_lower_bound(identity,inverse(X_88)) != inverse(least_upper_bound(X_88,identity))
| greatest_lower_bound(inverse(X_88),identity) != greatest_lower_bound(identity,inverse(X_88))
| greatest_lower_bound(inverse(X_88),identity) = inverse(least_upper_bound(X_88,identity)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(inverse(X_88),identity))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_88)))),bind(Z0,$fot(inverse(least_upper_bound(X_88,identity))))]]) ).
cnf(refute_0_3935,plain,
( greatest_lower_bound(identity,inverse(X_88)) != inverse(least_upper_bound(X_88,identity))
| greatest_lower_bound(inverse(X_88),identity) = inverse(least_upper_bound(X_88,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_88),identity),greatest_lower_bound(identity,inverse(X_88))) )],[refute_0_3933,refute_0_3934]) ).
cnf(refute_0_3936,plain,
greatest_lower_bound(inverse(X_88),identity) = inverse(least_upper_bound(X_88,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_88)),inverse(least_upper_bound(X_88,identity))) )],[refute_0_3932,refute_0_3935]) ).
cnf(refute_0_3937,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))),
inference(subst,[],[refute_0_1548:[bind(Y,$fot(identity)),bind(X_58,$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3938,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_3939,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != identity
| least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))
| greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity) ),[0,1],$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))]]) ).
cnf(refute_0_3940,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != identity
| greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) )],[refute_0_3890,refute_0_3939]) ).
cnf(refute_0_3941,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),identity) )],[refute_0_3938,refute_0_3940]) ).
cnf(refute_0_3942,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))) != identity
| greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) != greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(X_56,identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))),greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3943,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) != greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(X_56,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))),identity) )],[refute_0_3941,refute_0_3942]) ).
cnf(refute_0_3944,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(X_56,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_56,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))),greatest_lower_bound(X_56,greatest_lower_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))) )],[refute_0_3937,refute_0_3943]) ).
cnf(refute_0_3945,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = greatest_lower_bound(inverse(X_88),identity),
inference(subst,[],[refute_0_3944:[bind(X_56,$fot(inverse(X_88)))]]) ).
cnf(refute_0_3946,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) != greatest_lower_bound(inverse(X_88),identity)
| greatest_lower_bound(inverse(X_88),identity) != inverse(least_upper_bound(X_88,identity))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = inverse(least_upper_bound(X_88,identity)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_88),identity))),bind(Z0,$fot(inverse(least_upper_bound(X_88,identity))))]]) ).
cnf(refute_0_3947,plain,
( greatest_lower_bound(inverse(X_88),identity) != inverse(least_upper_bound(X_88,identity))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = inverse(least_upper_bound(X_88,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))),greatest_lower_bound(inverse(X_88),identity)) )],[refute_0_3945,refute_0_3946]) ).
cnf(refute_0_3948,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) = inverse(least_upper_bound(X_88,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_88),identity),inverse(least_upper_bound(X_88,identity))) )],[refute_0_3936,refute_0_3947]) ).
cnf(refute_0_3949,plain,
multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_118)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),
inference(subst,[],[refute_0_2916:[bind(X_163,$fot(least_upper_bound(identity,X_118))),bind(X_172,$fot(X_453))]]) ).
cnf(refute_0_3950,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_118)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| inverse(least_upper_bound(identity,X_118)) != inverse(least_upper_bound(X_118,identity))
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_118)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) ),[1,1,0],$fot(inverse(least_upper_bound(X_118,identity)))]]) ).
cnf(refute_0_3951,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_118)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_118)),inverse(least_upper_bound(X_118,identity))) )],[refute_0_3051,refute_0_3950]) ).
cnf(refute_0_3952,plain,
multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_118)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) )],[refute_0_3949,refute_0_3951]) ).
cnf(refute_0_3953,plain,
multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity) = greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118)))))]]) ).
cnf(refute_0_3954,plain,
greatest_lower_bound(identity,least_upper_bound(identity,X_118)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_118))]]) ).
cnf(refute_0_3955,plain,
multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))))]]) ).
cnf(refute_0_3956,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118)))
| greatest_lower_bound(identity,least_upper_bound(identity,X_118)) != identity
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3957,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_118)) != identity
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) )],[refute_0_3955,refute_0_3956]) ).
cnf(refute_0_3958,plain,
multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_118)),identity) )],[refute_0_3954,refute_0_3957]) ).
cnf(refute_0_3959,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity)
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity) != greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118)))
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity))),bind(Z0,$fot(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118)))))]]) ).
cnf(refute_0_3960,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity) != greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118)))
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity)) )],[refute_0_3958,refute_0_3959]) ).
cnf(refute_0_3961,plain,
multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),identity),greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118)))) )],[refute_0_3953,refute_0_3960]) ).
cnf(refute_0_3962,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118)))
| multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) ),[0],$fot(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))))]]) ).
cnf(refute_0_3963,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118)))) )],[refute_0_3961,refute_0_3962]) ).
cnf(refute_0_3964,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(greatest_lower_bound(inverse(X_118),X_453))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_3965,plain,
multiply(X_453,identity) = X_453,
inference(subst,[],[refute_0_51:[bind(X_48,$fot(X_453))]]) ).
cnf(refute_0_3966,plain,
multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))),
introduced(tautology,[refl,[$fot(multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))]]) ).
cnf(refute_0_3967,plain,
( multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))
| greatest_lower_bound(identity,least_upper_bound(identity,X_118)) != identity
| multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(X_453,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_3968,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_118)) != identity
| multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(X_453,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) )],[refute_0_3966,refute_0_3967]) ).
cnf(refute_0_3969,plain,
multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = multiply(X_453,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_118)),identity) )],[refute_0_3954,refute_0_3968]) ).
cnf(refute_0_3970,plain,
( multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != multiply(X_453,identity)
| multiply(X_453,identity) != X_453
| multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = X_453 ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),bind(Y0,$fot(multiply(X_453,identity))),bind(Z0,$fot(X_453))]]) ).
cnf(refute_0_3971,plain,
( multiply(X_453,identity) != X_453
| multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = X_453 ),
inference(resolve,[$cnf( $equal(multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))),multiply(X_453,identity)) )],[refute_0_3969,refute_0_3970]) ).
cnf(refute_0_3972,plain,
multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) = X_453,
inference(resolve,[$cnf( $equal(multiply(X_453,identity),X_453) )],[refute_0_3965,refute_0_3971]) ).
cnf(refute_0_3973,plain,
greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))]]) ).
cnf(refute_0_3974,plain,
( multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != X_453
| greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) != greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))
| greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(inverse(X_118),X_453) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))),greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) ),[1,1],$fot(X_453)]]) ).
cnf(refute_0_3975,plain,
( multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != X_453
| greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(inverse(X_118),X_453) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))),greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) )],[refute_0_3973,refute_0_3974]) ).
cnf(refute_0_3976,plain,
greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(inverse(X_118),X_453),
inference(resolve,[$cnf( $equal(multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))),X_453) )],[refute_0_3972,refute_0_3975]) ).
cnf(refute_0_3977,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))))]]) ).
cnf(refute_0_3978,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) != greatest_lower_bound(inverse(X_118),X_453)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) ),[1,1],$fot(greatest_lower_bound(inverse(X_118),X_453))]]) ).
cnf(refute_0_3979,plain,
( greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) != greatest_lower_bound(inverse(X_118),X_453)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) )],[refute_0_3977,refute_0_3978]) ).
cnf(refute_0_3980,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))),greatest_lower_bound(inverse(X_118),X_453)) )],[refute_0_3976,refute_0_3979]) ).
cnf(refute_0_3981,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) = greatest_lower_bound(greatest_lower_bound(identity,inverse(X_400)),Z),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_400)))]]) ).
cnf(refute_0_3982,plain,
inverse(least_upper_bound(X_400,identity)) = greatest_lower_bound(identity,inverse(X_400)),
inference(subst,[],[refute_0_3929:[bind(X_45,$fot(X_400))]]) ).
cnf(refute_0_3983,plain,
( inverse(least_upper_bound(X_400,identity)) != greatest_lower_bound(identity,inverse(X_400))
| greatest_lower_bound(identity,inverse(X_400)) = inverse(least_upper_bound(X_400,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_400,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_400))))]]) ).
cnf(refute_0_3984,plain,
greatest_lower_bound(identity,inverse(X_400)) = inverse(least_upper_bound(X_400,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_400,identity)),greatest_lower_bound(identity,inverse(X_400))) )],[refute_0_3982,refute_0_3983]) ).
cnf(refute_0_3985,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) != greatest_lower_bound(greatest_lower_bound(identity,inverse(X_400)),Z)
| greatest_lower_bound(identity,inverse(X_400)) != inverse(least_upper_bound(X_400,identity))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) = greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)),greatest_lower_bound(greatest_lower_bound(identity,inverse(X_400)),Z)) ),[1,0],$fot(inverse(least_upper_bound(X_400,identity)))]]) ).
cnf(refute_0_3986,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) != greatest_lower_bound(greatest_lower_bound(identity,inverse(X_400)),Z)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) = greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_400)),inverse(least_upper_bound(X_400,identity))) )],[refute_0_3984,refute_0_3985]) ).
cnf(refute_0_3987,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) = greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)),greatest_lower_bound(greatest_lower_bound(identity,inverse(X_400)),Z)) )],[refute_0_3981,refute_0_3986]) ).
cnf(refute_0_3988,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) != greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z)
| greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)))),bind(Y0,$fot(greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z)))]]) ).
cnf(refute_0_3989,plain,
greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_400),Z)),greatest_lower_bound(inverse(least_upper_bound(X_400,identity)),Z)) )],[refute_0_3987,refute_0_3988]) ).
cnf(refute_0_3990,plain,
greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),
inference(subst,[],[refute_0_3989:[bind(Z,$fot(multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),bind(X_400,$fot(X_118))]]) ).
cnf(refute_0_3991,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))
| greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))))]]) ).
cnf(refute_0_3992,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))
| greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) )],[refute_0_3990,refute_0_3991]) ).
cnf(refute_0_3993,plain,
greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) )],[refute_0_3980,refute_0_3992]) ).
cnf(refute_0_3994,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))))]]) ).
cnf(refute_0_3995,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) ),[1,1],$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)))]]) ).
cnf(refute_0_3996,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) )],[refute_0_3994,refute_0_3995]) ).
cnf(refute_0_3997,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) )],[refute_0_3993,refute_0_3996]) ).
cnf(refute_0_3998,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) != greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))))]]) ).
cnf(refute_0_3999,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)))) )],[refute_0_3997,refute_0_3998]) ).
cnf(refute_0_4000,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) )],[refute_0_3964,refute_0_3999]) ).
cnf(refute_0_4001,plain,
( greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))
| greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))))]]) ).
cnf(refute_0_4002,plain,
( greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118))))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453))) )],[refute_0_4000,refute_0_4001]) ).
cnf(refute_0_4003,plain,
( multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))
| greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) )],[refute_0_3963,refute_0_4002]) ).
cnf(refute_0_4004,plain,
greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_118),X_453)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_453,inverse(least_upper_bound(identity,X_118))),greatest_lower_bound(identity,least_upper_bound(identity,X_118))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X_118,identity)),multiply(X_453,greatest_lower_bound(identity,least_upper_bound(identity,X_118)))))) )],[refute_0_3952,refute_0_4003]) ).
cnf(refute_0_4005,plain,
greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))),
inference(subst,[],[refute_0_4004:[bind(X_118,$fot(X_88)),bind(X_453,$fot(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))]]) ).
cnf(refute_0_4006,plain,
( greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) != inverse(least_upper_bound(X_88,identity))
| greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(X_88,identity)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))))),bind(Z0,$fot(inverse(least_upper_bound(X_88,identity))))]]) ).
cnf(refute_0_4007,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))) != inverse(least_upper_bound(X_88,identity))
| greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(X_88,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity)))))) )],[refute_0_4005,refute_0_4006]) ).
cnf(refute_0_4008,plain,
greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) = inverse(least_upper_bound(X_88,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_88),multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))))),inverse(least_upper_bound(X_88,identity))) )],[refute_0_3948,refute_0_4007]) ).
cnf(refute_0_4009,plain,
( greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) != inverse(least_upper_bound(X_88,identity))
| greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) != inverse(least_upper_bound(identity,X_88))
| inverse(least_upper_bound(X_88,identity)) = inverse(least_upper_bound(identity,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))),inverse(least_upper_bound(identity,X_88))) ),[0],$fot(inverse(least_upper_bound(X_88,identity)))]]) ).
cnf(refute_0_4010,plain,
( greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))) != inverse(least_upper_bound(identity,X_88))
| inverse(least_upper_bound(X_88,identity)) = inverse(least_upper_bound(identity,X_88)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))),inverse(least_upper_bound(X_88,identity))) )],[refute_0_4008,refute_0_4009]) ).
cnf(refute_0_4011,plain,
inverse(least_upper_bound(X_88,identity)) = inverse(least_upper_bound(identity,X_88)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(a,least_upper_bound(c,identity)),inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,X_88))),inverse(least_upper_bound(identity,X_88))) )],[refute_0_3893,refute_0_4010]) ).
cnf(refute_0_4012,plain,
inverse(least_upper_bound(least_upper_bound(a,c),identity)) = inverse(least_upper_bound(identity,least_upper_bound(a,c))),
inference(subst,[],[refute_0_4011:[bind(X_88,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4013,plain,
( inverse(least_upper_bound(identity,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| inverse(least_upper_bound(least_upper_bound(a,c),identity)) != inverse(least_upper_bound(identity,least_upper_bound(a,c)))
| inverse(least_upper_bound(least_upper_bound(a,c),identity)) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(a,c),identity)))),bind(Y0,$fot(inverse(least_upper_bound(identity,least_upper_bound(a,c))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity)))))]]) ).
cnf(refute_0_4014,plain,
( inverse(least_upper_bound(identity,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| inverse(least_upper_bound(least_upper_bound(a,c),identity)) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),identity)),inverse(least_upper_bound(identity,least_upper_bound(a,c)))) )],[refute_0_4012,refute_0_4013]) ).
cnf(refute_0_4015,plain,
inverse(least_upper_bound(least_upper_bound(a,c),identity)) = inverse(least_upper_bound(a,least_upper_bound(c,identity))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_3693,refute_0_4014]) ).
cnf(refute_0_4016,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(least_upper_bound(a,c),identity)),
inference(subst,[],[refute_0_3931:[bind(X_45,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4017,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(least_upper_bound(a,c),identity))
| inverse(least_upper_bound(least_upper_bound(a,c),identity)) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),bind(Y0,$fot(inverse(least_upper_bound(least_upper_bound(a,c),identity)))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity)))))]]) ).
cnf(refute_0_4018,plain,
( inverse(least_upper_bound(least_upper_bound(a,c),identity)) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(a,c))),inverse(least_upper_bound(least_upper_bound(a,c),identity))) )],[refute_0_4016,refute_0_4017]) ).
cnf(refute_0_4019,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),identity)),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_4015,refute_0_4018]) ).
cnf(refute_0_4020,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) = greatest_lower_bound(identity,inverse(least_upper_bound(a,c))),
inference(subst,[],[refute_0_3423:[bind(Y,$fot(b)),bind(X_56,$fot(identity)),bind(X_58,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4021,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) != greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity)))))]]) ).
cnf(refute_0_4022,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) )],[refute_0_4020,refute_0_4021]) ).
cnf(refute_0_4023,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_4019,refute_0_4022]) ).
cnf(refute_0_4024,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_2134:[bind(X_154,$fot(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4025,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity)))))]]) ).
cnf(refute_0_4026,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) )],[refute_0_4024,refute_0_4025]) ).
cnf(refute_0_4027,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = inverse(least_upper_bound(a,least_upper_bound(c,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_4023,refute_0_4026]) ).
cnf(refute_0_4028,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| inverse(least_upper_bound(a,least_upper_bound(c,identity))) = multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)) ),[0],$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity))))]]) ).
cnf(refute_0_4029,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)
| inverse(least_upper_bound(a,least_upper_bound(c,identity))) = multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_4027,refute_0_4028]) ).
cnf(refute_0_4030,plain,
multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) = greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4031,plain,
( multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))
| inverse(least_upper_bound(a,least_upper_bound(c,identity))) != multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)
| inverse(least_upper_bound(a,least_upper_bound(c,identity))) = greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,identity))),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)) ),[1],$fot(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4032,plain,
( inverse(least_upper_bound(a,least_upper_bound(c,identity))) != multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)
| inverse(least_upper_bound(a,least_upper_bound(c,identity))) = greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) )],[refute_0_4030,refute_0_4031]) ).
cnf(refute_0_4033,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity) != multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)
| inverse(least_upper_bound(a,least_upper_bound(c,identity))) = greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,identity))),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)) )],[refute_0_4029,refute_0_4032]) ).
cnf(refute_0_4034,plain,
inverse(least_upper_bound(a,least_upper_bound(c,identity))) = greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity),multiply(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),identity)) )],[refute_0_3474,refute_0_4033]) ).
cnf(refute_0_4035,plain,
( inverse(least_upper_bound(a,least_upper_bound(c,identity))) != greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4036,plain,
greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,identity))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,identity))),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))) )],[refute_0_4034,refute_0_4035]) ).
cnf(refute_0_4037,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) ),[1,1],$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity))))]]) ).
cnf(refute_0_4038,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_4036,refute_0_4037]) ).
cnf(refute_0_4039,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) )],[refute_0_2795,refute_0_4038]) ).
cnf(refute_0_4040,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(subst,[],[refute_0_1173:[bind(X_58,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4041,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(X,X_380)))]]) ).
cnf(refute_0_4042,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))),
inference(subst,[],[refute_0_1530:[bind(Y,$fot(X_380)),bind(X_56,$fot(Y)),bind(X_57,$fot(X))]]) ).
cnf(refute_0_4043,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) != greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380)))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))) = greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_380)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380)))))]]) ).
cnf(refute_0_4044,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))) = greatest_lower_bound(Y,greatest_lower_bound(X,X_380)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X,X_380)),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380)))) )],[refute_0_4042,refute_0_4043]) ).
cnf(refute_0_4045,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))) != greatest_lower_bound(Y,greatest_lower_bound(X,X_380))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380))
| greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380))) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_380)))]]) ).
cnf(refute_0_4046,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380))
| greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))),greatest_lower_bound(Y,greatest_lower_bound(X,X_380))) )],[refute_0_4044,refute_0_4045]) ).
cnf(refute_0_4047,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,X_380))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380))) )],[refute_0_4041,refute_0_4046]) ).
cnf(refute_0_4048,plain,
greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(greatest_lower_bound(Y,X_380))),bind(X_17,$fot(X))]]) ).
cnf(refute_0_4049,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_380) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)),
inference(subst,[],[refute_0_566:[bind(Z,$fot(X_380))]]) ).
cnf(refute_0_4050,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) = greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)))]]) ).
cnf(refute_0_4051,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) != greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_380) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) = greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380))) ),[1,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_380)))]]) ).
cnf(refute_0_4052,plain,
( greatest_lower_bound(greatest_lower_bound(X,Y),X_380) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) = greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380))) )],[refute_0_4050,refute_0_4051]) ).
cnf(refute_0_4053,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) = greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_380),greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) )],[refute_0_4049,refute_0_4052]) ).
cnf(refute_0_4054,plain,
( greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) != greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380)))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))))),bind(Z0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_380))))]]) ).
cnf(refute_0_4055,plain,
( greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)),greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380)))) )],[refute_0_4053,refute_0_4054]) ).
cnf(refute_0_4056,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X,greatest_lower_bound(Y,X_380))),greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) )],[refute_0_4048,refute_0_4055]) ).
cnf(refute_0_4057,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)),
inference(subst,[],[refute_0_2909:[bind(Y,$fot(X_380)),bind(X_78,$fot(greatest_lower_bound(X,Y))),bind(X_79,$fot(X))]]) ).
cnf(refute_0_4058,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) != greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)))),bind(Z0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_380))))]]) ).
cnf(refute_0_4059,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380))) )],[refute_0_4057,refute_0_4058]) ).
cnf(refute_0_4060,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X,Y),X_380)),greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) )],[refute_0_4056,refute_0_4059]) ).
cnf(refute_0_4061,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X,X_380)),greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)))]]) ).
cnf(refute_0_4062,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380))
| greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380)),greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) )],[refute_0_4060,refute_0_4061]) ).
cnf(refute_0_4063,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_380)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X,X_380)),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,X_380))) )],[refute_0_4047,refute_0_4062]) ).
cnf(refute_0_4064,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_380))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_380)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_380)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_380))))]]) ).
cnf(refute_0_4065,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_380)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_380)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X,X_380)),greatest_lower_bound(X,greatest_lower_bound(Y,X_380))) )],[refute_0_4063,refute_0_4064]) ).
cnf(refute_0_4066,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_4065:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(b)),bind(X_380,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4067,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))))),bind(Z0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4068,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) )],[refute_0_4066,refute_0_4067]) ).
cnf(refute_0_4069,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c)))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4040,refute_0_4068]) ).
cnf(refute_0_4070,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)))]]) ).
cnf(refute_0_4071,plain,
greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)) = greatest_lower_bound(X_57,X_215),
inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_213)),bind(X_56,$fot(X_57)),bind(X_58,$fot(X_215))]]) ).
cnf(refute_0_4072,plain,
( greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)) != greatest_lower_bound(X_57,X_215)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)))) ),[1,1],$fot(greatest_lower_bound(X_57,X_215))]]) ).
cnf(refute_0_4073,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)),greatest_lower_bound(X_57,X_215)) )],[refute_0_4071,refute_0_4072]) ).
cnf(refute_0_4074,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)))) )],[refute_0_4070,refute_0_4073]) ).
cnf(refute_0_4075,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) = greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215))),bind(X_77,$fot(X_57)),bind(X_78,$fot(X_56))]]) ).
cnf(refute_0_4076,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)))
| greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215))) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215))) ),[0],$fot(greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215))))]]) ).
cnf(refute_0_4077,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)) != greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215))
| greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215))) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215)))) )],[refute_0_4075,refute_0_4076]) ).
cnf(refute_0_4078,plain,
greatest_lower_bound(X_57,greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(X_57,X_213),X_215))) = greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_57,X_213),X_215),greatest_lower_bound(X_56,X_57)),greatest_lower_bound(X_56,greatest_lower_bound(X_57,X_215))) )],[refute_0_4074,refute_0_4077]) ).
cnf(refute_0_4079,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(subst,[],[refute_0_4078:[bind(X_213,$fot(identity)),bind(X_215,$fot(inverse(least_upper_bound(a,c)))),bind(X_56,$fot(least_upper_bound(a,c))),bind(X_57,$fot(b))]]) ).
cnf(refute_0_4080,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),bind(Z0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4081,plain,
( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4079,refute_0_4080]) ).
cnf(refute_0_4082,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4069,refute_0_4081]) ).
cnf(refute_0_4083,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440)),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(X_438,X_440)))]]) ).
cnf(refute_0_4084,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)),
inference(subst,[],[refute_0_2891:[bind(Y,$fot(X_438)),bind(X_110,$fot(greatest_lower_bound(X,Y))),bind(X_111,$fot(X_440))]]) ).
cnf(refute_0_4085,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440)))]]) ).
cnf(refute_0_4086,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440)),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438))) )],[refute_0_4084,refute_0_4085]) ).
cnf(refute_0_4087,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_438,X_440))) )],[refute_0_4083,refute_0_4086]) ).
cnf(refute_0_4088,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438))),
inference(subst,[],[refute_0_566:[bind(Z,$fot(greatest_lower_bound(X_440,X_438)))]]) ).
cnf(refute_0_4089,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)) != greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438)))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)))]]) ).
cnf(refute_0_4090,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438)),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438)))) )],[refute_0_4088,refute_0_4089]) ).
cnf(refute_0_4091,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_440,X_438))) )],[refute_0_4087,refute_0_4090]) ).
cnf(refute_0_4092,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) != greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438)))
| greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438)))))]]) ).
cnf(refute_0_4093,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_438,X_440))),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_440,X_438)))) )],[refute_0_4091,refute_0_4092]) ).
cnf(refute_0_4094,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_4093:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(a,c))),bind(X_438,$fot(least_upper_bound(b,identity))),bind(X_440,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4095,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))))),bind(Z0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4096,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c)))))) )],[refute_0_4094,refute_0_4095]) ).
cnf(refute_0_4097,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(least_upper_bound(b,identity),inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4082,refute_0_4096]) ).
cnf(refute_0_4098,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))),
inference(subst,[],[refute_0_3440:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(inverse(least_upper_bound(a,c)))),bind(X_439,$fot(b)),bind(X_440,$fot(least_upper_bound(b,identity)))]]) ).
cnf(refute_0_4099,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity))))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))))),bind(Z0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4100,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_4098,refute_0_4099]) ).
cnf(refute_0_4101,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(inverse(least_upper_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4097,refute_0_4100]) ).
cnf(refute_0_4102,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))
| greatest_lower_bound(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))) ),[0],$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4103,plain,
( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))
| greatest_lower_bound(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4101,refute_0_4102]) ).
cnf(refute_0_4104,plain,
greatest_lower_bound(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(least_upper_bound(a,c),inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))) )],[refute_0_4039,refute_0_4103]) ).
cnf(refute_0_4105,plain,
( greatest_lower_bound(b,inverse(least_upper_bound(a,c))) != greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))
| greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),bind(Y0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))))]]) ).
cnf(refute_0_4106,plain,
greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))) )],[refute_0_4104,refute_0_4105]) ).
cnf(refute_0_4107,plain,
( greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| least_upper_bound(a,least_upper_bound(c,identity)) != greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))))
| least_upper_bound(a,least_upper_bound(c,identity)) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,identity)),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))))) ),[1,1,0],$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4108,plain,
( least_upper_bound(a,least_upper_bound(c,identity)) != greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))))
| least_upper_bound(a,least_upper_bound(c,identity)) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4106,refute_0_4107]) ).
cnf(refute_0_4109,plain,
least_upper_bound(a,least_upper_bound(c,identity)) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,identity)),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))))) )],[refute_0_2778,refute_0_4108]) ).
cnf(refute_0_4110,plain,
( least_upper_bound(a,least_upper_bound(c,identity)) != greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(c,identity)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(c,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4111,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(c,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,identity)),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4109,refute_0_4110]) ).
cnf(refute_0_4112,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(c,identity))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),[0,1],$fot(least_upper_bound(a,least_upper_bound(c,identity)))]]) ).
cnf(refute_0_4113,plain,
( least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(c,identity))) )],[refute_0_4111,refute_0_4112]) ).
cnf(refute_0_4114,plain,
least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,identity)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_2721,refute_0_4113]) ).
cnf(refute_0_4115,plain,
greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4116,plain,
( greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) ),[1,1],$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity))))]]) ).
cnf(refute_0_4117,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,identity)))
| greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) )],[refute_0_4115,refute_0_4116]) ).
cnf(refute_0_4118,plain,
greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(c,identity)))) )],[refute_0_4019,refute_0_4117]) ).
cnf(refute_0_4119,plain,
( greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))
| greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))),bind(Y0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))))),bind(Z0,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4120,plain,
( greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity))))) )],[refute_0_4118,refute_0_4119]) ).
cnf(refute_0_4121,plain,
greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(least_upper_bound(a,least_upper_bound(c,identity)))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4106,refute_0_4120]) ).
cnf(refute_0_4122,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4123,plain,
( greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))) ),[1,0],$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4124,plain,
( greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))) )],[refute_0_4122,refute_0_4123]) ).
cnf(refute_0_4125,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4121,refute_0_4124]) ).
cnf(refute_0_4126,plain,
inverse(greatest_lower_bound(b,X_59)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))),
inference(subst,[],[refute_0_495:[bind(X_69,$fot(greatest_lower_bound(b,X_59))),bind(X_95,$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))]]) ).
cnf(refute_0_4127,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(greatest_lower_bound(b,X_59))),bind(X_84,$fot(greatest_lower_bound(least_upper_bound(a,c),X_59)))]]) ).
cnf(refute_0_4128,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))
| least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59)) != greatest_lower_bound(least_upper_bound(a,c),X_59)
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))) ),[0,1],$fot(greatest_lower_bound(least_upper_bound(a,c),X_59))]]) ).
cnf(refute_0_4129,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) )],[refute_0_1181,refute_0_4128]) ).
cnf(refute_0_4130,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),least_upper_bound(greatest_lower_bound(b,X_59),greatest_lower_bound(least_upper_bound(a,c),X_59))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))) )],[refute_0_4127,refute_0_4129]) ).
cnf(refute_0_4131,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(least_upper_bound(a,c),X_59)))]]) ).
cnf(refute_0_4132,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) != identity
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))
| identity = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_4133,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))
| identity = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)),identity) )],[refute_0_4131,refute_0_4132]) ).
cnf(refute_0_4134,plain,
identity = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(least_upper_bound(a,c),X_59)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))) )],[refute_0_4130,refute_0_4133]) ).
cnf(refute_0_4135,plain,
( identity != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))))]]) ).
cnf(refute_0_4136,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))) )],[refute_0_4134,refute_0_4135]) ).
cnf(refute_0_4137,plain,
( inverse(greatest_lower_bound(b,X_59)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))) != identity
| inverse(greatest_lower_bound(b,X_59)) = multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,X_59)),multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_4138,plain,
( inverse(greatest_lower_bound(b,X_59)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))
| inverse(greatest_lower_bound(b,X_59)) = multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59))),identity) )],[refute_0_4136,refute_0_4137]) ).
cnf(refute_0_4139,plain,
inverse(greatest_lower_bound(b,X_59)) = multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,X_59)),multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),greatest_lower_bound(b,X_59)))),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))) )],[refute_0_4126,refute_0_4138]) ).
cnf(refute_0_4140,plain,
multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))]]) ).
cnf(refute_0_4141,plain,
multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))]]) ).
cnf(refute_0_4142,plain,
( multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) != multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))
| inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_4143,plain,
( inverse(identity) != identity
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))) )],[refute_0_4141,refute_0_4142]) ).
cnf(refute_0_4144,plain,
multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_4143]) ).
cnf(refute_0_4145,plain,
( multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) != least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) != multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))),bind(Z0,$fot(least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))]]) ).
cnf(refute_0_4146,plain,
( multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) != least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))) )],[refute_0_4144,refute_0_4145]) ).
cnf(refute_0_4147,plain,
multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) )],[refute_0_4140,refute_0_4146]) ).
cnf(refute_0_4148,plain,
multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) = multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),
inference(subst,[],[refute_0_320:[bind(X,$fot(inverse(identity))),bind(Y,$fot(inverse(greatest_lower_bound(b,X_59)))),bind(Z,$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))]]) ).
cnf(refute_0_4149,plain,
( multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) != least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) != multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))),bind(Z0,$fot(least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))]]) ).
cnf(refute_0_4150,plain,
( multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) != least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))
| multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))),multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))) )],[refute_0_4148,refute_0_4149]) ).
cnf(refute_0_4151,plain,
multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) )],[refute_0_4147,refute_0_4150]) ).
cnf(refute_0_4152,plain,
( multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))) != least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))
| inverse(greatest_lower_bound(b,X_59)) != multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))
| inverse(greatest_lower_bound(b,X_59)) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,X_59)),multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))) ),[1],$fot(least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))))]]) ).
cnf(refute_0_4153,plain,
( inverse(greatest_lower_bound(b,X_59)) != multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))
| inverse(greatest_lower_bound(b,X_59)) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59)))),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) )],[refute_0_4151,refute_0_4152]) ).
cnf(refute_0_4154,plain,
inverse(greatest_lower_bound(b,X_59)) = least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,X_59)),multiply(inverse(identity),least_upper_bound(inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)),inverse(greatest_lower_bound(b,X_59))))) )],[refute_0_4139,refute_0_4153]) ).
cnf(refute_0_4155,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))),
inference(subst,[],[refute_0_4154:[bind(X_59,$fot(greatest_lower_bound(X_111,Y)))]]) ).
cnf(refute_0_4156,plain,
greatest_lower_bound(b,greatest_lower_bound(Y,X_111)) = greatest_lower_bound(b,greatest_lower_bound(X_111,Y)),
inference(subst,[],[refute_0_2891:[bind(X_110,$fot(b))]]) ).
cnf(refute_0_4157,plain,
( greatest_lower_bound(b,greatest_lower_bound(Y,X_111)) != greatest_lower_bound(b,greatest_lower_bound(X_111,Y))
| greatest_lower_bound(b,greatest_lower_bound(X_111,Y)) = greatest_lower_bound(b,greatest_lower_bound(Y,X_111)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(Y,X_111)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))))]]) ).
cnf(refute_0_4158,plain,
greatest_lower_bound(b,greatest_lower_bound(X_111,Y)) = greatest_lower_bound(b,greatest_lower_bound(Y,X_111)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(Y,X_111)),greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) )],[refute_0_4156,refute_0_4157]) ).
cnf(refute_0_4159,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_111,Y)) != greatest_lower_bound(b,greatest_lower_bound(Y,X_111))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y))))) ),[0,0],$fot(greatest_lower_bound(b,greatest_lower_bound(Y,X_111)))]]) ).
cnf(refute_0_4160,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_111,Y)),greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) )],[refute_0_4158,refute_0_4159]) ).
cnf(refute_0_4161,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y))))) )],[refute_0_4155,refute_0_4160]) ).
cnf(refute_0_4162,plain,
( inverse(greatest_lower_bound(b,X_59)) != least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))
| least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) = inverse(greatest_lower_bound(b,X_59)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(b,X_59)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))))]]) ).
cnf(refute_0_4163,plain,
least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59))) = inverse(greatest_lower_bound(b,X_59)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,X_59)),least_upper_bound(inverse(greatest_lower_bound(b,X_59)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_59)))) )],[refute_0_4154,refute_0_4162]) ).
cnf(refute_0_4164,plain,
least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),
inference(subst,[],[refute_0_4163:[bind(X_59,$fot(greatest_lower_bound(X_111,Y)))]]) ).
cnf(refute_0_4165,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y))))
| least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y)))
| inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))))]]) ).
cnf(refute_0_4166,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y)))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y)))) )],[refute_0_4164,refute_0_4165]) ).
cnf(refute_0_4167,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_111,Y))))) )],[refute_0_4161,refute_0_4166]) ).
cnf(refute_0_4168,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y)))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))))),bind(Y0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y)))))]]) ).
cnf(refute_0_4169,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_111))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_111,Y)))) )],[refute_0_4167,refute_0_4168]) ).
cnf(refute_0_4170,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_4169:[bind(Y,$fot(identity)),bind(X_111,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4171,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))),
inference(subst,[],[refute_0_4154:[bind(X_59,$fot(greatest_lower_bound(X_57,X)))]]) ).
cnf(refute_0_4172,plain,
greatest_lower_bound(X,greatest_lower_bound(b,X_57)) = greatest_lower_bound(b,greatest_lower_bound(X_57,X)),
inference(subst,[],[refute_0_1521:[bind(X_56,$fot(b))]]) ).
cnf(refute_0_4173,plain,
( greatest_lower_bound(X,greatest_lower_bound(b,X_57)) != greatest_lower_bound(b,greatest_lower_bound(X_57,X))
| greatest_lower_bound(b,greatest_lower_bound(X_57,X)) = greatest_lower_bound(X,greatest_lower_bound(b,X_57)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(b,X_57)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_57,X))))]]) ).
cnf(refute_0_4174,plain,
greatest_lower_bound(b,greatest_lower_bound(X_57,X)) = greatest_lower_bound(X,greatest_lower_bound(b,X_57)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(b,X_57)),greatest_lower_bound(b,greatest_lower_bound(X_57,X))) )],[refute_0_4172,refute_0_4173]) ).
cnf(refute_0_4175,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_57,X)) != greatest_lower_bound(X,greatest_lower_bound(b,X_57))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X))))
| inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X))))) ),[0,0],$fot(greatest_lower_bound(X,greatest_lower_bound(b,X_57)))]]) ).
cnf(refute_0_4176,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X))))
| inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_57,X)),greatest_lower_bound(X,greatest_lower_bound(b,X_57))) )],[refute_0_4174,refute_0_4175]) ).
cnf(refute_0_4177,plain,
inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X))))) )],[refute_0_4171,refute_0_4176]) ).
cnf(refute_0_4178,plain,
least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),
inference(subst,[],[refute_0_4163:[bind(X_59,$fot(greatest_lower_bound(X_57,X)))]]) ).
cnf(refute_0_4179,plain,
( inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X))))
| least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X)))
| inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))))]]) ).
cnf(refute_0_4180,plain,
( inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X))))
| inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X)))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X)))) )],[refute_0_4178,refute_0_4179]) ).
cnf(refute_0_4181,plain,
inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(b,X_57))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_57,X))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_57,X))))) )],[refute_0_4177,refute_0_4180]) ).
cnf(refute_0_4182,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity))),
inference(subst,[],[refute_0_4181:[bind(X,$fot(identity)),bind(X_57,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4183,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4184,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity)))) )],[refute_0_4182,refute_0_4183]) ).
cnf(refute_0_4185,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(inverse(least_upper_bound(a,c)),identity))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))) )],[refute_0_4170,refute_0_4184]) ).
cnf(refute_0_4186,plain,
inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),bind(X_16,$fot(identity))]]) ).
cnf(refute_0_4187,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4188,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)),inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4186,refute_0_4187]) ).
cnf(refute_0_4189,plain,
inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))) )],[refute_0_4185,refute_0_4188]) ).
cnf(refute_0_4190,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4191,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4192,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity))) )],[refute_0_4190,refute_0_4191]) ).
cnf(refute_0_4193,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),identity)),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))) )],[refute_0_4189,refute_0_4192]) ).
cnf(refute_0_4194,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4195,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c)))))) )],[refute_0_4193,refute_0_4194]) ).
cnf(refute_0_4196,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4125,refute_0_4195]) ).
cnf(refute_0_4197,plain,
least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4198,plain,
( least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) ),[1,1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4199,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4197,refute_0_4198]) ).
cnf(refute_0_4200,plain,
least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4196,refute_0_4199]) ).
cnf(refute_0_4201,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4202,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) ),[1,1],$fot(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4203,plain,
( least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4201,refute_0_4202]) ).
cnf(refute_0_4204,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4200,refute_0_4203]) ).
cnf(refute_0_4205,plain,
least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c))),
inference(subst,[],[refute_0_680:[bind(X,$fot(least_upper_bound(X_463,c))),bind(X_20,$fot(a))]]) ).
cnf(refute_0_4206,plain,
least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(b,least_upper_bound(c,X_22)))) = least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(least_upper_bound(c,X_22))),bind(X_20,$fot(X_139)),bind(X_21,$fot(b))]]) ).
cnf(refute_0_4207,plain,
( least_upper_bound(b,least_upper_bound(c,X_22)) != least_upper_bound(a,least_upper_bound(c,X_22))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(b,least_upper_bound(c,X_22)))) != least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) = least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(b,least_upper_bound(c,X_22)))),least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))) ),[0,1,1],$fot(least_upper_bound(a,least_upper_bound(c,X_22)))]]) ).
cnf(refute_0_4208,plain,
( least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(b,least_upper_bound(c,X_22)))) != least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) = least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_22)),least_upper_bound(a,least_upper_bound(c,X_22))) )],[refute_0_135,refute_0_4207]) ).
cnf(refute_0_4209,plain,
least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) = least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(b,least_upper_bound(c,X_22)))),least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))) )],[refute_0_4206,refute_0_4208]) ).
cnf(refute_0_4210,plain,
least_upper_bound(X_22,least_upper_bound(c,X_22)) = least_upper_bound(X_22,c),
inference(subst,[],[refute_0_279:[bind(Y,$fot(c)),bind(X_13,$fot(X_22))]]) ).
cnf(refute_0_4211,plain,
least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))) = least_upper_bound(X_22,least_upper_bound(c,X_22)),
inference(subst,[],[refute_0_731:[bind(Y,$fot(X_22)),bind(X_20,$fot(X_22)),bind(X_21,$fot(c))]]) ).
cnf(refute_0_4212,plain,
( least_upper_bound(X_22,least_upper_bound(c,X_22)) != least_upper_bound(X_22,c)
| least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))) != least_upper_bound(X_22,least_upper_bound(c,X_22))
| least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))) = least_upper_bound(X_22,c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(c,X_22)))),bind(Z0,$fot(least_upper_bound(X_22,c)))]]) ).
cnf(refute_0_4213,plain,
( least_upper_bound(X_22,least_upper_bound(c,X_22)) != least_upper_bound(X_22,c)
| least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))) = least_upper_bound(X_22,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))),least_upper_bound(X_22,least_upper_bound(c,X_22))) )],[refute_0_4211,refute_0_4212]) ).
cnf(refute_0_4214,plain,
least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))) = least_upper_bound(X_22,c),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(c,X_22)),least_upper_bound(X_22,c)) )],[refute_0_4210,refute_0_4213]) ).
cnf(refute_0_4215,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)) = least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))),
inference(subst,[],[refute_0_1405:[bind(Y,$fot(c)),bind(X_139,$fot(least_upper_bound(c,X_22))),bind(X_140,$fot(X_22))]]) ).
cnf(refute_0_4216,plain,
( least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))) != least_upper_bound(X_22,c)
| least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)) != least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22)))
| least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)) = least_upper_bound(X_22,c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))))),bind(Z0,$fot(least_upper_bound(X_22,c)))]]) ).
cnf(refute_0_4217,plain,
( least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))) != least_upper_bound(X_22,c)
| least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)) = least_upper_bound(X_22,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)),least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22)))) )],[refute_0_4215,refute_0_4216]) ).
cnf(refute_0_4218,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)) = least_upper_bound(X_22,c),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_22,least_upper_bound(c,X_22))),least_upper_bound(X_22,c)) )],[refute_0_4214,refute_0_4217]) ).
cnf(refute_0_4219,plain,
least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))) = least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))))]]) ).
cnf(refute_0_4220,plain,
( least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))) != least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)))
| least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)) != least_upper_bound(X_22,c)
| least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))) = least_upper_bound(X_139,least_upper_bound(X_22,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))),least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)))) ),[1,1],$fot(least_upper_bound(X_22,c))]]) ).
cnf(refute_0_4221,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)) != least_upper_bound(X_22,c)
| least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))) = least_upper_bound(X_139,least_upper_bound(X_22,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))),least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)))) )],[refute_0_4219,refute_0_4220]) ).
cnf(refute_0_4222,plain,
least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))) = least_upper_bound(X_139,least_upper_bound(X_22,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)),least_upper_bound(X_22,c)) )],[refute_0_4218,refute_0_4221]) ).
cnf(refute_0_4223,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_40,X_41)))]]) ).
cnf(refute_0_4224,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41))
| least_upper_bound(Y,least_upper_bound(X_40,X_41)) != least_upper_bound(X_40,least_upper_bound(Y,X_41))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41))) ),[0,1],$fot(least_upper_bound(X_40,least_upper_bound(Y,X_41)))]]) ).
cnf(refute_0_4225,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_40,X_41)),least_upper_bound(X_40,least_upper_bound(Y,X_41))) )],[refute_0_1256,refute_0_4224]) ).
cnf(refute_0_4226,plain,
least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41))) )],[refute_0_4223,refute_0_4225]) ).
cnf(refute_0_4227,plain,
least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))),
inference(subst,[],[refute_0_131:[bind(Z,$fot(least_upper_bound(X_40,X_41)))]]) ).
cnf(refute_0_4228,plain,
( least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)) != least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41)))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41)))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)))]]) ).
cnf(refute_0_4229,plain,
( least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41)))) )],[refute_0_4227,refute_0_4228]) ).
cnf(refute_0_4230,plain,
least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_40,X_41))) )],[refute_0_4226,refute_0_4229]) ).
cnf(refute_0_4231,plain,
( least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) != least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41)))
| least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))) = least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41)))))]]) ).
cnf(refute_0_4232,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41))) = least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(Y,X_41))),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_40,X_41)))) )],[refute_0_4230,refute_0_4231]) ).
cnf(refute_0_4233,plain,
least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))) = least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))),
inference(subst,[],[refute_0_4232:[bind(X,$fot(X_139)),bind(Y,$fot(least_upper_bound(c,X_22))),bind(X_40,$fot(c)),bind(X_41,$fot(X_22))]]) ).
cnf(refute_0_4234,plain,
( least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))) != least_upper_bound(X_139,least_upper_bound(X_22,c))
| least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))) != least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)))
| least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))) = least_upper_bound(X_139,least_upper_bound(X_22,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))))),bind(Y0,$fot(least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))))),bind(Z0,$fot(least_upper_bound(X_139,least_upper_bound(X_22,c))))]]) ).
cnf(refute_0_4235,plain,
( least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))) != least_upper_bound(X_139,least_upper_bound(X_22,c))
| least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))) = least_upper_bound(X_139,least_upper_bound(X_22,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))),least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22)))) )],[refute_0_4233,refute_0_4234]) ).
cnf(refute_0_4236,plain,
least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))) = least_upper_bound(X_139,least_upper_bound(X_22,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_22),X_22))),least_upper_bound(X_139,least_upper_bound(X_22,c))) )],[refute_0_4222,refute_0_4235]) ).
cnf(refute_0_4237,plain,
least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))))]]) ).
cnf(refute_0_4238,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))) != least_upper_bound(X_139,least_upper_bound(X_22,c))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))) != least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))),least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))))) ),[1,1],$fot(least_upper_bound(X_139,least_upper_bound(X_22,c)))]]) ).
cnf(refute_0_4239,plain,
( least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))) != least_upper_bound(X_139,least_upper_bound(X_22,c))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))),least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))))) )],[refute_0_4237,refute_0_4238]) ).
cnf(refute_0_4240,plain,
least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))),least_upper_bound(X_139,least_upper_bound(X_22,c))) )],[refute_0_4236,refute_0_4239]) ).
cnf(refute_0_4241,plain,
least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_40,X_41))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)),
inference(subst,[],[refute_0_680:[bind(X_21,$fot(least_upper_bound(X_40,X_41)))]]) ).
cnf(refute_0_4242,plain,
least_upper_bound(X_20,least_upper_bound(X_40,X_41)) = least_upper_bound(X_40,least_upper_bound(X_20,X_41)),
inference(subst,[],[refute_0_747:[bind(Y,$fot(X_20)),bind(X_20,$fot(X_40)),bind(X_22,$fot(X_41))]]) ).
cnf(refute_0_4243,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_40,X_41))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))
| least_upper_bound(X_20,least_upper_bound(X_40,X_41)) != least_upper_bound(X_40,least_upper_bound(X_20,X_41))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_40,X_41))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))) ),[0,1],$fot(least_upper_bound(X_40,least_upper_bound(X_20,X_41)))]]) ).
cnf(refute_0_4244,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_40,X_41))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_40,X_41)),least_upper_bound(X_40,least_upper_bound(X_20,X_41))) )],[refute_0_4242,refute_0_4243]) ).
cnf(refute_0_4245,plain,
least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_40,X_41))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))) )],[refute_0_4241,refute_0_4244]) ).
cnf(refute_0_4246,plain,
least_upper_bound(least_upper_bound(X_40,X_41),X) = least_upper_bound(X_40,least_upper_bound(X_41,X)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_40)),bind(Y,$fot(X_41)),bind(Z,$fot(X))]]) ).
cnf(refute_0_4247,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)))]]) ).
cnf(refute_0_4248,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))
| least_upper_bound(least_upper_bound(X_40,X_41),X) != least_upper_bound(X_40,least_upper_bound(X_41,X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) = least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))) ),[1,1],$fot(least_upper_bound(X_40,least_upper_bound(X_41,X)))]]) ).
cnf(refute_0_4249,plain,
( least_upper_bound(least_upper_bound(X_40,X_41),X) != least_upper_bound(X_40,least_upper_bound(X_41,X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) = least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))) )],[refute_0_4247,refute_0_4248]) ).
cnf(refute_0_4250,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) = least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_40,X_41),X),least_upper_bound(X_40,least_upper_bound(X_41,X))) )],[refute_0_4246,refute_0_4249]) ).
cnf(refute_0_4251,plain,
( least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)) != least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X)))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) = least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))),least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X)))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)))]]) ).
cnf(refute_0_4252,plain,
( least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))
| least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) = least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X)),least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X)))) )],[refute_0_4250,refute_0_4251]) ).
cnf(refute_0_4253,plain,
least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))) = least_upper_bound(X_20,least_upper_bound(X_40,least_upper_bound(X_41,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_40,least_upper_bound(X_20,X_41))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_40,X_41),X))) )],[refute_0_4245,refute_0_4252]) ).
cnf(refute_0_4254,plain,
least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))),
inference(subst,[],[refute_0_4253:[bind(X,$fot(least_upper_bound(c,X_22))),bind(X_20,$fot(a)),bind(X_40,$fot(X_139)),bind(X_41,$fot(least_upper_bound(c,X_22)))]]) ).
cnf(refute_0_4255,plain,
( least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))) != least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c)))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) != least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c)))))]]) ).
cnf(refute_0_4256,plain,
( least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))) != least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c)))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))),least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22))))) )],[refute_0_4254,refute_0_4255]) ).
cnf(refute_0_4257,plain,
least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) = least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(c,X_22)))),least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c)))) )],[refute_0_4240,refute_0_4256]) ).
cnf(refute_0_4258,plain,
( least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) != least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c)))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) != least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) = least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))),least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))) ),[0],$fot(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))))]]) ).
cnf(refute_0_4259,plain,
( least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) != least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) = least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))),least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c)))) )],[refute_0_4257,refute_0_4258]) ).
cnf(refute_0_4260,plain,
least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))),
inference(subst,[],[refute_0_1163:[bind(X,$fot(X_139)),bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_4261,plain,
least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) = least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22))),
inference(subst,[],[refute_0_1368:[bind(X,$fot(b)),bind(X_20,$fot(X_139)),bind(X_21,$fot(least_upper_bound(c,X_22)))]]) ).
cnf(refute_0_4262,plain,
( least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139)))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) != least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22)))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139)))))]]) ).
cnf(refute_0_4263,plain,
( least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139)))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)),least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22)))) )],[refute_0_4261,refute_0_4262]) ).
cnf(refute_0_4264,plain,
least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_139,least_upper_bound(c,X_22))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139)))) )],[refute_0_4260,refute_0_4263]) ).
cnf(refute_0_4265,plain,
( least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) != least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))
| least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139)))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139)))) ),[0],$fot(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)))]]) ).
cnf(refute_0_4266,plain,
( least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) != least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b)),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139)))) )],[refute_0_4264,refute_0_4265]) ).
cnf(refute_0_4267,plain,
( least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))) != least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))
| least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))),least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))) )],[refute_0_4259,refute_0_4266]) ).
cnf(refute_0_4268,plain,
least_upper_bound(a,least_upper_bound(X_139,least_upper_bound(X_22,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_22,X_139))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,least_upper_bound(a,least_upper_bound(c,X_22)))),least_upper_bound(least_upper_bound(c,X_22),least_upper_bound(X_139,b))) )],[refute_0_4209,refute_0_4267]) ).
cnf(refute_0_4269,plain,
least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))),
inference(subst,[],[refute_0_4268:[bind(X_139,$fot(X_21)),bind(X_22,$fot(X_463))]]) ).
cnf(refute_0_4270,plain,
( least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c)))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c)))) ),[1],$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))))]]) ).
cnf(refute_0_4271,plain,
( least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c)))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))) )],[refute_0_4269,refute_0_4270]) ).
cnf(refute_0_4272,plain,
least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(X_21,least_upper_bound(X_463,c)))) )],[refute_0_4205,refute_0_4271]) ).
cnf(refute_0_4273,plain,
least_upper_bound(least_upper_bound(X_463,c),X_21) = least_upper_bound(X_463,least_upper_bound(c,X_21)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_463)),bind(Y,$fot(c)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_4274,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)) = least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)))]]) ).
cnf(refute_0_4275,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)) != least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21))
| least_upper_bound(least_upper_bound(X_463,c),X_21) != least_upper_bound(X_463,least_upper_bound(c,X_21))
| least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)),least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21))) ),[1,1],$fot(least_upper_bound(X_463,least_upper_bound(c,X_21)))]]) ).
cnf(refute_0_4276,plain,
( least_upper_bound(least_upper_bound(X_463,c),X_21) != least_upper_bound(X_463,least_upper_bound(c,X_21))
| least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)),least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21))) )],[refute_0_4274,refute_0_4275]) ).
cnf(refute_0_4277,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),X_21),least_upper_bound(X_463,least_upper_bound(c,X_21))) )],[refute_0_4273,refute_0_4276]) ).
cnf(refute_0_4278,plain,
least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)),
inference(subst,[],[refute_0_1069:[bind(X_20,$fot(least_upper_bound(X_463,c))),bind(X_21,$fot(a)),bind(X_312,$fot(X_21))]]) ).
cnf(refute_0_4279,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)) != least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21)))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21)))))]]) ).
cnf(refute_0_4280,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)) != least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21)))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21))) )],[refute_0_4278,refute_0_4279]) ).
cnf(refute_0_4281,plain,
least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(X_463,c),X_21)),least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21)))) )],[refute_0_4277,refute_0_4280]) ).
cnf(refute_0_4282,plain,
( least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21)))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))
| least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))) ),[0],$fot(least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))))]]) ).
cnf(refute_0_4283,plain,
( least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))
| least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21)))) )],[refute_0_4281,refute_0_4282]) ).
cnf(refute_0_4284,plain,
least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(a,X_21)),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))) )],[refute_0_4272,refute_0_4283]) ).
cnf(refute_0_4285,plain,
least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),
inference(subst,[],[refute_0_4284:[bind(X_21,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),bind(X_463,$fot(identity))]]) ).
cnf(refute_0_4286,plain,
least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_33))) = least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)),
inference(subst,[],[refute_0_680:[bind(X_20,$fot(b)),bind(X_21,$fot(least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_4287,plain,
( least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_33))) != least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))
| least_upper_bound(b,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(c,X_33))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) = least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_33))),least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))) ),[0,1],$fot(least_upper_bound(a,least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_4288,plain,
( least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_33))) != least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) = least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(c,X_33))) )],[refute_0_136,refute_0_4287]) ).
cnf(refute_0_4289,plain,
least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) = least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(b,least_upper_bound(c,X_33))),least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))) )],[refute_0_4286,refute_0_4288]) ).
cnf(refute_0_4290,plain,
least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X))),
inference(subst,[],[refute_0_135:[bind(X_22,$fot(least_upper_bound(X_33,X)))]]) ).
cnf(refute_0_4291,plain,
least_upper_bound(least_upper_bound(c,X_33),X) = least_upper_bound(c,least_upper_bound(X_33,X)),
inference(subst,[],[refute_0_131:[bind(X,$fot(c)),bind(Y,$fot(X_33)),bind(Z,$fot(X))]]) ).
cnf(refute_0_4292,plain,
least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) = least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)))]]) ).
cnf(refute_0_4293,plain,
( least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) != least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))
| least_upper_bound(least_upper_bound(c,X_33),X) != least_upper_bound(c,least_upper_bound(X_33,X))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) = least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)),least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))) ),[1,1],$fot(least_upper_bound(c,least_upper_bound(X_33,X)))]]) ).
cnf(refute_0_4294,plain,
( least_upper_bound(least_upper_bound(c,X_33),X) != least_upper_bound(c,least_upper_bound(X_33,X))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) = least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)),least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))) )],[refute_0_4292,refute_0_4293]) ).
cnf(refute_0_4295,plain,
least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) = least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_33),X),least_upper_bound(c,least_upper_bound(X_33,X))) )],[refute_0_4291,refute_0_4294]) ).
cnf(refute_0_4296,plain,
( least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X)))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) != least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X)))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X)))))]]) ).
cnf(refute_0_4297,plain,
( least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X)))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)),least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X)))) )],[refute_0_4295,refute_0_4296]) ).
cnf(refute_0_4298,plain,
least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_33,X))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X)))) )],[refute_0_4290,refute_0_4297]) ).
cnf(refute_0_4299,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) != least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))
| least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X)))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X)))) ),[0],$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)))]]) ).
cnf(refute_0_4300,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) != least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X)),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X)))) )],[refute_0_4298,refute_0_4299]) ).
cnf(refute_0_4301,plain,
least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_33,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_33))),least_upper_bound(b,least_upper_bound(least_upper_bound(c,X_33),X))) )],[refute_0_4289,refute_0_4300]) ).
cnf(refute_0_4302,plain,
least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))),
inference(subst,[],[refute_0_4301:[bind(X_33,$fot(least_upper_bound(X_463,c)))]]) ).
cnf(refute_0_4303,plain,
least_upper_bound(c,least_upper_bound(X_463,c)) = least_upper_bound(c,X_463),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_463)),bind(X_13,$fot(c))]]) ).
cnf(refute_0_4304,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))))]]) ).
cnf(refute_0_4305,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))
| least_upper_bound(c,least_upper_bound(X_463,c)) != least_upper_bound(c,X_463)
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))) = least_upper_bound(a,least_upper_bound(c,X_463)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) ),[1,1],$fot(least_upper_bound(c,X_463))]]) ).
cnf(refute_0_4306,plain,
( least_upper_bound(c,least_upper_bound(X_463,c)) != least_upper_bound(c,X_463)
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))) = least_upper_bound(a,least_upper_bound(c,X_463)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) )],[refute_0_4304,refute_0_4305]) ).
cnf(refute_0_4307,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))) = least_upper_bound(a,least_upper_bound(c,X_463)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_463,c)),least_upper_bound(c,X_463)) )],[refute_0_4303,refute_0_4306]) ).
cnf(refute_0_4308,plain,
least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) = least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))))]]) ).
cnf(refute_0_4309,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) != least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))) != least_upper_bound(a,least_upper_bound(c,X_463))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) = least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))),least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))))) ),[1,1],$fot(least_upper_bound(a,least_upper_bound(c,X_463)))]]) ).
cnf(refute_0_4310,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))) != least_upper_bound(a,least_upper_bound(c,X_463))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) = least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))),least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))))) )],[refute_0_4308,refute_0_4309]) ).
cnf(refute_0_4311,plain,
least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) = least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c))),least_upper_bound(a,least_upper_bound(c,X_463))) )],[refute_0_4307,refute_0_4310]) ).
cnf(refute_0_4312,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) != least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463)))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))) ),[0],$fot(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))))]]) ).
cnf(refute_0_4313,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))),least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463)))) )],[refute_0_4311,refute_0_4312]) ).
cnf(refute_0_4314,plain,
least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))) = least_upper_bound(X_463,least_upper_bound(c,X)),
inference(subst,[],[refute_0_731:[bind(Y,$fot(X)),bind(X_20,$fot(X_463)),bind(X_21,$fot(c))]]) ).
cnf(refute_0_4315,plain,
least_upper_bound(least_upper_bound(X_463,c),X) = least_upper_bound(X_463,least_upper_bound(c,X)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_463)),bind(Y,$fot(c)),bind(Z,$fot(X))]]) ).
cnf(refute_0_4316,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) = least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))]]) ).
cnf(refute_0_4317,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) != least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))
| least_upper_bound(least_upper_bound(X_463,c),X) != least_upper_bound(X_463,least_upper_bound(c,X))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) = least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)),least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) ),[1,1],$fot(least_upper_bound(X_463,least_upper_bound(c,X)))]]) ).
cnf(refute_0_4318,plain,
( least_upper_bound(least_upper_bound(X_463,c),X) != least_upper_bound(X_463,least_upper_bound(c,X))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) = least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)),least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) )],[refute_0_4316,refute_0_4317]) ).
cnf(refute_0_4319,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) = least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),X),least_upper_bound(X_463,least_upper_bound(c,X))) )],[refute_0_4315,refute_0_4318]) ).
cnf(refute_0_4320,plain,
( least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))) != least_upper_bound(X_463,least_upper_bound(c,X))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) != least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X)))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) = least_upper_bound(X_463,least_upper_bound(c,X)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))))),bind(Z0,$fot(least_upper_bound(X_463,least_upper_bound(c,X))))]]) ).
cnf(refute_0_4321,plain,
( least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))) != least_upper_bound(X_463,least_upper_bound(c,X))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) = least_upper_bound(X_463,least_upper_bound(c,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)),least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X)))) )],[refute_0_4319,refute_0_4320]) ).
cnf(refute_0_4322,plain,
least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) = least_upper_bound(X_463,least_upper_bound(c,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(c,X))),least_upper_bound(X_463,least_upper_bound(c,X))) )],[refute_0_4314,refute_0_4321]) ).
cnf(refute_0_4323,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))))]]) ).
cnf(refute_0_4324,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))
| least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) != least_upper_bound(X_463,least_upper_bound(c,X))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))) ),[1,1],$fot(least_upper_bound(X_463,least_upper_bound(c,X)))]]) ).
cnf(refute_0_4325,plain,
( least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)) != least_upper_bound(X_463,least_upper_bound(c,X))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))) )],[refute_0_4323,refute_0_4324]) ).
cnf(refute_0_4326,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)),least_upper_bound(X_463,least_upper_bound(c,X))) )],[refute_0_4322,refute_0_4325]) ).
cnf(refute_0_4327,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))) != least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X)))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))),least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X)))) ),[0],$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))))]]) ).
cnf(refute_0_4328,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X))),least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X)))) )],[refute_0_4326,refute_0_4327]) ).
cnf(refute_0_4329,plain,
( least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))
| least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))) )],[refute_0_4313,refute_0_4328]) ).
cnf(refute_0_4330,plain,
least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,X_463))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,c)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(X_463,c),X)))) )],[refute_0_4302,refute_0_4329]) ).
cnf(refute_0_4331,plain,
least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),
inference(subst,[],[refute_0_4330:[bind(X,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),bind(X_463,$fot(identity))]]) ).
cnf(refute_0_4332,plain,
( least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) != least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))))]]) ).
cnf(refute_0_4333,plain,
( least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))),least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4331,refute_0_4332]) ).
cnf(refute_0_4334,plain,
least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4285,refute_0_4333]) ).
cnf(refute_0_4335,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4336,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4334,refute_0_4335]) ).
cnf(refute_0_4337,plain,
least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4204,refute_0_4336]) ).
cnf(refute_0_4338,plain,
( least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),[0],$fot(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4339,plain,
( least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4337,refute_0_4338]) ).
cnf(refute_0_4340,plain,
least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,identity))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4114,refute_0_4339]) ).
cnf(refute_0_4341,plain,
( least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(b,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))
| least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))) ),[0,1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4342,plain,
( least_upper_bound(b,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))
| least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4340,refute_0_4341]) ).
cnf(refute_0_4343,plain,
least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))) )],[refute_0_2720,refute_0_4342]) ).
cnf(refute_0_4344,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_1453:[bind(X_20,$fot(a)),bind(X_21,$fot(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4345,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),[0],$fot(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4346,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4340,refute_0_4345]) ).
cnf(refute_0_4347,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4344,refute_0_4346]) ).
cnf(refute_0_4348,plain,
least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))),
inference(subst,[],[refute_0_729:[bind(Y,$fot(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(X_21,$fot(a))]]) ).
cnf(refute_0_4349,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))) ),[0,1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4350,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))
| least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4340,refute_0_4349]) ).
cnf(refute_0_4351,plain,
least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))) )],[refute_0_4348,refute_0_4350]) ).
cnf(refute_0_4352,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))) ),[1,1,1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4353,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))
| least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4340,refute_0_4352]) ).
cnf(refute_0_4354,plain,
least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))) )],[refute_0_4348,refute_0_4353]) ).
cnf(refute_0_4355,plain,
least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4356,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) ),[1,1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4357,plain,
( least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4355,refute_0_4356]) ).
cnf(refute_0_4358,plain,
least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4340,refute_0_4357]) ).
cnf(refute_0_4359,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) ),[0],$fot(least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4360,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4358,refute_0_4359]) ).
cnf(refute_0_4361,plain,
least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4354,refute_0_4360]) ).
cnf(refute_0_4362,plain,
( least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4363,plain,
least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4361,refute_0_4362]) ).
cnf(refute_0_4364,plain,
least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_4363:[bind(X_20,$fot(c))]]) ).
cnf(refute_0_4365,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) ),[1,1],$fot(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4366,plain,
( least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4355,refute_0_4365]) ).
cnf(refute_0_4367,plain,
least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4364,refute_0_4366]) ).
cnf(refute_0_4368,plain,
least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) = least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),
inference(subst,[],[refute_0_731:[bind(Y,$fot(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(X_21,$fot(a))]]) ).
cnf(refute_0_4369,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) != least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4370,plain,
( least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4368,refute_0_4369]) ).
cnf(refute_0_4371,plain,
least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4367,refute_0_4370]) ).
cnf(refute_0_4372,plain,
( least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) != least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) ),[0],$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))))]]) ).
cnf(refute_0_4373,plain,
( least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))
| least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))),least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4371,refute_0_4372]) ).
cnf(refute_0_4374,plain,
least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))) )],[refute_0_4351,refute_0_4373]) ).
cnf(refute_0_4375,plain,
( least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4376,plain,
least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(X_20,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4374,refute_0_4375]) ).
cnf(refute_0_4377,plain,
least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_4376:[bind(X_20,$fot(a))]]) ).
cnf(refute_0_4378,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))
| least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) = least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))),bind(Z0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4379,plain,
( least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) = least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) )],[refute_0_4344,refute_0_4378]) ).
cnf(refute_0_4380,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) = least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4377,refute_0_4379]) ).
cnf(refute_0_4381,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) != least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),[0],$fot(least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4382,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))),least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4380,refute_0_4381]) ).
cnf(refute_0_4383,plain,
least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4347,refute_0_4382]) ).
cnf(refute_0_4384,plain,
least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(Y,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),
inference(subst,[],[refute_0_927:[bind(X_30,$fot(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(X_31,$fot(a))]]) ).
cnf(refute_0_4385,plain,
( least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) != least_upper_bound(Y,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)),least_upper_bound(Y,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) ),[1,1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4386,plain,
( least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) != least_upper_bound(Y,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4340,refute_0_4385]) ).
cnf(refute_0_4387,plain,
least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)),least_upper_bound(Y,least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))) )],[refute_0_4384,refute_0_4386]) ).
cnf(refute_0_4388,plain,
least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y) = least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)),
inference(subst,[],[refute_0_131:[bind(X,$fot(c)),bind(Y,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),bind(Z,$fot(Y))]]) ).
cnf(refute_0_4389,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)) = least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)))]]) ).
cnf(refute_0_4390,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)) != least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y) != least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) ),[1,1],$fot(least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)))]]) ).
cnf(refute_0_4391,plain,
( least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y) != least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) )],[refute_0_4389,refute_0_4390]) ).
cnf(refute_0_4392,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y),least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) )],[refute_0_4388,refute_0_4391]) ).
cnf(refute_0_4393,plain,
least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)),
inference(subst,[],[refute_0_1069:[bind(X_20,$fot(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(X_21,$fot(a)),bind(X_312,$fot(Y))]]) ).
cnf(refute_0_4394,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) != least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)))))]]) ).
cnf(refute_0_4395,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)),least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y))) )],[refute_0_4393,refute_0_4394]) ).
cnf(refute_0_4396,plain,
least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),Y)),least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)))) )],[refute_0_4392,refute_0_4395]) ).
cnf(refute_0_4397,plain,
( least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) != least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) = least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)),least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) ),[0],$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))))]]) ).
cnf(refute_0_4398,plain,
( least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)) != least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) = least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)),least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y)))) )],[refute_0_4396,refute_0_4397]) ).
cnf(refute_0_4399,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),Y))) = least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,Y)),least_upper_bound(Y,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4387,refute_0_4398]) ).
cnf(refute_0_4400,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) = least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_4399:[bind(Y,$fot(a))]]) ).
cnf(refute_0_4401,plain,
( least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) != least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))))),bind(Y0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4402,plain,
( least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))),least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4400,refute_0_4401]) ).
cnf(refute_0_4403,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4383,refute_0_4402]) ).
cnf(refute_0_4404,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))
| least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))) ),[1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4405,plain,
( least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))
| least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4403,refute_0_4404]) ).
cnf(refute_0_4406,plain,
least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))),a)))) )],[refute_0_4343,refute_0_4405]) ).
cnf(refute_0_4407,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != identity
| least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),identity) ),[0,1,1],$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4408,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))) != identity
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) )],[refute_0_4406,refute_0_4407]) ).
cnf(refute_0_4409,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),least_upper_bound(b,inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),identity) )],[refute_0_2719,refute_0_4408]) ).
cnf(refute_0_4410,plain,
inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(b,inverse(least_upper_bound(a,c))),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4411,plain,
multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)) = multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_4412,plain,
( multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)) != multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))
| inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)),multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) ),[1,0],$fot(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_4413,plain,
( inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(b,inverse(least_upper_bound(a,c)))
| multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)),multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) )],[refute_0_4411,refute_0_4412]) ).
cnf(refute_0_4414,plain,
multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(b,inverse(least_upper_bound(a,c)))) )],[refute_0_4410,refute_0_4413]) ).
cnf(refute_0_4415,plain,
least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4416,plain,
( multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)) != multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))
| least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) ),[1,1],$fot(multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_4417,plain,
( multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)) != multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))
| least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) )],[refute_0_4415,refute_0_4416]) ).
cnf(refute_0_4418,plain,
least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)),multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) )],[refute_0_4414,refute_0_4417]) ).
cnf(refute_0_4419,plain,
inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4420,plain,
( inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))),inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))) ),[1,0],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4421,plain,
( least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))),inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))) )],[refute_0_4419,refute_0_4420]) ).
cnf(refute_0_4422,plain,
inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_4418,refute_0_4421]) ).
cnf(refute_0_4423,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) = inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_2054:[bind(X_83,$fot(greatest_lower_bound(a,c))),bind(X_84,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4424,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_2076:[bind(X_85,$fot(greatest_lower_bound(a,c))),bind(X_86,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4425,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4426,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))) != inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_4424,refute_0_4425]) ).
cnf(refute_0_4427,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))) )],[refute_0_4423,refute_0_4426]) ).
cnf(refute_0_4428,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))
| inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4429,plain,
( inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c))))) )],[refute_0_4427,refute_0_4428]) ).
cnf(refute_0_4430,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) = inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(a,c)))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4422,refute_0_4429]) ).
cnf(refute_0_4431,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != identity
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),identity) ),[0],$fot(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4432,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))) != identity
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4430,refute_0_4431]) ).
cnf(refute_0_4433,plain,
inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),inverse(greatest_lower_bound(b,inverse(least_upper_bound(a,c)))))),identity) )],[refute_0_4409,refute_0_4432]) ).
cnf(refute_0_4434,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != identity
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[0,0,0],$fot(identity)]]) ).
cnf(refute_0_4435,plain,
( multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),identity) )],[refute_0_4433,refute_0_4434]) ).
cnf(refute_0_4436,plain,
multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_2718,refute_0_4435]) ).
cnf(refute_0_4437,plain,
multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) = least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),multiply(inverse(X_86),least_upper_bound(identity,X_86))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(least_upper_bound(identity,X_86))),bind(Y,$fot(X_90)),bind(Z,$fot(inverse(X_86)))]]) ).
cnf(refute_0_4438,plain,
( multiply(inverse(X_86),least_upper_bound(identity,X_86)) != least_upper_bound(identity,inverse(X_86))
| multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) != least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),multiply(inverse(X_86),least_upper_bound(identity,X_86)))
| multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) = least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)),least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),multiply(inverse(X_86),least_upper_bound(identity,X_86)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_86)))]]) ).
cnf(refute_0_4439,plain,
( multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) != least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),multiply(inverse(X_86),least_upper_bound(identity,X_86)))
| multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) = least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) )],[refute_0_74,refute_0_4438]) ).
cnf(refute_0_4440,plain,
multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) = least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)),least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),multiply(inverse(X_86),least_upper_bound(identity,X_86)))) )],[refute_0_4437,refute_0_4439]) ).
cnf(refute_0_4441,plain,
least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86)))) = least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86)))),
inference(subst,[],[refute_0_1210:[bind(Y,$fot(multiply(X_90,least_upper_bound(identity,X_86)))),bind(X_31,$fot(inverse(X_86))),bind(X_32,$fot(identity))]]) ).
cnf(refute_0_4442,plain,
least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) = least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86)))),
inference(subst,[],[refute_0_1368:[bind(X,$fot(inverse(X_86))),bind(X_20,$fot(identity)),bind(X_21,$fot(multiply(X_90,least_upper_bound(identity,X_86))))]]) ).
cnf(refute_0_4443,plain,
( least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) != least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86))))
| least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86)))) != least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86))))
| least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) = least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))))),bind(Y0,$fot(least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86))))))]]) ).
cnf(refute_0_4444,plain,
( least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86)))) != least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86))))
| least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) = least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))),least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86))))) )],[refute_0_4442,refute_0_4443]) ).
cnf(refute_0_4445,plain,
least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) = least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_86),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,X_86)))),least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86))))) )],[refute_0_4441,refute_0_4444]) ).
cnf(refute_0_4446,plain,
( multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) != least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86)))
| least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) != least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86))))
| multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) = least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)),least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86))))) ),[0],$fot(least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))))]]) ).
cnf(refute_0_4447,plain,
( multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) != least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86)))
| multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) = least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))),least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86))))) )],[refute_0_4445,refute_0_4446]) ).
cnf(refute_0_4448,plain,
multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)) = least_upper_bound(identity,least_upper_bound(inverse(X_86),multiply(X_90,least_upper_bound(identity,X_86)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(X_86)),least_upper_bound(identity,X_86)),least_upper_bound(multiply(X_90,least_upper_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86)))) )],[refute_0_4440,refute_0_4447]) ).
cnf(refute_0_4449,plain,
multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),
inference(subst,[],[refute_0_4448:[bind(X_86,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4450,plain,
( multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != identity
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))) ),[1,1,0],$fot(identity)]]) ).
cnf(refute_0_4451,plain,
( multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),identity) )],[refute_0_4433,refute_0_4450]) ).
cnf(refute_0_4452,plain,
multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))) )],[refute_0_4449,refute_0_4451]) ).
cnf(refute_0_4453,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_4454,plain,
multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4455,plain,
( multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[1,1],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4456,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4454,refute_0_4455]) ).
cnf(refute_0_4457,plain,
multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_4453,refute_0_4456]) ).
cnf(refute_0_4458,plain,
least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4459,plain,
( inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != identity
| least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(X_90,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_4460,plain,
( inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != identity
| least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(X_90,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4458,refute_0_4459]) ).
cnf(refute_0_4461,plain,
least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(X_90,identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),identity) )],[refute_0_4433,refute_0_4460]) ).
cnf(refute_0_4462,plain,
multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4463,plain,
( multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(X_90,identity)
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[1,0],$fot(least_upper_bound(X_90,identity))]]) ).
cnf(refute_0_4464,plain,
( least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(X_90,identity)
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4462,refute_0_4463]) ).
cnf(refute_0_4465,plain,
multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(X_90,identity)) )],[refute_0_4461,refute_0_4464]) ).
cnf(refute_0_4466,plain,
( multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),bind(Z0,$fot(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4467,plain,
( multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4465,refute_0_4466]) ).
cnf(refute_0_4468,plain,
multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4457,refute_0_4467]) ).
cnf(refute_0_4469,plain,
( multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))
| multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))) ),[0],$fot(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4470,plain,
( multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))
| multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4468,refute_0_4469]) ).
cnf(refute_0_4471,plain,
multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
introduced(tautology,[refl,[$fot(multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4472,plain,
( multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[1,1],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4473,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4471,refute_0_4472]) ).
cnf(refute_0_4474,plain,
multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_4453,refute_0_4473]) ).
cnf(refute_0_4475,plain,
least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))]]) ).
cnf(refute_0_4476,plain,
( multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) != least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))
| least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) ),[1,1],$fot(multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4477,plain,
( multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) )],[refute_0_4475,refute_0_4476]) ).
cnf(refute_0_4478,plain,
least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4474,refute_0_4477]) ).
cnf(refute_0_4479,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_4480,plain,
( least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) != least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) != least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))]]) ).
cnf(refute_0_4481,plain,
( least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) != least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) )],[refute_0_4479,refute_0_4480]) ).
cnf(refute_0_4482,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4478,refute_0_4481]) ).
cnf(refute_0_4483,plain,
( multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))) != least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))))]]) ).
cnf(refute_0_4484,plain,
( multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))
| multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4482,refute_0_4483]) ).
cnf(refute_0_4485,plain,
( multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))
| multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))) )],[refute_0_4470,refute_0_4484]) ).
cnf(refute_0_4486,plain,
multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))) )],[refute_0_4452,refute_0_4485]) ).
cnf(refute_0_4487,plain,
( multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))))]]) ).
cnf(refute_0_4488,plain,
least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_90,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,multiply(X_90,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4486,refute_0_4487]) ).
cnf(refute_0_4489,plain,
least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_4488:[bind(X_90,$fot(X_91))]]) ).
cnf(refute_0_4490,plain,
( multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),[0],$fot(least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_4491,plain,
( multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4489,refute_0_4490]) ).
cnf(refute_0_4492,plain,
multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,multiply(X_91,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))) )],[refute_0_4436,refute_0_4491]) ).
cnf(refute_0_4493,plain,
multiply(least_upper_bound(identity,X_91),identity) = least_upper_bound(identity,X_91),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(least_upper_bound(identity,X_91)))]]) ).
cnf(refute_0_4494,plain,
inverse(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4495,plain,
( inverse(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != identity
| inverse(identity) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4496,plain,
( inverse(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| inverse(identity) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),identity) )],[refute_0_4433,refute_0_4495]) ).
cnf(refute_0_4497,plain,
inverse(identity) = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_4494,refute_0_4496]) ).
cnf(refute_0_4498,plain,
( inverse(identity) != identity
| inverse(identity) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_4499,plain,
( inverse(identity) != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_858,refute_0_4498]) ).
cnf(refute_0_4500,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_4497,refute_0_4499]) ).
cnf(refute_0_4501,plain,
( identity != least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4502,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) )],[refute_0_4500,refute_0_4501]) ).
cnf(refute_0_4503,plain,
multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4504,plain,
( multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) != identity
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(identity,X_91),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_4505,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) != identity
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(identity,X_91),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4503,refute_0_4504]) ).
cnf(refute_0_4506,plain,
multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(identity,X_91),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))),identity) )],[refute_0_4502,refute_0_4505]) ).
cnf(refute_0_4507,plain,
( multiply(least_upper_bound(identity,X_91),identity) != least_upper_bound(identity,X_91)
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != multiply(least_upper_bound(identity,X_91),identity)
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,X_91) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_91),identity))),bind(Z0,$fot(least_upper_bound(identity,X_91)))]]) ).
cnf(refute_0_4508,plain,
( multiply(least_upper_bound(identity,X_91),identity) != least_upper_bound(identity,X_91)
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,X_91) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(identity,X_91),identity)) )],[refute_0_4506,refute_0_4507]) ).
cnf(refute_0_4509,plain,
multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(identity,X_91),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),identity),least_upper_bound(identity,X_91)) )],[refute_0_4493,refute_0_4508]) ).
cnf(refute_0_4510,plain,
( multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(identity,X_91)
| least_upper_bound(identity,X_91) = multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),[0],$fot(least_upper_bound(identity,X_91))]]) ).
cnf(refute_0_4511,plain,
( multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,X_91) = multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(identity,X_91)) )],[refute_0_4509,refute_0_4510]) ).
cnf(refute_0_4512,plain,
multiply(least_upper_bound(X_91,identity),identity) = least_upper_bound(X_91,identity),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(least_upper_bound(X_91,identity)))]]) ).
cnf(refute_0_4513,plain,
multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4514,plain,
( multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) != identity
| multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(X_91,identity),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_4515,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))) != identity
| multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(X_91,identity),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4513,refute_0_4514]) ).
cnf(refute_0_4516,plain,
multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = multiply(least_upper_bound(X_91,identity),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))),identity) )],[refute_0_4502,refute_0_4515]) ).
cnf(refute_0_4517,plain,
( multiply(least_upper_bound(X_91,identity),identity) != least_upper_bound(X_91,identity)
| multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != multiply(least_upper_bound(X_91,identity),identity)
| multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(X_91,identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(least_upper_bound(X_91,identity),identity))),bind(Z0,$fot(least_upper_bound(X_91,identity)))]]) ).
cnf(refute_0_4518,plain,
( multiply(least_upper_bound(X_91,identity),identity) != least_upper_bound(X_91,identity)
| multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(X_91,identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(X_91,identity),identity)) )],[refute_0_4516,refute_0_4517]) ).
cnf(refute_0_4519,plain,
multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) = least_upper_bound(X_91,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),identity),least_upper_bound(X_91,identity)) )],[refute_0_4512,refute_0_4518]) ).
cnf(refute_0_4520,plain,
( multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != least_upper_bound(X_91,identity)
| least_upper_bound(identity,X_91) != multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,X_91) = least_upper_bound(X_91,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_91),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) ),[1],$fot(least_upper_bound(X_91,identity))]]) ).
cnf(refute_0_4521,plain,
( least_upper_bound(identity,X_91) != multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,X_91) = least_upper_bound(X_91,identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),least_upper_bound(X_91,identity)) )],[refute_0_4519,refute_0_4520]) ).
cnf(refute_0_4522,plain,
( multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))) != multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))
| least_upper_bound(identity,X_91) = least_upper_bound(X_91,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_91),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4511,refute_0_4521]) ).
cnf(refute_0_4523,plain,
least_upper_bound(identity,X_91) = least_upper_bound(X_91,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_91),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c)))),multiply(least_upper_bound(X_91,identity),least_upper_bound(identity,multiply(greatest_lower_bound(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(a,c))))) )],[refute_0_4492,refute_0_4522]) ).
cnf(refute_0_4524,plain,
( least_upper_bound(identity,X_91) != least_upper_bound(X_91,identity)
| least_upper_bound(X_91,identity) = least_upper_bound(identity,X_91) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(identity,X_91))),bind(Y0,$fot(least_upper_bound(X_91,identity)))]]) ).
cnf(refute_0_4525,plain,
least_upper_bound(X_91,identity) = least_upper_bound(identity,X_91),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_91),least_upper_bound(X_91,identity)) )],[refute_0_4523,refute_0_4524]) ).
cnf(refute_0_4526,plain,
least_upper_bound(multiply(a,inverse(c)),identity) = least_upper_bound(identity,multiply(a,inverse(c))),
inference(subst,[],[refute_0_4525:[bind(X_91,$fot(multiply(a,inverse(c))))]]) ).
cnf(refute_0_4527,plain,
( least_upper_bound(multiply(a,inverse(c)),identity) != least_upper_bound(identity,multiply(a,inverse(c)))
| least_upper_bound(identity,multiply(a,inverse(c))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(multiply(a,inverse(c)),identity) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(a,inverse(c)),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(a,inverse(c))))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(c,a)))))]]) ).
cnf(refute_0_4528,plain,
( least_upper_bound(identity,multiply(a,inverse(c))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(multiply(a,inverse(c)),identity) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,inverse(c)),identity),least_upper_bound(identity,multiply(a,inverse(c)))) )],[refute_0_4526,refute_0_4527]) ).
cnf(refute_0_4529,plain,
least_upper_bound(multiply(a,inverse(c)),identity) = multiply(a,inverse(greatest_lower_bound(c,a))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,inverse(c))),multiply(a,inverse(greatest_lower_bound(c,a)))) )],[refute_0_2717,refute_0_4528]) ).
cnf(refute_0_4530,plain,
least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))) = least_upper_bound(multiply(a,inverse(c)),identity),
inference(subst,[],[refute_0_933:[bind(X_31,$fot(multiply(a,inverse(c)))),bind(X_32,$fot(identity))]]) ).
cnf(refute_0_4531,plain,
( least_upper_bound(multiply(a,inverse(c)),identity) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))) != least_upper_bound(multiply(a,inverse(c)),identity)
| least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))))),bind(Y0,$fot(least_upper_bound(multiply(a,inverse(c)),identity))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(c,a)))))]]) ).
cnf(refute_0_4532,plain,
( least_upper_bound(multiply(a,inverse(c)),identity) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))),least_upper_bound(multiply(a,inverse(c)),identity)) )],[refute_0_4530,refute_0_4531]) ).
cnf(refute_0_4533,plain,
least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))) = multiply(a,inverse(greatest_lower_bound(c,a))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,inverse(c)),identity),multiply(a,inverse(greatest_lower_bound(c,a)))) )],[refute_0_4529,refute_0_4532]) ).
cnf(refute_0_4534,plain,
least_upper_bound(X_355,least_upper_bound(identity,multiply(X_90,inverse(X_91)))) = least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(multiply(X_90,inverse(X_91)))),bind(X_30,$fot(X_355)),bind(X_31,$fot(identity))]]) ).
cnf(refute_0_4535,plain,
( least_upper_bound(X_355,least_upper_bound(identity,multiply(X_90,inverse(X_91)))) != least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355))
| least_upper_bound(identity,multiply(X_90,inverse(X_91))) != multiply(least_upper_bound(X_90,X_91),inverse(X_91))
| least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) = least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(identity,multiply(X_90,inverse(X_91)))),least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355))) ),[0,1],$fot(multiply(least_upper_bound(X_90,X_91),inverse(X_91)))]]) ).
cnf(refute_0_4536,plain,
( least_upper_bound(X_355,least_upper_bound(identity,multiply(X_90,inverse(X_91)))) != least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355))
| least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) = least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_90,inverse(X_91))),multiply(least_upper_bound(X_90,X_91),inverse(X_91))) )],[refute_0_1845,refute_0_4535]) ).
cnf(refute_0_4537,plain,
least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) = least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(identity,multiply(X_90,inverse(X_91)))),least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355))) )],[refute_0_4534,refute_0_4536]) ).
cnf(refute_0_4538,plain,
least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)) = least_upper_bound(identity,least_upper_bound(multiply(X_90,inverse(X_91)),X_355)),
inference(subst,[],[refute_0_1069:[bind(X_20,$fot(multiply(X_90,inverse(X_91)))),bind(X_21,$fot(identity)),bind(X_312,$fot(X_355))]]) ).
cnf(refute_0_4539,plain,
( least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) != least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355))
| least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)) != least_upper_bound(identity,least_upper_bound(multiply(X_90,inverse(X_91)),X_355))
| least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) = least_upper_bound(identity,least_upper_bound(multiply(X_90,inverse(X_91)),X_355)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))),least_upper_bound(identity,least_upper_bound(multiply(X_90,inverse(X_91)),X_355))) ),[0],$fot(least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)))]]) ).
cnf(refute_0_4540,plain,
( least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) != least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355))
| least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) = least_upper_bound(identity,least_upper_bound(multiply(X_90,inverse(X_91)),X_355)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355)),least_upper_bound(identity,least_upper_bound(multiply(X_90,inverse(X_91)),X_355))) )],[refute_0_4538,refute_0_4539]) ).
cnf(refute_0_4541,plain,
least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))) = least_upper_bound(identity,least_upper_bound(multiply(X_90,inverse(X_91)),X_355)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,multiply(least_upper_bound(X_90,X_91),inverse(X_91))),least_upper_bound(multiply(X_90,inverse(X_91)),least_upper_bound(identity,X_355))) )],[refute_0_4537,refute_0_4540]) ).
cnf(refute_0_4542,plain,
least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))) = least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))),
inference(subst,[],[refute_0_4541:[bind(X_355,$fot(greatest_lower_bound(identity,Y))),bind(X_90,$fot(a)),bind(X_91,$fot(c))]]) ).
cnf(refute_0_4543,plain,
( least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))) != least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(c,a)))))]]) ).
cnf(refute_0_4544,plain,
( least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))),least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y)))) )],[refute_0_4542,refute_0_4543]) ).
cnf(refute_0_4545,plain,
least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))) = multiply(a,inverse(greatest_lower_bound(c,a))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(a,inverse(c)),greatest_lower_bound(identity,Y))),multiply(a,inverse(greatest_lower_bound(c,a)))) )],[refute_0_4533,refute_0_4544]) ).
cnf(refute_0_4546,plain,
least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) = least_upper_bound(Y,least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),
inference(subst,[],[refute_0_927:[bind(X_30,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),bind(X_31,$fot(identity))]]) ).
cnf(refute_0_4547,plain,
( least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) != least_upper_bound(Y,least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != multiply(least_upper_bound(a,c),inverse(c))
| least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) = least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)),least_upper_bound(Y,least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))) ),[1,1],$fot(multiply(least_upper_bound(a,c),inverse(c)))]]) ).
cnf(refute_0_4548,plain,
( least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) != least_upper_bound(Y,least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))
| least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) = least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2659,refute_0_4547]) ).
cnf(refute_0_4549,plain,
least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) = least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)),least_upper_bound(Y,least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))) )],[refute_0_4546,refute_0_4548]) ).
cnf(refute_0_4550,plain,
multiply(greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)),
inference(subst,[],[refute_0_3703:[bind(X_154,$fot(X_423)),bind(X_155,$fot(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))]]) ).
cnf(refute_0_4551,plain,
greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))) = X_423,
inference(subst,[],[refute_0_1234:[bind(X,$fot(X_423))]]) ).
cnf(refute_0_4552,plain,
( multiply(greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) != least_upper_bound(X_20,least_upper_bound(X_21,X_423))
| greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))) != X_423
| multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) ),[0,0],$fot(X_423)]]) ).
cnf(refute_0_4553,plain,
( multiply(greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) != least_upper_bound(X_20,least_upper_bound(X_21,X_423))
| multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423) )],[refute_0_4551,refute_0_4552]) ).
cnf(refute_0_4554,plain,
multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_423,least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) )],[refute_0_4550,refute_0_4553]) ).
cnf(refute_0_4555,plain,
inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423))) = inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),bind(X_16,$fot(inverse(X_423)))]]) ).
cnf(refute_0_4556,plain,
multiply(X_55,inverse(multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55))) = inverse(greatest_lower_bound(X_343,inverse(X_55))),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(greatest_lower_bound(X_343,inverse(X_55))))]]) ).
cnf(refute_0_4557,plain,
multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55) = greatest_lower_bound(identity,multiply(X_343,X_55)),
inference(subst,[],[refute_0_2562:[bind(X_171,$fot(X_55)),bind(X_172,$fot(X_343))]]) ).
cnf(refute_0_4558,plain,
( multiply(X_55,inverse(multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55))) != inverse(greatest_lower_bound(X_343,inverse(X_55)))
| multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55) != greatest_lower_bound(identity,multiply(X_343,X_55))
| multiply(X_55,inverse(greatest_lower_bound(identity,multiply(X_343,X_55)))) = inverse(greatest_lower_bound(X_343,inverse(X_55))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,inverse(multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55))),inverse(greatest_lower_bound(X_343,inverse(X_55)))) ),[0,1,0],$fot(greatest_lower_bound(identity,multiply(X_343,X_55)))]]) ).
cnf(refute_0_4559,plain,
( multiply(X_55,inverse(multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55))) != inverse(greatest_lower_bound(X_343,inverse(X_55)))
| multiply(X_55,inverse(greatest_lower_bound(identity,multiply(X_343,X_55)))) = inverse(greatest_lower_bound(X_343,inverse(X_55))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55),greatest_lower_bound(identity,multiply(X_343,X_55))) )],[refute_0_4557,refute_0_4558]) ).
cnf(refute_0_4560,plain,
multiply(X_55,inverse(greatest_lower_bound(identity,multiply(X_343,X_55)))) = inverse(greatest_lower_bound(X_343,inverse(X_55))),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(multiply(greatest_lower_bound(X_343,inverse(X_55)),X_55))),inverse(greatest_lower_bound(X_343,inverse(X_55)))) )],[refute_0_4556,refute_0_4559]) ).
cnf(refute_0_4561,plain,
multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423))),
inference(subst,[],[refute_0_4560:[bind(X_343,$fot(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),bind(X_55,$fot(X_423))]]) ).
cnf(refute_0_4562,plain,
( multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) != inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423)))
| inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423))) != inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423)))))
| multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423))))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423)))))))]]) ).
cnf(refute_0_4563,plain,
( inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423))) != inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423)))))
| multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) ),
inference(resolve,[$cnf( $equal(multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))),inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423)))) )],[refute_0_4561,refute_0_4562]) ).
cnf(refute_0_4564,plain,
multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) = inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),inverse(X_423))),inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423)))))) )],[refute_0_4555,refute_0_4563]) ).
cnf(refute_0_4565,plain,
( multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) != inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423)))))
| multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) != least_upper_bound(X_20,least_upper_bound(X_21,X_423))
| inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) ),[0],$fot(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))))]]) ).
cnf(refute_0_4566,plain,
( multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))) != least_upper_bound(X_20,least_upper_bound(X_21,X_423))
| inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)) ),
inference(resolve,[$cnf( $equal(multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))),inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423)))))) )],[refute_0_4564,refute_0_4565]) ).
cnf(refute_0_4567,plain,
inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)),
inference(resolve,[$cnf( $equal(multiply(X_423,inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))),X_423)))),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) )],[refute_0_4554,refute_0_4566]) ).
cnf(refute_0_4568,plain,
least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(least_upper_bound(X_20,X_21))),bind(X_19,$fot(X_423))]]) ).
cnf(refute_0_4569,plain,
inverse(inverse(X_423)) = X_423,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_423))]]) ).
cnf(refute_0_4570,plain,
least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)) = least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_4571,plain,
( inverse(inverse(X_423)) != X_423
| least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)) != least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))
| least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)),least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) ),[1,0],$fot(X_423)]]) ).
cnf(refute_0_4572,plain,
( inverse(inverse(X_423)) != X_423
| least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)),least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) )],[refute_0_4570,refute_0_4571]) ).
cnf(refute_0_4573,plain,
least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_423)),X_423) )],[refute_0_4569,refute_0_4572]) ).
cnf(refute_0_4574,plain,
least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))))]]) ).
cnf(refute_0_4575,plain,
( least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) != least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))
| least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)) != least_upper_bound(X_423,least_upper_bound(X_20,X_21))
| least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))),least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))) ),[1,1],$fot(least_upper_bound(X_423,least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_4576,plain,
( least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)) != least_upper_bound(X_423,least_upper_bound(X_20,X_21))
| least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))),least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))) )],[refute_0_4574,refute_0_4575]) ).
cnf(refute_0_4577,plain,
least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)),least_upper_bound(X_423,least_upper_bound(X_20,X_21))) )],[refute_0_4573,refute_0_4576]) ).
cnf(refute_0_4578,plain,
( least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))) != least_upper_bound(X_423,least_upper_bound(X_20,X_21))
| least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) != least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21)))
| least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))))),bind(Y0,$fot(least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))))),bind(Z0,$fot(least_upper_bound(X_423,least_upper_bound(X_20,X_21))))]]) ).
cnf(refute_0_4579,plain,
( least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))) != least_upper_bound(X_423,least_upper_bound(X_20,X_21))
| least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))),least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21)))) )],[refute_0_4577,refute_0_4578]) ).
cnf(refute_0_4580,plain,
least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_423,least_upper_bound(X_423,least_upper_bound(X_20,X_21))),least_upper_bound(X_423,least_upper_bound(X_20,X_21))) )],[refute_0_4568,refute_0_4579]) ).
cnf(refute_0_4581,plain,
least_upper_bound(X_355,least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))) = least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(least_upper_bound(X_20,least_upper_bound(X_356,Y)))),bind(X_30,$fot(X_355)),bind(X_31,$fot(X_356))]]) ).
cnf(refute_0_4582,plain,
least_upper_bound(X_20,least_upper_bound(X_356,Y)) = least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y))),
inference(subst,[],[refute_0_729:[bind(X_21,$fot(X_356))]]) ).
cnf(refute_0_4583,plain,
( least_upper_bound(X_20,least_upper_bound(X_356,Y)) != least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))
| least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(X_20,least_upper_bound(X_356,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_356,Y)))),bind(Y0,$fot(least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))))]]) ).
cnf(refute_0_4584,plain,
least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(X_20,least_upper_bound(X_356,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))) )],[refute_0_4582,refute_0_4583]) ).
cnf(refute_0_4585,plain,
( least_upper_bound(X_355,least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))) != least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355))
| least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y))) != least_upper_bound(X_20,least_upper_bound(X_356,Y))
| least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))),least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355))) ),[0,1],$fot(least_upper_bound(X_20,least_upper_bound(X_356,Y)))]]) ).
cnf(refute_0_4586,plain,
( least_upper_bound(X_355,least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))) != least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355))
| least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y))),least_upper_bound(X_20,least_upper_bound(X_356,Y))) )],[refute_0_4584,refute_0_4585]) ).
cnf(refute_0_4587,plain,
least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,Y)))),least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355))) )],[refute_0_4581,refute_0_4586]) ).
cnf(refute_0_4588,plain,
least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))),
inference(subst,[],[refute_0_731:[bind(Y,$fot(least_upper_bound(Y,X_355))),bind(X_21,$fot(X_356))]]) ).
cnf(refute_0_4589,plain,
least_upper_bound(least_upper_bound(X_356,Y),X_355) = least_upper_bound(X_356,least_upper_bound(Y,X_355)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_356)),bind(Z,$fot(X_355))]]) ).
cnf(refute_0_4590,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)))]]) ).
cnf(refute_0_4591,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355))
| least_upper_bound(least_upper_bound(X_356,Y),X_355) != least_upper_bound(X_356,least_upper_bound(Y,X_355))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355))) ),[1,1],$fot(least_upper_bound(X_356,least_upper_bound(Y,X_355)))]]) ).
cnf(refute_0_4592,plain,
( least_upper_bound(least_upper_bound(X_356,Y),X_355) != least_upper_bound(X_356,least_upper_bound(Y,X_355))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355))) )],[refute_0_4590,refute_0_4591]) ).
cnf(refute_0_4593,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,Y),X_355),least_upper_bound(X_356,least_upper_bound(Y,X_355))) )],[refute_0_4589,refute_0_4592]) ).
cnf(refute_0_4594,plain,
least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_20)),bind(Y,$fot(least_upper_bound(X_356,Y))),bind(Z,$fot(X_355))]]) ).
cnf(refute_0_4595,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))))]]) ).
cnf(refute_0_4596,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355))) )],[refute_0_4594,refute_0_4595]) ).
cnf(refute_0_4597,plain,
least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,Y),X_355)),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) )],[refute_0_4593,refute_0_4596]) ).
cnf(refute_0_4598,plain,
least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) = least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)))]]) ).
cnf(refute_0_4599,plain,
( least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) != least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) = least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)),least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355))) ),[1,1],$fot(least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))))]]) ).
cnf(refute_0_4600,plain,
( least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) = least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)),least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355))) )],[refute_0_4598,refute_0_4599]) ).
cnf(refute_0_4601,plain,
least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) = least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) )],[refute_0_4597,refute_0_4600]) ).
cnf(refute_0_4602,plain,
( least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) != least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))))
| least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)))),bind(Y0,$fot(least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))))]]) ).
cnf(refute_0_4603,plain,
( least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)),least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))))) )],[refute_0_4601,refute_0_4602]) ).
cnf(refute_0_4604,plain,
least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) )],[refute_0_4588,refute_0_4603]) ).
cnf(refute_0_4605,plain,
least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) = least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)),
inference(subst,[],[refute_0_1069:[bind(X_20,$fot(least_upper_bound(X_20,least_upper_bound(X_356,Y)))),bind(X_21,$fot(X_356)),bind(X_312,$fot(X_355))]]) ).
cnf(refute_0_4606,plain,
( least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) != least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)))),bind(Y0,$fot(least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))))]]) ).
cnf(refute_0_4607,plain,
( least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)),least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355))) )],[refute_0_4605,refute_0_4606]) ).
cnf(refute_0_4608,plain,
least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_356,least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),X_355)),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) )],[refute_0_4604,refute_0_4607]) ).
cnf(refute_0_4609,plain,
( least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) != least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355))
| least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)))]]) ).
cnf(refute_0_4610,plain,
( least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) != least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355))
| least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355)),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) )],[refute_0_4608,refute_0_4609]) ).
cnf(refute_0_4611,plain,
least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))),least_upper_bound(least_upper_bound(X_20,least_upper_bound(X_356,Y)),least_upper_bound(X_356,X_355))) )],[refute_0_4587,refute_0_4610]) ).
cnf(refute_0_4612,plain,
( least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))
| least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) = least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))))]]) ).
cnf(refute_0_4613,plain,
least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355))) = least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_355,least_upper_bound(X_20,least_upper_bound(X_356,Y))),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(Y,X_355)))) )],[refute_0_4611,refute_0_4612]) ).
cnf(refute_0_4614,plain,
least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) = least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))),
inference(subst,[],[refute_0_4613:[bind(Y,$fot(X_21)),bind(X_20,$fot(inverse(inverse(X_423)))),bind(X_355,$fot(X_423)),bind(X_356,$fot(X_20))]]) ).
cnf(refute_0_4615,plain,
least_upper_bound(inverse(X_474),X_475) = multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)))),
inference(subst,[],[refute_0_417:[bind(X_46,$fot(least_upper_bound(inverse(X_474),X_475))),bind(X_95,$fot(inverse(X_475)))]]) ).
cnf(refute_0_4616,plain,
( multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| least_upper_bound(inverse(X_474),X_475) != multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475))))
| least_upper_bound(inverse(X_474),X_475) = multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_474),X_475),multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475))))) ),[1,1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))]]) ).
cnf(refute_0_4617,plain,
( least_upper_bound(inverse(X_474),X_475) != multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475))))
| least_upper_bound(inverse(X_474),X_475) = multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475)),inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) )],[refute_0_2548,refute_0_4616]) ).
cnf(refute_0_4618,plain,
least_upper_bound(inverse(X_474),X_475) = multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_474),X_475),multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,multiply(inverse(X_475),least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_4615,refute_0_4617]) ).
cnf(refute_0_4619,plain,
multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) = inverse(greatest_lower_bound(X_474,inverse(X_475))),
inference(subst,[],[refute_0_4560:[bind(X_343,$fot(X_474)),bind(X_55,$fot(X_475))]]) ).
cnf(refute_0_4620,plain,
multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),
introduced(tautology,[refl,[$fot(multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))]]) ).
cnf(refute_0_4621,plain,
( multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))]]) ).
cnf(refute_0_4622,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))
| multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
inference(resolve,[$cnf( $equal(multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) )],[refute_0_4620,refute_0_4621]) ).
cnf(refute_0_4623,plain,
multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) )],[refute_0_2596,refute_0_4622]) ).
cnf(refute_0_4624,plain,
greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)) = X_475,
inference(subst,[],[refute_0_262:[bind(X,$fot(X_475)),bind(Y,$fot(inverse(X_474)))]]) ).
cnf(refute_0_4625,plain,
inverse(inverse(least_upper_bound(inverse(X_474),X_475))) = least_upper_bound(inverse(X_474),X_475),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(least_upper_bound(inverse(X_474),X_475)))]]) ).
cnf(refute_0_4626,plain,
greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))))]]) ).
cnf(refute_0_4627,plain,
( greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) != greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475))))
| inverse(inverse(least_upper_bound(inverse(X_474),X_475))) != least_upper_bound(inverse(X_474),X_475)
| greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))),greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475))))) ),[1,1],$fot(least_upper_bound(inverse(X_474),X_475))]]) ).
cnf(refute_0_4628,plain,
( inverse(inverse(least_upper_bound(inverse(X_474),X_475))) != least_upper_bound(inverse(X_474),X_475)
| greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))),greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_4626,refute_0_4627]) ).
cnf(refute_0_4629,plain,
greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X_474),X_475))),least_upper_bound(inverse(X_474),X_475)) )],[refute_0_4625,refute_0_4628]) ).
cnf(refute_0_4630,plain,
( greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) != greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475))
| greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)) != X_475
| greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) = X_475 ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))))),bind(Y0,$fot(greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)))),bind(Z0,$fot(X_475))]]) ).
cnf(refute_0_4631,plain,
( greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)) != X_475
| greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) = X_475 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))),greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475))) )],[refute_0_4629,refute_0_4630]) ).
cnf(refute_0_4632,plain,
greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) = X_475,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_475,least_upper_bound(inverse(X_474),X_475)),X_475) )],[refute_0_4624,refute_0_4631]) ).
cnf(refute_0_4633,plain,
inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))),
inference(subst,[],[refute_0_2616:[bind(X_474,$fot(X_475)),bind(X_475,$fot(inverse(least_upper_bound(inverse(X_474),X_475))))]]) ).
cnf(refute_0_4634,plain,
( greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) != X_475
| inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475))))
| inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = X_475 ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))))),bind(Y0,$fot(greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))))),bind(Z0,$fot(X_475))]]) ).
cnf(refute_0_4635,plain,
( greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))) != X_475
| inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = X_475 ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475))))) )],[refute_0_4633,refute_0_4634]) ).
cnf(refute_0_4636,plain,
inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) = X_475,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_475,inverse(inverse(least_upper_bound(inverse(X_474),X_475)))),X_475) )],[refute_0_4632,refute_0_4635]) ).
cnf(refute_0_4637,plain,
multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))]]) ).
cnf(refute_0_4638,plain,
( multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))
| inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != X_475
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) ),[1,0],$fot(X_475)]]) ).
cnf(refute_0_4639,plain,
( inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))) != X_475
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) )],[refute_0_4637,refute_0_4638]) ).
cnf(refute_0_4640,plain,
multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),X_475) )],[refute_0_4636,refute_0_4639]) ).
cnf(refute_0_4641,plain,
( multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))),bind(Y0,$fot(multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))),bind(Z0,$fot(multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))]]) ).
cnf(refute_0_4642,plain,
( multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) )],[refute_0_4640,refute_0_4641]) ).
cnf(refute_0_4643,plain,
multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),
inference(resolve,[$cnf( $equal(multiply(X_475,least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) )],[refute_0_4623,refute_0_4642]) ).
cnf(refute_0_4644,plain,
( multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(X_474,inverse(X_475)))
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = inverse(greatest_lower_bound(X_474,inverse(X_475))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))))),bind(Y0,$fot(multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_474,inverse(X_475)))))]]) ).
cnf(refute_0_4645,plain,
( multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))) != inverse(greatest_lower_bound(X_474,inverse(X_475)))
| multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = inverse(greatest_lower_bound(X_474,inverse(X_475))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) )],[refute_0_4643,refute_0_4644]) ).
cnf(refute_0_4646,plain,
multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) = inverse(greatest_lower_bound(X_474,inverse(X_475))),
inference(resolve,[$cnf( $equal(multiply(X_475,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))),inverse(greatest_lower_bound(X_474,inverse(X_475)))) )],[refute_0_4619,refute_0_4645]) ).
cnf(refute_0_4647,plain,
( multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))) != inverse(greatest_lower_bound(X_474,inverse(X_475)))
| least_upper_bound(inverse(X_474),X_475) != multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))
| least_upper_bound(inverse(X_474),X_475) = inverse(greatest_lower_bound(X_474,inverse(X_475))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_474),X_475),multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) ),[1],$fot(inverse(greatest_lower_bound(X_474,inverse(X_475))))]]) ).
cnf(refute_0_4648,plain,
( least_upper_bound(inverse(X_474),X_475) != multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))
| least_upper_bound(inverse(X_474),X_475) = inverse(greatest_lower_bound(X_474,inverse(X_475))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475))))),inverse(greatest_lower_bound(X_474,inverse(X_475)))) )],[refute_0_4646,refute_0_4647]) ).
cnf(refute_0_4649,plain,
least_upper_bound(inverse(X_474),X_475) = inverse(greatest_lower_bound(X_474,inverse(X_475))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_474),X_475),multiply(inverse(least_upper_bound(inverse(X_475),inverse(least_upper_bound(inverse(X_474),X_475)))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_475)))))) )],[refute_0_4618,refute_0_4648]) ).
cnf(refute_0_4650,plain,
( least_upper_bound(inverse(X_474),X_475) != inverse(greatest_lower_bound(X_474,inverse(X_475)))
| inverse(greatest_lower_bound(X_474,inverse(X_475))) = least_upper_bound(inverse(X_474),X_475) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(inverse(X_474),X_475))),bind(Y0,$fot(inverse(greatest_lower_bound(X_474,inverse(X_475)))))]]) ).
cnf(refute_0_4651,plain,
inverse(greatest_lower_bound(X_474,inverse(X_475))) = least_upper_bound(inverse(X_474),X_475),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_474),X_475),inverse(greatest_lower_bound(X_474,inverse(X_475)))) )],[refute_0_4649,refute_0_4650]) ).
cnf(refute_0_4652,plain,
inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423))),
inference(subst,[],[refute_0_4651:[bind(X_474,$fot(inverse(X_423))),bind(X_475,$fot(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))]]) ).
cnf(refute_0_4653,plain,
( inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) != least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423)))
| least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) != least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))
| inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))))),bind(Y0,$fot(least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),bind(Z0,$fot(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))))]]) ).
cnf(refute_0_4654,plain,
( least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) != least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))
| inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423)))) )],[refute_0_4652,refute_0_4653]) ).
cnf(refute_0_4655,plain,
inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,least_upper_bound(X_21,X_423))),least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))) )],[refute_0_4614,refute_0_4654]) ).
cnf(refute_0_4656,plain,
( inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) != least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))
| least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) != least_upper_bound(X_423,least_upper_bound(X_20,X_21))
| inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))))),bind(Y0,$fot(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))))),bind(Z0,$fot(least_upper_bound(X_423,least_upper_bound(X_20,X_21))))]]) ).
cnf(refute_0_4657,plain,
( least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))) != least_upper_bound(X_423,least_upper_bound(X_20,X_21))
| inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21)))) )],[refute_0_4655,refute_0_4656]) ).
cnf(refute_0_4658,plain,
inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) = least_upper_bound(X_423,least_upper_bound(X_20,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_423,least_upper_bound(inverse(inverse(X_423)),least_upper_bound(X_20,X_21))),least_upper_bound(X_423,least_upper_bound(X_20,X_21))) )],[refute_0_4580,refute_0_4657]) ).
cnf(refute_0_4659,plain,
( inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) != least_upper_bound(X_20,least_upper_bound(X_21,X_423))
| inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) != least_upper_bound(X_423,least_upper_bound(X_20,X_21))
| least_upper_bound(X_423,least_upper_bound(X_20,X_21)) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) ),[0],$fot(least_upper_bound(X_423,least_upper_bound(X_20,X_21)))]]) ).
cnf(refute_0_4660,plain,
( inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))) != least_upper_bound(X_20,least_upper_bound(X_21,X_423))
| least_upper_bound(X_423,least_upper_bound(X_20,X_21)) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),least_upper_bound(X_423,least_upper_bound(X_20,X_21))) )],[refute_0_4658,refute_0_4659]) ).
cnf(refute_0_4661,plain,
least_upper_bound(X_423,least_upper_bound(X_20,X_21)) = least_upper_bound(X_20,least_upper_bound(X_21,X_423)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_423),inverse(least_upper_bound(X_20,least_upper_bound(X_21,X_423))))),least_upper_bound(X_20,least_upper_bound(X_21,X_423))) )],[refute_0_4567,refute_0_4660]) ).
cnf(refute_0_4662,plain,
least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),
inference(subst,[],[refute_0_4661:[bind(X_20,$fot(identity)),bind(X_21,$fot(Y)),bind(X_423,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_4663,plain,
( least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) != least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c)))
| least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) != least_upper_bound(identity,least_upper_bound(Y,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))
| least_upper_bound(identity,least_upper_bound(Y,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)),least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(Y,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))))]]) ).
cnf(refute_0_4664,plain,
( least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)) != least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c)))
| least_upper_bound(identity,least_upper_bound(Y,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)),least_upper_bound(identity,least_upper_bound(Y,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))) )],[refute_0_4662,refute_0_4663]) ).
cnf(refute_0_4665,plain,
least_upper_bound(identity,least_upper_bound(Y,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),least_upper_bound(identity,Y)),least_upper_bound(Y,multiply(least_upper_bound(a,c),inverse(c)))) )],[refute_0_4549,refute_0_4664]) ).
cnf(refute_0_4666,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))),
inference(subst,[],[refute_0_4665:[bind(Y,$fot(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_4667,plain,
( least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) != least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(c,a)))))]]) ).
cnf(refute_0_4668,plain,
( least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(a,inverse(greatest_lower_bound(c,a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c)))) )],[refute_0_4666,refute_0_4667]) ).
cnf(refute_0_4669,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(a,inverse(greatest_lower_bound(c,a))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,Y),multiply(least_upper_bound(a,c),inverse(c))),multiply(a,inverse(greatest_lower_bound(c,a)))) )],[refute_0_4545,refute_0_4668]) ).
cnf(refute_0_4670,plain,
( multiply(a,inverse(greatest_lower_bound(c,a))) != multiply(a,inverse(greatest_lower_bound(a,c)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) != multiply(a,inverse(greatest_lower_bound(c,a)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))))),bind(Y0,$fot(multiply(a,inverse(greatest_lower_bound(c,a))))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_4671,plain,
( multiply(a,inverse(greatest_lower_bound(c,a))) != multiply(a,inverse(greatest_lower_bound(a,c)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),multiply(a,inverse(greatest_lower_bound(c,a)))) )],[refute_0_4669,refute_0_4670]) ).
cnf(refute_0_4672,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) = multiply(a,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(c,a))),multiply(a,inverse(greatest_lower_bound(a,c)))) )],[refute_0_2667,refute_0_4671]) ).
cnf(refute_0_4673,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) != multiply(a,inverse(greatest_lower_bound(a,c)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) != multiply(least_upper_bound(a,c),inverse(c))
| multiply(a,inverse(greatest_lower_bound(a,c))) = multiply(least_upper_bound(a,c),inverse(c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),multiply(least_upper_bound(a,c),inverse(c))) ),[0],$fot(multiply(a,inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4674,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))) != multiply(least_upper_bound(a,c),inverse(c))
| multiply(a,inverse(greatest_lower_bound(a,c))) = multiply(least_upper_bound(a,c),inverse(c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),multiply(a,inverse(greatest_lower_bound(a,c)))) )],[refute_0_4672,refute_0_4673]) ).
cnf(refute_0_4675,plain,
multiply(a,inverse(greatest_lower_bound(a,c))) = multiply(least_upper_bound(a,c),inverse(c)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2662,refute_0_4674]) ).
cnf(refute_0_4676,plain,
( multiply(a,inverse(greatest_lower_bound(a,c))) != multiply(least_upper_bound(a,c),inverse(c))
| multiply(least_upper_bound(a,c),inverse(c)) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(a,inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),inverse(c))))]]) ).
cnf(refute_0_4677,plain,
multiply(least_upper_bound(a,c),inverse(c)) = multiply(a,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_4675,refute_0_4676]) ).
cnf(refute_0_4678,plain,
( multiply(inverse(c),inverse(multiply(least_upper_bound(a,c),inverse(c)))) != inverse(least_upper_bound(a,c))
| multiply(least_upper_bound(a,c),inverse(c)) != multiply(a,inverse(greatest_lower_bound(a,c)))
| multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),inverse(multiply(least_upper_bound(a,c),inverse(c)))),inverse(least_upper_bound(a,c))) ),[0,1,0],$fot(multiply(a,inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4679,plain,
( multiply(inverse(c),inverse(multiply(least_upper_bound(a,c),inverse(c)))) != inverse(least_upper_bound(a,c))
| multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(c)),multiply(a,inverse(greatest_lower_bound(a,c)))) )],[refute_0_4677,refute_0_4678]) ).
cnf(refute_0_4680,plain,
multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(c),inverse(multiply(least_upper_bound(a,c),inverse(c)))),inverse(least_upper_bound(a,c))) )],[refute_0_544,refute_0_4679]) ).
cnf(refute_0_4681,plain,
multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(inverse(greatest_lower_bound(a,c)))),bind(Z,$fot(c))]]) ).
cnf(refute_0_4682,plain,
inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)) = inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)))]]) ).
cnf(refute_0_4683,plain,
( multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)) != inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c))
| inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)) = inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)),inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c))) ),[1,0],$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_4684,plain,
( multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)) = inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)),inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c))) )],[refute_0_4682,refute_0_4683]) ).
cnf(refute_0_4685,plain,
inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)) = inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_4681,refute_0_4684]) ).
cnf(refute_0_4686,plain,
multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(multiply(a,inverse(greatest_lower_bound(a,c))))),bind(X_46,$fot(c))]]) ).
cnf(refute_0_4687,plain,
( multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) != inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c))
| inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)) != inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))
| multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)))),bind(Z0,$fot(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_4688,plain,
( inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)) != inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))
| multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))),inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c))) )],[refute_0_4686,refute_0_4687]) ).
cnf(refute_0_4689,plain,
multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) = inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),c)),inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_4685,refute_0_4688]) ).
cnf(refute_0_4690,plain,
( multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) != inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))
| multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) != inverse(least_upper_bound(a,c))
| inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) = inverse(least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))),inverse(least_upper_bound(a,c))) ),[0],$fot(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_4691,plain,
( multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))) != inverse(least_upper_bound(a,c))
| inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) = inverse(least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))),inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_4689,refute_0_4690]) ).
cnf(refute_0_4692,plain,
inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) = inverse(least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(c),inverse(multiply(a,inverse(greatest_lower_bound(a,c))))),inverse(least_upper_bound(a,c))) )],[refute_0_4680,refute_0_4691]) ).
cnf(refute_0_4693,plain,
( inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) != inverse(least_upper_bound(a,c))
| inverse(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(inverse(least_upper_bound(a,c))) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) ),[0,0],$fot(inverse(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4694,plain,
( inverse(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(inverse(least_upper_bound(a,c))) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(a,c))) )],[refute_0_4692,refute_0_4693]) ).
cnf(refute_0_4695,plain,
inverse(inverse(least_upper_bound(a,c))) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_543,refute_0_4694]) ).
cnf(refute_0_4696,plain,
inverse(inverse(least_upper_bound(a,c))) = least_upper_bound(a,c),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4697,plain,
( inverse(inverse(least_upper_bound(a,c))) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))
| inverse(inverse(least_upper_bound(a,c))) != least_upper_bound(a,c)
| least_upper_bound(a,c) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(a,c))),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) ),[0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_4698,plain,
( inverse(inverse(least_upper_bound(a,c))) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(a,c) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) )],[refute_0_4696,refute_0_4697]) ).
cnf(refute_0_4699,plain,
least_upper_bound(a,c) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(a,c))),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_4695,refute_0_4698]) ).
cnf(refute_0_4700,plain,
( least_upper_bound(a,c) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))
| multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(a,c) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(a,c))),bind(Y0,$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_4701,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(a,c),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_4699,refute_0_4700]) ).
cnf(refute_0_4702,plain,
( multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)) != least_upper_bound(a,c)
| multiply(inverse(greatest_lower_bound(a,c)),c) != multiply(inverse(a),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))
| multiply(inverse(greatest_lower_bound(a,c)),c) = multiply(inverse(a),least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),c),multiply(inverse(a),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))) ),[1,1],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_4703,plain,
( multiply(inverse(greatest_lower_bound(a,c)),c) != multiply(inverse(a),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))
| multiply(inverse(greatest_lower_bound(a,c)),c) = multiply(inverse(a),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)),least_upper_bound(a,c)) )],[refute_0_4701,refute_0_4702]) ).
cnf(refute_0_4704,plain,
multiply(inverse(greatest_lower_bound(a,c)),c) = multiply(inverse(a),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),c),multiply(inverse(a),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_542,refute_0_4703]) ).
cnf(refute_0_4705,plain,
least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_4706,plain,
( multiply(inverse(greatest_lower_bound(a,c)),c) != multiply(inverse(a),least_upper_bound(a,c))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) ),[1,1],$fot(multiply(inverse(a),least_upper_bound(a,c)))]]) ).
cnf(refute_0_4707,plain,
( multiply(inverse(greatest_lower_bound(a,c)),c) != multiply(inverse(a),least_upper_bound(a,c))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_4705,refute_0_4706]) ).
cnf(refute_0_4708,plain,
least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),c),multiply(inverse(a),least_upper_bound(a,c))) )],[refute_0_4704,refute_0_4707]) ).
cnf(refute_0_4709,plain,
inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_4710,plain,
( inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),[1,0],$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))]]) ).
cnf(refute_0_4711,plain,
( least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_4709,refute_0_4710]) ).
cnf(refute_0_4712,plain,
inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)),least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) )],[refute_0_4708,refute_0_4711]) ).
cnf(refute_0_4713,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_4714,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) ),[1,1],$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4715,plain,
( inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_4713,refute_0_4714]) ).
cnf(refute_0_4716,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) )],[refute_0_4712,refute_0_4715]) ).
cnf(refute_0_4717,plain,
multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)),
introduced(tautology,[refl,[$fot(multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_4718,plain,
( multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))
| multiply(inverse(greatest_lower_bound(a,c)),c) != multiply(inverse(a),least_upper_bound(a,c))
| multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(b,multiply(inverse(a),least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) ),[1,1],$fot(multiply(inverse(a),least_upper_bound(a,c)))]]) ).
cnf(refute_0_4719,plain,
( multiply(inverse(greatest_lower_bound(a,c)),c) != multiply(inverse(a),least_upper_bound(a,c))
| multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(b,multiply(inverse(a),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) )],[refute_0_4717,refute_0_4718]) ).
cnf(refute_0_4720,plain,
multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(b,multiply(inverse(a),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),c),multiply(inverse(a),least_upper_bound(a,c))) )],[refute_0_4704,refute_0_4719]) ).
cnf(refute_0_4721,plain,
least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) = least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))))]]) ).
cnf(refute_0_4722,plain,
( multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(b,multiply(inverse(a),least_upper_bound(a,c)))
| least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) != least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))
| least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) = least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) ),[1,1],$fot(multiply(b,multiply(inverse(a),least_upper_bound(a,c))))]]) ).
cnf(refute_0_4723,plain,
( multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(b,multiply(inverse(a),least_upper_bound(a,c)))
| least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) = least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)))) )],[refute_0_4721,refute_0_4722]) ).
cnf(refute_0_4724,plain,
least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) = least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) )],[refute_0_4720,refute_0_4723]) ).
cnf(refute_0_4725,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))]]) ).
cnf(refute_0_4726,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) != least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c))))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) ),[1,0],$fot(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_4727,plain,
( least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))) != least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c))))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_4725,refute_0_4726]) ).
cnf(refute_0_4728,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c))))) )],[refute_0_4724,refute_0_4727]) ).
cnf(refute_0_4729,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))),bind(Y0,$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))))),bind(Z0,$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4730,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_4728,refute_0_4729]) ).
cnf(refute_0_4731,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))) )],[refute_0_4716,refute_0_4730]) ).
cnf(refute_0_4732,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))
| b != multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) ),[1],$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4733,plain,
( b != multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))
| b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c)))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))) )],[refute_0_4731,refute_0_4732]) ).
cnf(refute_0_4734,plain,
b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(b,multiply(least_upper_bound(a,multiply(b,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(greatest_lower_bound(a,c)),c))))) )],[refute_0_541,refute_0_4733]) ).
cnf(refute_0_4735,plain,
inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),a),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(a)),bind(X_69,$fot(multiply(inverse(greatest_lower_bound(a,c)),c)))]]) ).
cnf(refute_0_4736,plain,
( inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))) != inverse(least_upper_bound(a,c))
| inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),a)
| inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(inverse(least_upper_bound(a,c)),a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),a)) ),[1,0],$fot(inverse(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4737,plain,
( inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),a)
| inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(inverse(least_upper_bound(a,c)),a) ),
inference(resolve,[$cnf( $equal(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),inverse(least_upper_bound(a,c))) )],[refute_0_4692,refute_0_4736]) ).
cnf(refute_0_4738,plain,
inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(inverse(least_upper_bound(a,c)),a),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(inverse(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),c))),a)) )],[refute_0_4735,refute_0_4737]) ).
cnf(refute_0_4739,plain,
inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) = multiply(inverse(c),greatest_lower_bound(a,c)),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(greatest_lower_bound(a,c))),bind(X_74,$fot(c))]]) ).
cnf(refute_0_4740,plain,
( inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(inverse(c),greatest_lower_bound(a,c))
| inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(inverse(least_upper_bound(a,c)),a)
| multiply(inverse(c),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(inverse(least_upper_bound(a,c)),a)) ),[0],$fot(multiply(inverse(c),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_4741,plain,
( inverse(multiply(inverse(greatest_lower_bound(a,c)),c)) != multiply(inverse(least_upper_bound(a,c)),a)
| multiply(inverse(c),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),a) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(inverse(c),greatest_lower_bound(a,c))) )],[refute_0_4739,refute_0_4740]) ).
cnf(refute_0_4742,plain,
multiply(inverse(c),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),a),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(a,c)),c)),multiply(inverse(least_upper_bound(a,c)),a)) )],[refute_0_4738,refute_0_4741]) ).
cnf(refute_0_4743,plain,
( multiply(inverse(c),greatest_lower_bound(a,c)) != multiply(inverse(least_upper_bound(a,c)),a)
| multiply(inverse(least_upper_bound(a,c)),a) = multiply(inverse(c),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(c),greatest_lower_bound(a,c)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),a)))]]) ).
cnf(refute_0_4744,plain,
multiply(inverse(least_upper_bound(a,c)),a) = multiply(inverse(c),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(c),greatest_lower_bound(a,c)),multiply(inverse(least_upper_bound(a,c)),a)) )],[refute_0_4742,refute_0_4743]) ).
cnf(refute_0_4745,plain,
inverse(multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(a,c)),a),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(a)),bind(X_74,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4746,plain,
( multiply(inverse(least_upper_bound(a,c)),a) != multiply(inverse(c),greatest_lower_bound(a,c))
| inverse(multiply(inverse(a),least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(a,c)),a)
| inverse(multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(c),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(multiply(inverse(a),least_upper_bound(a,c))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),a))),bind(Z0,$fot(multiply(inverse(c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4747,plain,
( multiply(inverse(least_upper_bound(a,c)),a) != multiply(inverse(c),greatest_lower_bound(a,c))
| inverse(multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(c),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),a)) )],[refute_0_4745,refute_0_4746]) ).
cnf(refute_0_4748,plain,
inverse(multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(c),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),a),multiply(inverse(c),greatest_lower_bound(a,c))) )],[refute_0_4744,refute_0_4747]) ).
cnf(refute_0_4749,plain,
multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),
inference(subst,[],[refute_0_172:[bind(X_90,$fot(identity)),bind(X_91,$fot(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))]]) ).
cnf(refute_0_4750,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),
inference(subst,[],[refute_0_844:[bind(X_18,$fot(X_132)),bind(X_85,$fot(X_133))]]) ).
cnf(refute_0_4751,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))]]) ).
cnf(refute_0_4752,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) )],[refute_0_4750,refute_0_4751]) ).
cnf(refute_0_4753,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) != identity
| multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4754,plain,
( multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity) )],[refute_0_4752,refute_0_4753]) ).
cnf(refute_0_4755,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))) )],[refute_0_4749,refute_0_4754]) ).
cnf(refute_0_4756,plain,
inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) = multiply(inverse(X_133),least_upper_bound(X_133,X_132)),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(least_upper_bound(X_133,X_132))),bind(X_74,$fot(X_133))]]) ).
cnf(refute_0_4757,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))]]) ).
cnf(refute_0_4758,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))
| inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) != multiply(inverse(X_133),least_upper_bound(X_133,X_132))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = multiply(inverse(X_133),least_upper_bound(X_133,X_132)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))),bind(Y0,$fot(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),bind(Z0,$fot(multiply(inverse(X_133),least_upper_bound(X_133,X_132))))]]) ).
cnf(refute_0_4759,plain,
( inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) != multiply(inverse(X_133),least_upper_bound(X_133,X_132))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = multiply(inverse(X_133),least_upper_bound(X_133,X_132)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) )],[refute_0_4757,refute_0_4758]) ).
cnf(refute_0_4760,plain,
multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = multiply(inverse(X_133),least_upper_bound(X_133,X_132)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),multiply(inverse(X_133),least_upper_bound(X_133,X_132))) )],[refute_0_4756,refute_0_4759]) ).
cnf(refute_0_4761,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != multiply(inverse(X_133),least_upper_bound(X_133,X_132))
| multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| multiply(inverse(X_133),least_upper_bound(X_133,X_132)) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))) ),[0],$fot(multiply(inverse(X_133),least_upper_bound(X_133,X_132)))]]) ).
cnf(refute_0_4762,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| multiply(inverse(X_133),least_upper_bound(X_133,X_132)) = least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),multiply(inverse(X_133),least_upper_bound(X_133,X_132))) )],[refute_0_4760,refute_0_4761]) ).
cnf(refute_0_4763,plain,
least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))]]) ).
cnf(refute_0_4764,plain,
( inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) != multiply(inverse(X_133),least_upper_bound(X_133,X_132))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) ),[1,1],$fot(multiply(inverse(X_133),least_upper_bound(X_133,X_132)))]]) ).
cnf(refute_0_4765,plain,
( inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)) != multiply(inverse(X_133),least_upper_bound(X_133,X_132))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) )],[refute_0_4763,refute_0_4764]) ).
cnf(refute_0_4766,plain,
least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),multiply(inverse(X_133),least_upper_bound(X_133,X_132))) )],[refute_0_4756,refute_0_4765]) ).
cnf(refute_0_4767,plain,
multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))))]]) ).
cnf(refute_0_4768,plain,
multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)) = multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),
inference(subst,[],[refute_0_320:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))]]) ).
cnf(refute_0_4769,plain,
( multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)) != multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))))]]) ).
cnf(refute_0_4770,plain,
( multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))
| multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)),multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))) )],[refute_0_4768,refute_0_4769]) ).
cnf(refute_0_4771,plain,
multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) )],[refute_0_4767,refute_0_4770]) ).
cnf(refute_0_4772,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)),
inference(subst,[],[refute_0_337:[bind(X_82,$fot(identity)),bind(X_83,$fot(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))]]) ).
cnf(refute_0_4773,plain,
( multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) != multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))))]]) ).
cnf(refute_0_4774,plain,
( multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity))) )],[refute_0_4772,refute_0_4773]) ).
cnf(refute_0_4775,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)),identity)),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) )],[refute_0_4771,refute_0_4774]) ).
cnf(refute_0_4776,plain,
( least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) != least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))
| least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))))]]) ).
cnf(refute_0_4777,plain,
( least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) )],[refute_0_4775,refute_0_4776]) ).
cnf(refute_0_4778,plain,
least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))) )],[refute_0_4766,refute_0_4777]) ).
cnf(refute_0_4779,plain,
( multiply(inverse(X_133),least_upper_bound(X_133,X_132)) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))) != least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))
| multiply(inverse(X_133),least_upper_bound(X_133,X_132)) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_133),least_upper_bound(X_133,X_132)),least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))))]]) ).
cnf(refute_0_4780,plain,
( multiply(inverse(X_133),least_upper_bound(X_133,X_132)) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| multiply(inverse(X_133),least_upper_bound(X_133,X_132)) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133)))),least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))) )],[refute_0_4778,refute_0_4779]) ).
cnf(refute_0_4781,plain,
( multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))) != least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))
| multiply(inverse(X_133),least_upper_bound(X_133,X_132)) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_133),least_upper_bound(X_133,X_132)),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))) )],[refute_0_4762,refute_0_4780]) ).
cnf(refute_0_4782,plain,
multiply(inverse(X_133),least_upper_bound(X_133,X_132)) = least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))),least_upper_bound(identity,multiply(identity,inverse(multiply(inverse(least_upper_bound(X_133,X_132)),X_133))))) )],[refute_0_4755,refute_0_4781]) ).
cnf(refute_0_4783,plain,
( multiply(inverse(X_133),least_upper_bound(X_133,X_132)) != least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))
| least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) = multiply(inverse(X_133),least_upper_bound(X_133,X_132)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(X_133),least_upper_bound(X_133,X_132)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))))]]) ).
cnf(refute_0_4784,plain,
least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132))) = multiply(inverse(X_133),least_upper_bound(X_133,X_132)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_133),least_upper_bound(X_133,X_132)),least_upper_bound(identity,multiply(inverse(X_133),least_upper_bound(X_133,X_132)))) )],[refute_0_4782,refute_0_4783]) ).
cnf(refute_0_4785,plain,
least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(a),least_upper_bound(a,c)),
inference(subst,[],[refute_0_4784:[bind(X_132,$fot(c)),bind(X_133,$fot(a))]]) ).
cnf(refute_0_4786,plain,
inverse(b) = multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))),
inference(subst,[],[refute_0_495:[bind(X_69,$fot(b)),bind(X_95,$fot(inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_4787,plain,
multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))),
inference(subst,[],[refute_0_1146:[bind(X_45,$fot(inverse(least_upper_bound(a,c)))),bind(X_86,$fot(c))]]) ).
cnf(refute_0_4788,plain,
multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = greatest_lower_bound(identity,multiply(inverse(X_155),greatest_lower_bound(X_162,X_155))),
inference(subst,[],[refute_0_110:[bind(X_154,$fot(greatest_lower_bound(X_162,X_155)))]]) ).
cnf(refute_0_4789,plain,
multiply(inverse(X_155),greatest_lower_bound(X_162,X_155)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_162)),
inference(subst,[],[refute_0_110:[bind(X_154,$fot(X_162))]]) ).
cnf(refute_0_4790,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_162,X_155)) != greatest_lower_bound(identity,multiply(inverse(X_155),X_162))
| multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) != greatest_lower_bound(identity,multiply(inverse(X_155),greatest_lower_bound(X_162,X_155)))
| multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)),greatest_lower_bound(identity,multiply(inverse(X_155),greatest_lower_bound(X_162,X_155)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))]]) ).
cnf(refute_0_4791,plain,
( multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) != greatest_lower_bound(identity,multiply(inverse(X_155),greatest_lower_bound(X_162,X_155)))
| multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_162,X_155)),greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) )],[refute_0_4789,refute_0_4790]) ).
cnf(refute_0_4792,plain,
multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)),greatest_lower_bound(identity,multiply(inverse(X_155),greatest_lower_bound(X_162,X_155)))) )],[refute_0_4788,refute_0_4791]) ).
cnf(refute_0_4793,plain,
greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)) = greatest_lower_bound(X_155,X_162),
inference(subst,[],[refute_0_570:[bind(Y,$fot(X_162)),bind(X_15,$fot(X_155))]]) ).
cnf(refute_0_4794,plain,
multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))) = multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))))]]) ).
cnf(refute_0_4795,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))) != multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)))
| greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)) != greatest_lower_bound(X_155,X_162)
| multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))),multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)))) ),[1,1],$fot(greatest_lower_bound(X_155,X_162))]]) ).
cnf(refute_0_4796,plain,
( greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)) != greatest_lower_bound(X_155,X_162)
| multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))),multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)))) )],[refute_0_4794,refute_0_4795]) ).
cnf(refute_0_4797,plain,
multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)),greatest_lower_bound(X_155,X_162)) )],[refute_0_4793,refute_0_4796]) ).
cnf(refute_0_4798,plain,
greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_153,X_155))),bind(X_17,$fot(multiply(X_153,X_154)))]]) ).
cnf(refute_0_4799,plain,
multiply(X_153,greatest_lower_bound(X_154,X_155)) = greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_153)),bind(Y,$fot(X_154)),bind(Z,$fot(X_155))]]) ).
cnf(refute_0_4800,plain,
( multiply(X_153,greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))
| greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)) = multiply(X_153,greatest_lower_bound(X_154,X_155)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_153,greatest_lower_bound(X_154,X_155)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))))]]) ).
cnf(refute_0_4801,plain,
greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)) = multiply(X_153,greatest_lower_bound(X_154,X_155)),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,X_155)),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) )],[refute_0_4799,refute_0_4800]) ).
cnf(refute_0_4802,plain,
( greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)) != multiply(X_153,greatest_lower_bound(X_154,X_155))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_154,X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) ),[1],$fot(multiply(X_153,greatest_lower_bound(X_154,X_155)))]]) ).
cnf(refute_0_4803,plain,
( greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_154,X_155)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)),multiply(X_153,greatest_lower_bound(X_154,X_155))) )],[refute_0_4801,refute_0_4802]) ).
cnf(refute_0_4804,plain,
greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_154,X_155)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) )],[refute_0_4798,refute_0_4803]) ).
cnf(refute_0_4805,plain,
greatest_lower_bound(X_154,X_154) = X_154,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_154))]]) ).
cnf(refute_0_4806,plain,
greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)) = greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))]]) ).
cnf(refute_0_4807,plain,
( greatest_lower_bound(X_154,X_154) != X_154
| greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)) != greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))
| greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)) = greatest_lower_bound(X_155,X_154) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)),greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) ),[1,1],$fot(X_154)]]) ).
cnf(refute_0_4808,plain,
( greatest_lower_bound(X_154,X_154) != X_154
| greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)) = greatest_lower_bound(X_155,X_154) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)),greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) )],[refute_0_4806,refute_0_4807]) ).
cnf(refute_0_4809,plain,
greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)) = greatest_lower_bound(X_155,X_154),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_154,X_154),X_154) )],[refute_0_4805,refute_0_4808]) ).
cnf(refute_0_4810,plain,
multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) = multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))),
introduced(tautology,[refl,[$fot(multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))))]]) ).
cnf(refute_0_4811,plain,
( multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) != multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))
| greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)) != greatest_lower_bound(X_155,X_154)
| multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) = multiply(X_153,greatest_lower_bound(X_155,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))),multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))) ),[1,1],$fot(greatest_lower_bound(X_155,X_154))]]) ).
cnf(refute_0_4812,plain,
( greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)) != greatest_lower_bound(X_155,X_154)
| multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) = multiply(X_153,greatest_lower_bound(X_155,X_154)) ),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))),multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))) )],[refute_0_4810,refute_0_4811]) ).
cnf(refute_0_4813,plain,
multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) = multiply(X_153,greatest_lower_bound(X_155,X_154)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)),greatest_lower_bound(X_155,X_154)) )],[refute_0_4809,refute_0_4812]) ).
cnf(refute_0_4814,plain,
greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154))) = multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))),
inference(subst,[],[refute_0_296:[bind(X,$fot(X_153)),bind(Y,$fot(X_155)),bind(Z,$fot(greatest_lower_bound(X_154,X_154)))]]) ).
cnf(refute_0_4815,plain,
greatest_lower_bound(X,greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X)),
inference(subst,[],[refute_0_1521:[bind(X_56,$fot(multiply(X_153,X_154))),bind(X_57,$fot(multiply(X_153,X_155)))]]) ).
cnf(refute_0_4816,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X))
| greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)) != multiply(X_153,greatest_lower_bound(X_154,X_155))
| greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))) = greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X))) ),[0,1],$fot(multiply(X_153,greatest_lower_bound(X_154,X_155)))]]) ).
cnf(refute_0_4817,plain,
( greatest_lower_bound(X,greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X))
| greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))) = greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155)),multiply(X_153,greatest_lower_bound(X_154,X_155))) )],[refute_0_4801,refute_0_4816]) ).
cnf(refute_0_4818,plain,
greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))) = greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X))) )],[refute_0_4815,refute_0_4817]) ).
cnf(refute_0_4819,plain,
( greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))) != greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X)) = greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X))))]]) ).
cnf(refute_0_4820,plain,
greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X)) = greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(X_153,greatest_lower_bound(X_154,X_155))),greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_155),X))) )],[refute_0_4818,refute_0_4819]) ).
cnf(refute_0_4821,plain,
greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154))),
inference(subst,[],[refute_0_4820:[bind(X,$fot(multiply(X_153,X_155))),bind(X_155,$fot(X_154))]]) ).
cnf(refute_0_4822,plain,
( greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154)))
| greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154))) != multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154))))),bind(Z0,$fot(multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))))]]) ).
cnf(refute_0_4823,plain,
( greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154))) != multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154)))) )],[refute_0_4821,refute_0_4822]) ).
cnf(refute_0_4824,plain,
greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_155),multiply(X_153,greatest_lower_bound(X_154,X_154))),multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))) )],[refute_0_4814,refute_0_4823]) ).
cnf(refute_0_4825,plain,
( multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) != multiply(X_153,greatest_lower_bound(X_155,X_154))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_155,X_154)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))))),bind(Y0,$fot(multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))))),bind(Z0,$fot(multiply(X_153,greatest_lower_bound(X_155,X_154))))]]) ).
cnf(refute_0_4826,plain,
( multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))) != multiply(X_153,greatest_lower_bound(X_155,X_154))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_155,X_154)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154)))) )],[refute_0_4824,refute_0_4825]) ).
cnf(refute_0_4827,plain,
greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) = multiply(X_153,greatest_lower_bound(X_155,X_154)),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_155,greatest_lower_bound(X_154,X_154))),multiply(X_153,greatest_lower_bound(X_155,X_154))) )],[refute_0_4813,refute_0_4826]) ).
cnf(refute_0_4828,plain,
( greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != multiply(X_153,greatest_lower_bound(X_154,X_155))
| greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != multiply(X_153,greatest_lower_bound(X_155,X_154))
| multiply(X_153,greatest_lower_bound(X_155,X_154)) = multiply(X_153,greatest_lower_bound(X_154,X_155)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),multiply(X_153,greatest_lower_bound(X_154,X_155))) ),[0],$fot(multiply(X_153,greatest_lower_bound(X_155,X_154)))]]) ).
cnf(refute_0_4829,plain,
( greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))) != multiply(X_153,greatest_lower_bound(X_154,X_155))
| multiply(X_153,greatest_lower_bound(X_155,X_154)) = multiply(X_153,greatest_lower_bound(X_154,X_155)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),multiply(X_153,greatest_lower_bound(X_155,X_154))) )],[refute_0_4827,refute_0_4828]) ).
cnf(refute_0_4830,plain,
multiply(X_153,greatest_lower_bound(X_155,X_154)) = multiply(X_153,greatest_lower_bound(X_154,X_155)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_153,X_154),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,X_155))),multiply(X_153,greatest_lower_bound(X_154,X_155))) )],[refute_0_4804,refute_0_4829]) ).
cnf(refute_0_4831,plain,
( multiply(X_153,greatest_lower_bound(X_155,X_154)) != multiply(X_153,greatest_lower_bound(X_154,X_155))
| multiply(X_153,greatest_lower_bound(X_154,X_155)) = multiply(X_153,greatest_lower_bound(X_155,X_154)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_153,greatest_lower_bound(X_155,X_154)))),bind(Y0,$fot(multiply(X_153,greatest_lower_bound(X_154,X_155))))]]) ).
cnf(refute_0_4832,plain,
multiply(X_153,greatest_lower_bound(X_154,X_155)) = multiply(X_153,greatest_lower_bound(X_155,X_154)),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_155,X_154)),multiply(X_153,greatest_lower_bound(X_154,X_155))) )],[refute_0_4830,refute_0_4831]) ).
cnf(refute_0_4833,plain,
multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))),
inference(subst,[],[refute_0_4832:[bind(X_153,$fot(inverse(X_155))),bind(X_154,$fot(greatest_lower_bound(X_162,X_155)))]]) ).
cnf(refute_0_4834,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))) != multiply(inverse(X_155),greatest_lower_bound(X_155,X_162))
| multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) != multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)))
| multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)))),bind(Y0,$fot(multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))))),bind(Z0,$fot(multiply(inverse(X_155),greatest_lower_bound(X_155,X_162))))]]) ).
cnf(refute_0_4835,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))) != multiply(inverse(X_155),greatest_lower_bound(X_155,X_162))
| multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)),multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155)))) )],[refute_0_4833,refute_0_4834]) ).
cnf(refute_0_4836,plain,
multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_155,greatest_lower_bound(X_162,X_155))),multiply(inverse(X_155),greatest_lower_bound(X_155,X_162))) )],[refute_0_4797,refute_0_4835]) ).
cnf(refute_0_4837,plain,
( multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) != multiply(inverse(X_155),greatest_lower_bound(X_155,X_162))
| multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))
| multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))) ),[0],$fot(multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)))]]) ).
cnf(refute_0_4838,plain,
( multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))
| multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)),multiply(inverse(X_155),greatest_lower_bound(X_155,X_162))) )],[refute_0_4836,refute_0_4837]) ).
cnf(refute_0_4839,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) = greatest_lower_bound(identity,multiply(inverse(X_155),X_162)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(inverse(X_155),X_162))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_4840,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) != greatest_lower_bound(identity,multiply(inverse(X_155),X_162))
| multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_162)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)),greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))))]]) ).
cnf(refute_0_4841,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))
| multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_162)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162))),greatest_lower_bound(identity,multiply(inverse(X_155),X_162))) )],[refute_0_4839,refute_0_4840]) ).
cnf(refute_0_4842,plain,
( multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))
| multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_162)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))) )],[refute_0_4838,refute_0_4841]) ).
cnf(refute_0_4843,plain,
multiply(inverse(X_155),greatest_lower_bound(X_155,X_162)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_162)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(greatest_lower_bound(X_162,X_155),X_155)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_155),X_162)))) )],[refute_0_4792,refute_0_4842]) ).
cnf(refute_0_4844,plain,
multiply(inverse(b),greatest_lower_bound(b,c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(subst,[],[refute_0_4843:[bind(X_155,$fot(b)),bind(X_162,$fot(c))]]) ).
cnf(refute_0_4845,plain,
( multiply(inverse(b),greatest_lower_bound(b,c)) != greatest_lower_bound(identity,multiply(inverse(b),c))
| greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
| multiply(inverse(b),greatest_lower_bound(a,c)) = greatest_lower_bound(identity,multiply(inverse(b),c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(b,c)),greatest_lower_bound(identity,multiply(inverse(b),c))) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_4846,plain,
( multiply(inverse(b),greatest_lower_bound(b,c)) != greatest_lower_bound(identity,multiply(inverse(b),c))
| multiply(inverse(b),greatest_lower_bound(a,c)) = greatest_lower_bound(identity,multiply(inverse(b),c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_176,refute_0_4845]) ).
cnf(refute_0_4847,plain,
multiply(inverse(b),greatest_lower_bound(a,c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(b,c)),greatest_lower_bound(identity,multiply(inverse(b),c))) )],[refute_0_4844,refute_0_4846]) ).
cnf(refute_0_4848,plain,
inverse(least_upper_bound(b,c)) = inverse(least_upper_bound(b,c)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(b,c)))]]) ).
cnf(refute_0_4849,plain,
( inverse(least_upper_bound(b,c)) != inverse(least_upper_bound(b,c))
| least_upper_bound(b,c) != least_upper_bound(a,c)
| inverse(least_upper_bound(b,c)) = inverse(least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(b,c)),inverse(least_upper_bound(b,c))) ),[1,0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_4850,plain,
( least_upper_bound(b,c) != least_upper_bound(a,c)
| inverse(least_upper_bound(b,c)) = inverse(least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(b,c)),inverse(least_upper_bound(b,c))) )],[refute_0_4848,refute_0_4849]) ).
cnf(refute_0_4851,plain,
inverse(least_upper_bound(b,c)) = inverse(least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_126,refute_0_4850]) ).
cnf(refute_0_4852,plain,
multiply(inverse(least_upper_bound(b,c)),c) = multiply(inverse(least_upper_bound(b,c)),c),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(b,c)),c))]]) ).
cnf(refute_0_4853,plain,
( multiply(inverse(least_upper_bound(b,c)),c) != multiply(inverse(least_upper_bound(b,c)),c)
| inverse(least_upper_bound(b,c)) != inverse(least_upper_bound(a,c))
| multiply(inverse(least_upper_bound(b,c)),c) = multiply(inverse(least_upper_bound(a,c)),c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(b,c)),c),multiply(inverse(least_upper_bound(b,c)),c)) ),[1,0],$fot(inverse(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4854,plain,
( inverse(least_upper_bound(b,c)) != inverse(least_upper_bound(a,c))
| multiply(inverse(least_upper_bound(b,c)),c) = multiply(inverse(least_upper_bound(a,c)),c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(b,c)),c),multiply(inverse(least_upper_bound(b,c)),c)) )],[refute_0_4852,refute_0_4853]) ).
cnf(refute_0_4855,plain,
multiply(inverse(least_upper_bound(b,c)),c) = multiply(inverse(least_upper_bound(a,c)),c),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(b,c)),inverse(least_upper_bound(a,c))) )],[refute_0_4851,refute_0_4854]) ).
cnf(refute_0_4856,plain,
inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) = multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(inverse(X_86))),bind(X_46,$fot(least_upper_bound(X_85,X_86)))]]) ).
cnf(refute_0_4857,plain,
( multiply(inverse(X_86),least_upper_bound(X_85,X_86)) != least_upper_bound(identity,multiply(inverse(X_86),X_85))
| inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) != multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))
| inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) = multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))) ),[0,0],$fot(least_upper_bound(identity,multiply(inverse(X_86),X_85)))]]) ).
cnf(refute_0_4858,plain,
( inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) != multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))
| inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) = multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_86),least_upper_bound(X_85,X_86)),least_upper_bound(identity,multiply(inverse(X_86),X_85))) )],[refute_0_576,refute_0_4857]) ).
cnf(refute_0_4859,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) = multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))) )],[refute_0_4856,refute_0_4858]) ).
cnf(refute_0_4860,plain,
multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) = inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(inverse(X_86))),bind(X_46,$fot(least_upper_bound(X_85,X_86)))]]) ).
cnf(refute_0_4861,plain,
( multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) != inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86)))
| inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))))),bind(Y0,$fot(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_85,X_86)),X_86)))]]) ).
cnf(refute_0_4862,plain,
( inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))),inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86)))) )],[refute_0_4860,refute_0_4861]) ).
cnf(refute_0_4863,plain,
multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_86),least_upper_bound(X_85,X_86))),multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) )],[refute_0_2060,refute_0_4862]) ).
cnf(refute_0_4864,plain,
( multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))) != multiply(inverse(least_upper_bound(X_85,X_86)),X_86)
| inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) != multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))
| inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_85,X_86)),X_86))]]) ).
cnf(refute_0_4865,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) != multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))
| inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86))),multiply(inverse(least_upper_bound(X_85,X_86)),X_86)) )],[refute_0_4863,refute_0_4864]) ).
cnf(refute_0_4866,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))) = multiply(inverse(least_upper_bound(X_85,X_86)),X_86),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_86),X_85))),multiply(inverse(least_upper_bound(X_85,X_86)),inverse(inverse(X_86)))) )],[refute_0_4859,refute_0_4865]) ).
cnf(refute_0_4867,plain,
inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),
inference(subst,[],[refute_0_4866:[bind(X_86,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_4868,plain,
multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) = inverse(c),
inference(subst,[],[refute_0_55:[bind(X_45,$fot(c)),bind(X_55,$fot(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4869,plain,
inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)) = inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),bind(X_16,$fot(c))]]) ).
cnf(refute_0_4870,plain,
multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))) = multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))),
introduced(tautology,[refl,[$fot(multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))))]]) ).
cnf(refute_0_4871,plain,
( multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))) != multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)))
| inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)) != inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))),multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)))) ),[1,1],$fot(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4872,plain,
( inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)) != inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))
| multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))),multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)))) )],[refute_0_4870,refute_0_4871]) ).
cnf(refute_0_4873,plain,
multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)),inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) )],[refute_0_4869,refute_0_4872]) ).
cnf(refute_0_4874,plain,
least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))),
inference(subst,[],[refute_0_2716:[bind(X_172,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),bind(X_173,$fot(c))]]) ).
cnf(refute_0_4875,plain,
( multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))) != multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)))
| least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Y0,$fot(multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))))),bind(Z0,$fot(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4876,plain,
( multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))) != multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c)))) )],[refute_0_4874,refute_0_4875]) ).
cnf(refute_0_4877,plain,
least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),c))),multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_4873,refute_0_4876]) ).
cnf(refute_0_4878,plain,
( multiply(least_upper_bound(a,b),inverse(b)) != least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(least_upper_bound(a,b),inverse(b)) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,b),inverse(b)),multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),[0],$fot(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4879,plain,
( multiply(least_upper_bound(a,b),inverse(b)) != least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(least_upper_bound(a,b),inverse(b)) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_4877,refute_0_4878]) ).
cnf(refute_0_4880,plain,
multiply(least_upper_bound(a,b),inverse(b)) = multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),inverse(b)),least_upper_bound(identity,multiply(c,inverse(multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_2314,refute_0_4879]) ).
cnf(refute_0_4881,plain,
( multiply(least_upper_bound(a,b),inverse(b)) != multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),inverse(b)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(least_upper_bound(a,b),inverse(b)))),bind(Y0,$fot(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))))]]) ).
cnf(refute_0_4882,plain,
multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),inverse(b)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),inverse(b)),multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_4880,refute_0_4881]) ).
cnf(refute_0_4883,plain,
( multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(least_upper_bound(a,b),inverse(b))
| multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) != inverse(c)
| multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),inverse(c)) ),[0,1,0],$fot(multiply(least_upper_bound(a,b),inverse(b)))]]) ).
cnf(refute_0_4884,plain,
( multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))) != inverse(c)
| multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(least_upper_bound(a,b),inverse(b))) )],[refute_0_4882,refute_0_4883]) ).
cnf(refute_0_4885,plain,
multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) = inverse(c),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(c,inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),inverse(c)) )],[refute_0_4868,refute_0_4884]) ).
cnf(refute_0_4886,plain,
greatest_lower_bound(X,greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))) = greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)),
inference(subst,[],[refute_0_1521:[bind(X_57,$fot(inverse(greatest_lower_bound(X_469,inverse(X_56)))))]]) ).
cnf(refute_0_4887,plain,
X_56 = greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56)))),
inference(subst,[],[refute_0_2777:[bind(X_464,$fot(X_469)),bind(X_465,$fot(X_56))]]) ).
cnf(refute_0_4888,plain,
( X_56 != greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))
| greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56)))) = X_56 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_56)),bind(Y0,$fot(greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))))]]) ).
cnf(refute_0_4889,plain,
greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56)))) = X_56,
inference(resolve,[$cnf( $equal(X_56,greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))) )],[refute_0_4887,refute_0_4888]) ).
cnf(refute_0_4890,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))) != greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))
| greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56)))) != X_56
| greatest_lower_bound(X,X_56) = greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))),greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))) ),[0,1],$fot(X_56)]]) ).
cnf(refute_0_4891,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))) != greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))
| greatest_lower_bound(X,X_56) = greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56)))),X_56) )],[refute_0_4889,refute_0_4890]) ).
cnf(refute_0_4892,plain,
greatest_lower_bound(X,X_56) = greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_56,inverse(greatest_lower_bound(X_469,inverse(X_56))))),greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))) )],[refute_0_4886,refute_0_4891]) ).
cnf(refute_0_4893,plain,
greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)) = greatest_lower_bound(X_56,X),
inference(subst,[],[refute_0_3423:[bind(Y,$fot(inverse(X_469))),bind(X_58,$fot(X))]]) ).
cnf(refute_0_4894,plain,
inverse(greatest_lower_bound(X_469,inverse(X_56))) = least_upper_bound(inverse(X_469),X_56),
inference(subst,[],[refute_0_4651:[bind(X_474,$fot(X_469)),bind(X_475,$fot(X_56))]]) ).
cnf(refute_0_4895,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X) = greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))]]) ).
cnf(refute_0_4896,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X) != greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)
| inverse(greatest_lower_bound(X_469,inverse(X_56))) != least_upper_bound(inverse(X_469),X_56)
| greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X) = greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X),greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) ),[1,0],$fot(least_upper_bound(inverse(X_469),X_56))]]) ).
cnf(refute_0_4897,plain,
( inverse(greatest_lower_bound(X_469,inverse(X_56))) != least_upper_bound(inverse(X_469),X_56)
| greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X) = greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X),greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) )],[refute_0_4895,refute_0_4896]) ).
cnf(refute_0_4898,plain,
greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X) = greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_469,inverse(X_56))),least_upper_bound(inverse(X_469),X_56)) )],[refute_0_4894,refute_0_4897]) ).
cnf(refute_0_4899,plain,
greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) = greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)))]]) ).
cnf(refute_0_4900,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) != greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))
| greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X) != greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)
| greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) = greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)),greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))) ),[1,1],$fot(greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X))]]) ).
cnf(refute_0_4901,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X) != greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)
| greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) = greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)),greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))) )],[refute_0_4899,refute_0_4900]) ).
cnf(refute_0_4902,plain,
greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) = greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X),greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)) )],[refute_0_4898,refute_0_4901]) ).
cnf(refute_0_4903,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) != greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X))
| greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)) != greatest_lower_bound(X_56,X)
| greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) = greatest_lower_bound(X_56,X) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)))),bind(Y0,$fot(greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)))),bind(Z0,$fot(greatest_lower_bound(X_56,X)))]]) ).
cnf(refute_0_4904,plain,
( greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)) != greatest_lower_bound(X_56,X)
| greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) = greatest_lower_bound(X_56,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)),greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X))) )],[refute_0_4902,refute_0_4903]) ).
cnf(refute_0_4905,plain,
greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) = greatest_lower_bound(X_56,X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(least_upper_bound(inverse(X_469),X_56),X)),greatest_lower_bound(X_56,X)) )],[refute_0_4893,refute_0_4904]) ).
cnf(refute_0_4906,plain,
( greatest_lower_bound(X,X_56) != greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))
| greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)) != greatest_lower_bound(X_56,X)
| greatest_lower_bound(X,X_56) = greatest_lower_bound(X_56,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,X_56),greatest_lower_bound(X_56,X)) ),[0],$fot(greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)))]]) ).
cnf(refute_0_4907,plain,
( greatest_lower_bound(X,X_56) != greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))
| greatest_lower_bound(X,X_56) = greatest_lower_bound(X_56,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X)),greatest_lower_bound(X_56,X)) )],[refute_0_4905,refute_0_4906]) ).
cnf(refute_0_4908,plain,
greatest_lower_bound(X,X_56) = greatest_lower_bound(X_56,X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,X_56),greatest_lower_bound(X_56,greatest_lower_bound(inverse(greatest_lower_bound(X_469,inverse(X_56))),X))) )],[refute_0_4892,refute_0_4907]) ).
cnf(refute_0_4909,plain,
( greatest_lower_bound(X,X_56) != greatest_lower_bound(X_56,X)
| greatest_lower_bound(X_56,X) = greatest_lower_bound(X,X_56) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,X_56))),bind(Y0,$fot(greatest_lower_bound(X_56,X)))]]) ).
cnf(refute_0_4910,plain,
greatest_lower_bound(X_56,X) = greatest_lower_bound(X,X_56),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,X_56),greatest_lower_bound(X_56,X)) )],[refute_0_4908,refute_0_4909]) ).
cnf(refute_0_4911,plain,
greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c)) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),
inference(subst,[],[refute_0_4910:[bind(X,$fot(least_upper_bound(a,c))),bind(X_56,$fot(multiply(least_upper_bound(a,b),multiply(inverse(b),c))))]]) ).
cnf(refute_0_4912,plain,
multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))) = greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,multiply(inverse(X_153),X_46))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_153)),bind(Y,$fot(X_154)),bind(Z,$fot(multiply(inverse(X_153),X_46)))]]) ).
cnf(refute_0_4913,plain,
X_46 = multiply(X_153,multiply(inverse(X_153),X_46)),
inference(subst,[],[refute_0_823:[bind(X_50,$fot(X_153))]]) ).
cnf(refute_0_4914,plain,
( X_46 != multiply(X_153,multiply(inverse(X_153),X_46))
| multiply(X_153,multiply(inverse(X_153),X_46)) = X_46 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(X_153,multiply(inverse(X_153),X_46))))]]) ).
cnf(refute_0_4915,plain,
multiply(X_153,multiply(inverse(X_153),X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(X_153,multiply(inverse(X_153),X_46))) )],[refute_0_4913,refute_0_4914]) ).
cnf(refute_0_4916,plain,
( multiply(X_153,multiply(inverse(X_153),X_46)) != X_46
| multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,multiply(inverse(X_153),X_46)))
| multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))) = greatest_lower_bound(multiply(X_153,X_154),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,multiply(inverse(X_153),X_46)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_4917,plain,
( multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))) != greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,multiply(inverse(X_153),X_46)))
| multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))) = greatest_lower_bound(multiply(X_153,X_154),X_46) ),
inference(resolve,[$cnf( $equal(multiply(X_153,multiply(inverse(X_153),X_46)),X_46) )],[refute_0_4915,refute_0_4916]) ).
cnf(refute_0_4918,plain,
multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))) = greatest_lower_bound(multiply(X_153,X_154),X_46),
inference(resolve,[$cnf( $equal(multiply(X_153,greatest_lower_bound(X_154,multiply(inverse(X_153),X_46))),greatest_lower_bound(multiply(X_153,X_154),multiply(X_153,multiply(inverse(X_153),X_46)))) )],[refute_0_4912,refute_0_4917]) ).
cnf(refute_0_4919,plain,
multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c)),
inference(subst,[],[refute_0_4918:[bind(X_153,$fot(least_upper_bound(a,b))),bind(X_154,$fot(multiply(inverse(b),c))),bind(X_46,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_4920,plain,
( multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c))
| greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c)) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_4921,plain,
( greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c)) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c))) )],[refute_0_4919,refute_0_4920]) ).
cnf(refute_0_4922,plain,
multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(a,b),multiply(inverse(b),c)),least_upper_bound(a,c)),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) )],[refute_0_4911,refute_0_4921]) ).
cnf(refute_0_4923,plain,
multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))) = greatest_lower_bound(multiply(inverse(X_45),X_154),multiply(inverse(X_45),multiply(X_45,X_46))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_154)),bind(Z,$fot(multiply(X_45,X_46)))]]) ).
cnf(refute_0_4924,plain,
( multiply(inverse(X_45),multiply(X_45,X_46)) != X_46
| multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))) != greatest_lower_bound(multiply(inverse(X_45),X_154),multiply(inverse(X_45),multiply(X_45,X_46)))
| multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))) = greatest_lower_bound(multiply(inverse(X_45),X_154),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))),greatest_lower_bound(multiply(inverse(X_45),X_154),multiply(inverse(X_45),multiply(X_45,X_46)))) ),[1,1],$fot(X_46)]]) ).
cnf(refute_0_4925,plain,
( multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))) != greatest_lower_bound(multiply(inverse(X_45),X_154),multiply(inverse(X_45),multiply(X_45,X_46)))
| multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))) = greatest_lower_bound(multiply(inverse(X_45),X_154),X_46) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),multiply(X_45,X_46)),X_46) )],[refute_0_212,refute_0_4924]) ).
cnf(refute_0_4926,plain,
multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))) = greatest_lower_bound(multiply(inverse(X_45),X_154),X_46),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),greatest_lower_bound(X_154,multiply(X_45,X_46))),greatest_lower_bound(multiply(inverse(X_45),X_154),multiply(inverse(X_45),multiply(X_45,X_46)))) )],[refute_0_4923,refute_0_4925]) ).
cnf(refute_0_4927,plain,
multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))),
inference(subst,[],[refute_0_4926:[bind(X_154,$fot(c)),bind(X_45,$fot(b)),bind(X_46,$fot(multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))]]) ).
cnf(refute_0_4928,plain,
multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4929,plain,
( multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),[1,1],$fot(greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))]]) ).
cnf(refute_0_4930,plain,
( multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))
| multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_4928,refute_0_4929]) ).
cnf(refute_0_4931,plain,
multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) )],[refute_0_4927,refute_0_4930]) ).
cnf(refute_0_4932,plain,
( multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))
| multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Y0,$fot(multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_4933,plain,
( multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) )],[refute_0_4931,refute_0_4932]) ).
cnf(refute_0_4934,plain,
multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),greatest_lower_bound(multiply(inverse(b),c),multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) )],[refute_0_4922,refute_0_4933]) ).
cnf(refute_0_4935,plain,
multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(a,b))),bind(Y,$fot(inverse(b))),bind(Z,$fot(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4936,plain,
( multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))),bind(Y0,$fot(multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_4937,plain,
( multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_4935,refute_0_4936]) ).
cnf(refute_0_4938,plain,
multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) )],[refute_0_4934,refute_0_4937]) ).
cnf(refute_0_4939,plain,
inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_4940,plain,
( multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) ),[1,0],$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))]]) ).
cnf(refute_0_4941,plain,
( multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_4939,refute_0_4940]) ).
cnf(refute_0_4942,plain,
inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) = inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) )],[refute_0_4938,refute_0_4941]) ).
cnf(refute_0_4943,plain,
multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) = inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(multiply(least_upper_bound(a,b),inverse(b)))),bind(X_46,$fot(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_4944,plain,
( multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) != inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))
| inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) = inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))))),bind(Y0,$fot(inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))))),bind(Z0,$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))]]) ).
cnf(refute_0_4945,plain,
( inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))) != inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) = inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))),inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))))) )],[refute_0_4943,refute_0_4944]) ).
cnf(refute_0_4946,plain,
multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) = inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(least_upper_bound(a,b),inverse(b)),greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c)))))),inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) )],[refute_0_4942,refute_0_4945]) ).
cnf(refute_0_4947,plain,
( multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) != inverse(c)
| multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) != inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))),inverse(c)) ),[0],$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_4948,plain,
( multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))) != inverse(c)
| inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))),inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) )],[refute_0_4946,refute_0_4947]) ).
cnf(refute_0_4949,plain,
inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = inverse(c),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(c,multiply(b,multiply(inverse(least_upper_bound(a,b)),least_upper_bound(a,c))))),inverse(multiply(least_upper_bound(a,b),inverse(b)))),inverse(c)) )],[refute_0_4885,refute_0_4948]) ).
cnf(refute_0_4950,plain,
( inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != inverse(c)
| inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) != multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) = multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) ),[0,0,1,0],$fot(inverse(c))]]) ).
cnf(refute_0_4951,plain,
( inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) != multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) = multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),inverse(c)) )],[refute_0_4949,refute_0_4950]) ).
cnf(refute_0_4952,plain,
inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) = multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) )],[refute_0_4867,refute_0_4951]) ).
cnf(refute_0_4953,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_473),least_upper_bound(X_83,X_473)))) = multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473),
inference(subst,[],[refute_0_4866:[bind(X_85,$fot(least_upper_bound(X_83,X_473))),bind(X_86,$fot(X_473))]]) ).
cnf(refute_0_4954,plain,
multiply(inverse(X_473),least_upper_bound(X_83,X_473)) = least_upper_bound(identity,multiply(inverse(X_473),X_83)),
inference(subst,[],[refute_0_67:[bind(X_84,$fot(X_473))]]) ).
cnf(refute_0_4955,plain,
( multiply(inverse(X_473),least_upper_bound(X_83,X_473)) != least_upper_bound(identity,multiply(inverse(X_473),X_83))
| inverse(least_upper_bound(identity,multiply(inverse(X_473),least_upper_bound(X_83,X_473)))) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) = multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_473),least_upper_bound(X_83,X_473)))),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) ),[0,0,1],$fot(least_upper_bound(identity,multiply(inverse(X_473),X_83)))]]) ).
cnf(refute_0_4956,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_473),least_upper_bound(X_83,X_473)))) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) = multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_473),least_upper_bound(X_83,X_473)),least_upper_bound(identity,multiply(inverse(X_473),X_83))) )],[refute_0_4954,refute_0_4955]) ).
cnf(refute_0_4957,plain,
inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) = multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_473),least_upper_bound(X_83,X_473)))),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) )],[refute_0_4953,refute_0_4956]) ).
cnf(refute_0_4958,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83))) = least_upper_bound(identity,multiply(inverse(X_473),X_83)),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(multiply(inverse(X_473),X_83))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_4959,plain,
inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) = inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))))]]) ).
cnf(refute_0_4960,plain,
( inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) != inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83))) != least_upper_bound(identity,multiply(inverse(X_473),X_83))
| inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) = inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))),inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83))))) ),[1,0],$fot(least_upper_bound(identity,multiply(inverse(X_473),X_83)))]]) ).
cnf(refute_0_4961,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83))) != least_upper_bound(identity,multiply(inverse(X_473),X_83))
| inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) = inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))),inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83))))) )],[refute_0_4959,refute_0_4960]) ).
cnf(refute_0_4962,plain,
inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) = inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83))),least_upper_bound(identity,multiply(inverse(X_473),X_83))) )],[refute_0_4958,refute_0_4961]) ).
cnf(refute_0_4963,plain,
( inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) != inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83)))
| inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) = multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) ),[0],$fot(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))))]]) ).
cnf(refute_0_4964,plain,
( inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) = multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))),inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83)))) )],[refute_0_4962,refute_0_4963]) ).
cnf(refute_0_4965,plain,
least_upper_bound(X_473,least_upper_bound(X_83,X_473)) = least_upper_bound(X_473,X_83),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_83)),bind(X_13,$fot(X_473))]]) ).
cnf(refute_0_4966,plain,
inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))) = inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))))]]) ).
cnf(refute_0_4967,plain,
( inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))) != inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473)))
| least_upper_bound(X_473,least_upper_bound(X_83,X_473)) != least_upper_bound(X_473,X_83)
| inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))) = inverse(least_upper_bound(X_473,X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))),inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473)))) ),[1,0],$fot(least_upper_bound(X_473,X_83))]]) ).
cnf(refute_0_4968,plain,
( least_upper_bound(X_473,least_upper_bound(X_83,X_473)) != least_upper_bound(X_473,X_83)
| inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))) = inverse(least_upper_bound(X_473,X_83)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))),inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473)))) )],[refute_0_4966,refute_0_4967]) ).
cnf(refute_0_4969,plain,
inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))) = inverse(least_upper_bound(X_473,X_83)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_473,least_upper_bound(X_83,X_473)),least_upper_bound(X_473,X_83)) )],[refute_0_4965,refute_0_4968]) ).
cnf(refute_0_4970,plain,
inverse(least_upper_bound(X_323,X_324)) = multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))),bind(X_69,$fot(least_upper_bound(X_323,X_324)))]]) ).
cnf(refute_0_4971,plain,
X_323 = multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324)),
inference(subst,[],[refute_0_2509:[bind(X_100,$fot(X_323)),bind(X_101,$fot(X_324))]]) ).
cnf(refute_0_4972,plain,
( X_323 != multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))
| multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324)) = X_323 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_323)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))))]]) ).
cnf(refute_0_4973,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324)) = X_323,
inference(resolve,[$cnf( $equal(X_323,multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))) )],[refute_0_4971,refute_0_4972]) ).
cnf(refute_0_4974,plain,
( multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324)) != X_323
| inverse(least_upper_bound(X_323,X_324)) != multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))
| inverse(least_upper_bound(X_323,X_324)) = multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_323,X_324)),multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))) ),[1,0,0],$fot(X_323)]]) ).
cnf(refute_0_4975,plain,
( inverse(least_upper_bound(X_323,X_324)) != multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))
| inverse(least_upper_bound(X_323,X_324)) = multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324)),X_323) )],[refute_0_4973,refute_0_4974]) ).
cnf(refute_0_4976,plain,
inverse(least_upper_bound(X_323,X_324)) = multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_323,X_324)),multiply(inverse(multiply(inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))),least_upper_bound(X_323,X_324))),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))) )],[refute_0_4970,refute_0_4975]) ).
cnf(refute_0_4977,plain,
inverse(inverse(X_323)) = X_323,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(X_323))]]) ).
cnf(refute_0_4978,plain,
least_upper_bound(X_324,inverse(inverse(X_323))) = least_upper_bound(X_324,inverse(inverse(X_323))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_324,inverse(inverse(X_323))))]]) ).
cnf(refute_0_4979,plain,
( inverse(inverse(X_323)) != X_323
| least_upper_bound(X_324,inverse(inverse(X_323))) != least_upper_bound(X_324,inverse(inverse(X_323)))
| least_upper_bound(X_324,inverse(inverse(X_323))) = least_upper_bound(X_324,X_323) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_324,inverse(inverse(X_323))),least_upper_bound(X_324,inverse(inverse(X_323)))) ),[1,1],$fot(X_323)]]) ).
cnf(refute_0_4980,plain,
( inverse(inverse(X_323)) != X_323
| least_upper_bound(X_324,inverse(inverse(X_323))) = least_upper_bound(X_324,X_323) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_324,inverse(inverse(X_323))),least_upper_bound(X_324,inverse(inverse(X_323)))) )],[refute_0_4978,refute_0_4979]) ).
cnf(refute_0_4981,plain,
least_upper_bound(X_324,inverse(inverse(X_323))) = least_upper_bound(X_324,X_323),
inference(resolve,[$cnf( $equal(inverse(inverse(X_323)),X_323) )],[refute_0_4977,refute_0_4980]) ).
cnf(refute_0_4982,plain,
inverse(least_upper_bound(X_324,inverse(inverse(X_323)))) = inverse(least_upper_bound(X_324,inverse(inverse(X_323)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_324,inverse(inverse(X_323)))))]]) ).
cnf(refute_0_4983,plain,
( inverse(least_upper_bound(X_324,inverse(inverse(X_323)))) != inverse(least_upper_bound(X_324,inverse(inverse(X_323))))
| least_upper_bound(X_324,inverse(inverse(X_323))) != least_upper_bound(X_324,X_323)
| inverse(least_upper_bound(X_324,inverse(inverse(X_323)))) = inverse(least_upper_bound(X_324,X_323)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_324,inverse(inverse(X_323)))),inverse(least_upper_bound(X_324,inverse(inverse(X_323))))) ),[1,0],$fot(least_upper_bound(X_324,X_323))]]) ).
cnf(refute_0_4984,plain,
( least_upper_bound(X_324,inverse(inverse(X_323))) != least_upper_bound(X_324,X_323)
| inverse(least_upper_bound(X_324,inverse(inverse(X_323)))) = inverse(least_upper_bound(X_324,X_323)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_324,inverse(inverse(X_323)))),inverse(least_upper_bound(X_324,inverse(inverse(X_323))))) )],[refute_0_4982,refute_0_4983]) ).
cnf(refute_0_4985,plain,
inverse(least_upper_bound(X_324,inverse(inverse(X_323)))) = inverse(least_upper_bound(X_324,X_323)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_324,inverse(inverse(X_323))),least_upper_bound(X_324,X_323)) )],[refute_0_4981,refute_0_4984]) ).
cnf(refute_0_4986,plain,
multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) = inverse(least_upper_bound(X_324,inverse(inverse(X_323)))),
inference(subst,[],[refute_0_511:[bind(X_240,$fot(inverse(X_323))),bind(X_241,$fot(X_324))]]) ).
cnf(refute_0_4987,plain,
( multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) != inverse(least_upper_bound(X_324,inverse(inverse(X_323))))
| inverse(least_upper_bound(X_324,inverse(inverse(X_323)))) != inverse(least_upper_bound(X_324,X_323))
| multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) = inverse(least_upper_bound(X_324,X_323)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))))),bind(Y0,$fot(inverse(least_upper_bound(X_324,inverse(inverse(X_323)))))),bind(Z0,$fot(inverse(least_upper_bound(X_324,X_323))))]]) ).
cnf(refute_0_4988,plain,
( inverse(least_upper_bound(X_324,inverse(inverse(X_323)))) != inverse(least_upper_bound(X_324,X_323))
| multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) = inverse(least_upper_bound(X_324,X_323)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))),inverse(least_upper_bound(X_324,inverse(inverse(X_323))))) )],[refute_0_4986,refute_0_4987]) ).
cnf(refute_0_4989,plain,
multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) = inverse(least_upper_bound(X_324,X_323)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_324,inverse(inverse(X_323)))),inverse(least_upper_bound(X_324,X_323))) )],[refute_0_4985,refute_0_4988]) ).
cnf(refute_0_4990,plain,
( multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))) != inverse(least_upper_bound(X_324,X_323))
| inverse(least_upper_bound(X_323,X_324)) != multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))
| inverse(least_upper_bound(X_323,X_324)) = inverse(least_upper_bound(X_324,X_323)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_323,X_324)),multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))) ),[1],$fot(inverse(least_upper_bound(X_324,X_323)))]]) ).
cnf(refute_0_4991,plain,
( inverse(least_upper_bound(X_323,X_324)) != multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))
| inverse(least_upper_bound(X_323,X_324)) = inverse(least_upper_bound(X_324,X_323)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323))))),inverse(least_upper_bound(X_324,X_323))) )],[refute_0_4989,refute_0_4990]) ).
cnf(refute_0_4992,plain,
inverse(least_upper_bound(X_323,X_324)) = inverse(least_upper_bound(X_324,X_323)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_323,X_324)),multiply(inverse(X_323),inverse(least_upper_bound(identity,multiply(X_324,inverse(X_323)))))) )],[refute_0_4976,refute_0_4991]) ).
cnf(refute_0_4993,plain,
( inverse(least_upper_bound(X_323,X_324)) != inverse(least_upper_bound(X_324,X_323))
| inverse(least_upper_bound(X_324,X_323)) = inverse(least_upper_bound(X_323,X_324)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_323,X_324)))),bind(Y0,$fot(inverse(least_upper_bound(X_324,X_323))))]]) ).
cnf(refute_0_4994,plain,
inverse(least_upper_bound(X_324,X_323)) = inverse(least_upper_bound(X_323,X_324)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_323,X_324)),inverse(least_upper_bound(X_324,X_323))) )],[refute_0_4992,refute_0_4993]) ).
cnf(refute_0_4995,plain,
inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)) = inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))),
inference(subst,[],[refute_0_4994:[bind(X_323,$fot(X_473)),bind(X_324,$fot(least_upper_bound(X_83,X_473)))]]) ).
cnf(refute_0_4996,plain,
( inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))) != inverse(least_upper_bound(X_473,X_83))
| inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)) != inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473)))
| inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)) = inverse(least_upper_bound(X_473,X_83)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)))),bind(Y0,$fot(inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))))),bind(Z0,$fot(inverse(least_upper_bound(X_473,X_83))))]]) ).
cnf(refute_0_4997,plain,
( inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))) != inverse(least_upper_bound(X_473,X_83))
| inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)) = inverse(least_upper_bound(X_473,X_83)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473)))) )],[refute_0_4995,refute_0_4996]) ).
cnf(refute_0_4998,plain,
inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)) = inverse(least_upper_bound(X_473,X_83)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_473,least_upper_bound(X_83,X_473))),inverse(least_upper_bound(X_473,X_83))) )],[refute_0_4969,refute_0_4997]) ).
cnf(refute_0_4999,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) = multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473))]]) ).
cnf(refute_0_5000,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)) != inverse(least_upper_bound(X_473,X_83))
| multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) = multiply(inverse(least_upper_bound(X_473,X_83)),X_473) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) ),[1,0],$fot(inverse(least_upper_bound(X_473,X_83)))]]) ).
cnf(refute_0_5001,plain,
( inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)) != inverse(least_upper_bound(X_473,X_83))
| multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) = multiply(inverse(least_upper_bound(X_473,X_83)),X_473) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) )],[refute_0_4999,refute_0_5000]) ).
cnf(refute_0_5002,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) = multiply(inverse(least_upper_bound(X_473,X_83)),X_473),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),inverse(least_upper_bound(X_473,X_83))) )],[refute_0_4998,refute_0_5001]) ).
cnf(refute_0_5003,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473) != multiply(inverse(least_upper_bound(X_473,X_83)),X_473)
| inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) = multiply(inverse(least_upper_bound(X_473,X_83)),X_473) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) ),[1],$fot(multiply(inverse(least_upper_bound(X_473,X_83)),X_473))]]) ).
cnf(refute_0_5004,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) = multiply(inverse(least_upper_bound(X_473,X_83)),X_473) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473),multiply(inverse(least_upper_bound(X_473,X_83)),X_473)) )],[refute_0_5002,refute_0_5003]) ).
cnf(refute_0_5005,plain,
( inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))) != multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)
| inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) = multiply(inverse(least_upper_bound(X_473,X_83)),X_473) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) )],[refute_0_4964,refute_0_5004]) ).
cnf(refute_0_5006,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_473),X_83))) = multiply(inverse(least_upper_bound(X_473,X_83)),X_473),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_473),X_83)))),multiply(inverse(least_upper_bound(least_upper_bound(X_83,X_473),X_473)),X_473)) )],[refute_0_4957,refute_0_5005]) ).
cnf(refute_0_5007,plain,
inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) = multiply(inverse(least_upper_bound(c,X_85)),c),
inference(subst,[],[refute_0_5006:[bind(X_473,$fot(c)),bind(X_83,$fot(X_85))]]) ).
cnf(refute_0_5008,plain,
( inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) != multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) != multiply(inverse(least_upper_bound(c,X_85)),c)
| multiply(inverse(least_upper_bound(c,X_85)),c) = multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),X_85))),multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) ),[0],$fot(multiply(inverse(least_upper_bound(c,X_85)),c))]]) ).
cnf(refute_0_5009,plain,
( inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) != multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| multiply(inverse(least_upper_bound(c,X_85)),c) = multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),X_85))),multiply(inverse(least_upper_bound(c,X_85)),c)) )],[refute_0_5007,refute_0_5008]) ).
cnf(refute_0_5010,plain,
inverse(multiply(inverse(c),least_upper_bound(X_85,c))) = multiply(inverse(least_upper_bound(X_85,c)),c),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(c)),bind(X_74,$fot(least_upper_bound(X_85,c)))]]) ).
cnf(refute_0_5011,plain,
least_upper_bound(identity,multiply(inverse(c),X_85)) = multiply(inverse(c),least_upper_bound(X_85,c)),
inference(subst,[],[refute_0_2042:[bind(X_83,$fot(X_85)),bind(X_84,$fot(c))]]) ).
cnf(refute_0_5012,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85) = multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))]]) ).
cnf(refute_0_5013,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85) != multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)
| inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != inverse(c)
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85) = multiply(inverse(c),X_85) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85),multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) ),[1,0],$fot(inverse(c))]]) ).
cnf(refute_0_5014,plain,
( inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != inverse(c)
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85) = multiply(inverse(c),X_85) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85),multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) )],[refute_0_5012,refute_0_5013]) ).
cnf(refute_0_5015,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85) = multiply(inverse(c),X_85),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),inverse(c)) )],[refute_0_4949,refute_0_5014]) ).
cnf(refute_0_5016,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)))]]) ).
cnf(refute_0_5017,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85) != multiply(inverse(c),X_85)
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) = least_upper_bound(identity,multiply(inverse(c),X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) ),[1,1],$fot(multiply(inverse(c),X_85))]]) ).
cnf(refute_0_5018,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85) != multiply(inverse(c),X_85)
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) = least_upper_bound(identity,multiply(inverse(c),X_85)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) )],[refute_0_5016,refute_0_5017]) ).
cnf(refute_0_5019,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) = least_upper_bound(identity,multiply(inverse(c),X_85)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85),multiply(inverse(c),X_85)) )],[refute_0_5015,refute_0_5018]) ).
cnf(refute_0_5020,plain,
( least_upper_bound(identity,multiply(inverse(c),X_85)) != multiply(inverse(c),least_upper_bound(X_85,c))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) != least_upper_bound(identity,multiply(inverse(c),X_85))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) = multiply(inverse(c),least_upper_bound(X_85,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(c),X_85)))),bind(Z0,$fot(multiply(inverse(c),least_upper_bound(X_85,c))))]]) ).
cnf(refute_0_5021,plain,
( least_upper_bound(identity,multiply(inverse(c),X_85)) != multiply(inverse(c),least_upper_bound(X_85,c))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) = multiply(inverse(c),least_upper_bound(X_85,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)),least_upper_bound(identity,multiply(inverse(c),X_85))) )],[refute_0_5019,refute_0_5020]) ).
cnf(refute_0_5022,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) = multiply(inverse(c),least_upper_bound(X_85,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(c),X_85)),multiply(inverse(c),least_upper_bound(X_85,c))) )],[refute_0_5011,refute_0_5021]) ).
cnf(refute_0_5023,plain,
inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))))]]) ).
cnf(refute_0_5024,plain,
( inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) != inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) != multiply(inverse(c),least_upper_bound(X_85,c))
| inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = inverse(multiply(inverse(c),least_upper_bound(X_85,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)))) ),[1,0],$fot(multiply(inverse(c),least_upper_bound(X_85,c)))]]) ).
cnf(refute_0_5025,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)) != multiply(inverse(c),least_upper_bound(X_85,c))
| inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = inverse(multiply(inverse(c),least_upper_bound(X_85,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)))) )],[refute_0_5023,refute_0_5024]) ).
cnf(refute_0_5026,plain,
inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = inverse(multiply(inverse(c),least_upper_bound(X_85,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)),multiply(inverse(c),least_upper_bound(X_85,c))) )],[refute_0_5022,refute_0_5025]) ).
cnf(refute_0_5027,plain,
( inverse(multiply(inverse(c),least_upper_bound(X_85,c))) != multiply(inverse(least_upper_bound(X_85,c)),c)
| inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) != inverse(multiply(inverse(c),least_upper_bound(X_85,c)))
| inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = multiply(inverse(least_upper_bound(X_85,c)),c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))))),bind(Y0,$fot(inverse(multiply(inverse(c),least_upper_bound(X_85,c))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_85,c)),c)))]]) ).
cnf(refute_0_5028,plain,
( inverse(multiply(inverse(c),least_upper_bound(X_85,c))) != multiply(inverse(least_upper_bound(X_85,c)),c)
| inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = multiply(inverse(least_upper_bound(X_85,c)),c) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),inverse(multiply(inverse(c),least_upper_bound(X_85,c)))) )],[refute_0_5026,refute_0_5027]) ).
cnf(refute_0_5029,plain,
inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) = multiply(inverse(least_upper_bound(X_85,c)),c),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(c),least_upper_bound(X_85,c))),multiply(inverse(least_upper_bound(X_85,c)),c)) )],[refute_0_5010,refute_0_5028]) ).
cnf(refute_0_5030,plain,
multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),
inference(subst,[],[refute_0_2054:[bind(X_83,$fot(X_85)),bind(X_84,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_5031,plain,
( multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)))
| inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) != multiply(inverse(least_upper_bound(X_85,c)),c)
| multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = multiply(inverse(least_upper_bound(X_85,c)),c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_85,c)),c)))]]) ).
cnf(refute_0_5032,plain,
( inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))) != multiply(inverse(least_upper_bound(X_85,c)),c)
| multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = multiply(inverse(least_upper_bound(X_85,c)),c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85)))) )],[refute_0_5030,refute_0_5031]) ).
cnf(refute_0_5033,plain,
multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = multiply(inverse(least_upper_bound(X_85,c)),c),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_85))),multiply(inverse(least_upper_bound(X_85,c)),c)) )],[refute_0_5029,refute_0_5032]) ).
cnf(refute_0_5034,plain,
( multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != multiply(inverse(least_upper_bound(X_85,c)),c)
| multiply(inverse(least_upper_bound(c,X_85)),c) != multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| multiply(inverse(least_upper_bound(c,X_85)),c) = multiply(inverse(least_upper_bound(X_85,c)),c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(c,X_85)),c),multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) ),[1],$fot(multiply(inverse(least_upper_bound(X_85,c)),c))]]) ).
cnf(refute_0_5035,plain,
( multiply(inverse(least_upper_bound(c,X_85)),c) != multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| multiply(inverse(least_upper_bound(c,X_85)),c) = multiply(inverse(least_upper_bound(X_85,c)),c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),multiply(inverse(least_upper_bound(X_85,c)),c)) )],[refute_0_5033,refute_0_5034]) ).
cnf(refute_0_5036,plain,
( inverse(least_upper_bound(identity,multiply(inverse(c),X_85))) != multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| multiply(inverse(least_upper_bound(c,X_85)),c) = multiply(inverse(least_upper_bound(X_85,c)),c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(c,X_85)),c),multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) )],[refute_0_5009,refute_0_5035]) ).
cnf(refute_0_5037,plain,
multiply(inverse(least_upper_bound(c,X_85)),c) = multiply(inverse(least_upper_bound(X_85,c)),c),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),X_85))),multiply(inverse(least_upper_bound(X_85,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) )],[refute_0_4952,refute_0_5036]) ).
cnf(refute_0_5038,plain,
multiply(inverse(least_upper_bound(c,b)),c) = multiply(inverse(least_upper_bound(b,c)),c),
inference(subst,[],[refute_0_5037:[bind(X_85,$fot(b))]]) ).
cnf(refute_0_5039,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))),multiply(inverse(X_473),X_472)),
inference(subst,[],[refute_0_4866:[bind(X_85,$fot(identity)),bind(X_86,$fot(multiply(inverse(X_473),X_472)))]]) ).
cnf(refute_0_5040,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))) = multiply(inverse(least_upper_bound(X_472,X_473)),X_473),
inference(subst,[],[refute_0_4866:[bind(X_85,$fot(X_472)),bind(X_86,$fot(X_473))]]) ).
cnf(refute_0_5041,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))) != multiply(inverse(least_upper_bound(X_472,X_473)),X_473)
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))),multiply(inverse(X_473),X_472))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))),multiply(inverse(X_473),X_472))) ),[1,0],$fot(multiply(inverse(least_upper_bound(X_472,X_473)),X_473))]]) ).
cnf(refute_0_5042,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))),multiply(inverse(X_473),X_472))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))),multiply(inverse(least_upper_bound(X_472,X_473)),X_473)) )],[refute_0_5040,refute_0_5041]) ).
cnf(refute_0_5043,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_473),X_472))),multiply(inverse(X_473),X_472))) )],[refute_0_5039,refute_0_5042]) ).
cnf(refute_0_5044,plain,
inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) = greatest_lower_bound(identity,multiply(inverse(X_473),X_472)),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))))]]) ).
cnf(refute_0_5045,plain,
inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(multiply(inverse(X_473),X_472))),bind(X_16,$fot(identity))]]) ).
cnf(refute_0_5046,plain,
least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))) = inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(multiply(inverse(X_473),X_472)))]]) ).
cnf(refute_0_5047,plain,
( inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))) != inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity))
| least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))))),bind(Y0,$fot(inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))))]]) ).
cnf(refute_0_5048,plain,
( inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity))) )],[refute_0_5046,refute_0_5047]) ).
cnf(refute_0_5049,plain,
least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X_473),X_472),identity)),inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) )],[refute_0_5045,refute_0_5048]) ).
cnf(refute_0_5050,plain,
multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity) = least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472)))))]]) ).
cnf(refute_0_5051,plain,
( multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity) != least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472)))
| least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))))]]) ).
cnf(refute_0_5052,plain,
( least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity),least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472)))) )],[refute_0_5050,refute_0_5051]) ).
cnf(refute_0_5053,plain,
multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) )],[refute_0_5049,refute_0_5052]) ).
cnf(refute_0_5054,plain,
multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity) = multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity),
inference(subst,[],[refute_0_2389:[bind(X,$fot(identity)),bind(Y,$fot(inverse(multiply(inverse(X_473),X_472)))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_5055,plain,
( multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity) != multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity)
| multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))))]]) ).
cnf(refute_0_5056,plain,
( multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity),multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity)) )],[refute_0_5054,refute_0_5055]) ).
cnf(refute_0_5057,plain,
multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(inverse(X_473),X_472))),identity),inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) )],[refute_0_5053,refute_0_5056]) ).
cnf(refute_0_5058,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)) = multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity),
inference(subst,[],[refute_0_701:[bind(X_89,$fot(identity)),bind(X_90,$fot(inverse(multiply(inverse(X_473),X_472))))]]) ).
cnf(refute_0_5059,plain,
( multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)) != multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity)
| least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))))]]) ).
cnf(refute_0_5060,plain,
( multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)),multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity)) )],[refute_0_5058,refute_0_5059]) ).
cnf(refute_0_5061,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(inverse(X_473),X_472)),identity),identity),inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) )],[refute_0_5057,refute_0_5060]) ).
cnf(refute_0_5062,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))))]]) ).
cnf(refute_0_5063,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)))
| least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))))]]) ).
cnf(refute_0_5064,plain,
( least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)))) )],[refute_0_5062,refute_0_5063]) ).
cnf(refute_0_5065,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity)),inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) )],[refute_0_5061,refute_0_5064]) ).
cnf(refute_0_5066,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) != greatest_lower_bound(identity,multiply(inverse(X_473),X_472))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))))]]) ).
cnf(refute_0_5067,plain,
( inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))) != greatest_lower_bound(identity,multiply(inverse(X_473),X_472))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472))))) )],[refute_0_5065,refute_0_5066]) ).
cnf(refute_0_5068,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) = greatest_lower_bound(identity,multiply(inverse(X_473),X_472)),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))),greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) )],[refute_0_5044,refute_0_5067]) ).
cnf(refute_0_5069,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != greatest_lower_bound(identity,multiply(inverse(X_473),X_472))
| greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) = multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)))]]) ).
cnf(refute_0_5070,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))
| greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) = multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),greatest_lower_bound(identity,multiply(inverse(X_473),X_472))) )],[refute_0_5068,refute_0_5069]) ).
cnf(refute_0_5071,plain,
multiply(X_473,multiply(inverse(X_473),X_472)) = X_472,
inference(subst,[],[refute_0_3743:[bind(X_46,$fot(X_472)),bind(X_50,$fot(X_473))]]) ).
cnf(refute_0_5072,plain,
multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))) = multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))))]]) ).
cnf(refute_0_5073,plain,
( multiply(X_473,multiply(inverse(X_473),X_472)) != X_472
| multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))) != multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472)))
| multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))),multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472)))) ),[1,1],$fot(X_472)]]) ).
cnf(refute_0_5074,plain,
( multiply(X_473,multiply(inverse(X_473),X_472)) != X_472
| multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))),multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472)))) )],[refute_0_5072,refute_0_5073]) ).
cnf(refute_0_5075,plain,
multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472),
inference(resolve,[$cnf( $equal(multiply(X_473,multiply(inverse(X_473),X_472)),X_472) )],[refute_0_5071,refute_0_5074]) ).
cnf(refute_0_5076,plain,
multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(least_upper_bound(X_472,X_473)))),bind(Y,$fot(X_473)),bind(Z,$fot(multiply(inverse(X_473),X_472)))]]) ).
cnf(refute_0_5077,plain,
( multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) != multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472)))
| multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))) != multiply(inverse(least_upper_bound(X_472,X_473)),X_472)
| multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_472,X_473)),X_472)))]]) ).
cnf(refute_0_5078,plain,
( multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))) != multiply(inverse(least_upper_bound(X_472,X_473)),X_472)
| multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)),multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472)))) )],[refute_0_5076,refute_0_5077]) ).
cnf(refute_0_5079,plain,
multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_472,X_473)),multiply(X_473,multiply(inverse(X_473),X_472))),multiply(inverse(least_upper_bound(X_472,X_473)),X_472)) )],[refute_0_5075,refute_0_5078]) ).
cnf(refute_0_5080,plain,
( multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)) != multiply(inverse(least_upper_bound(X_472,X_473)),X_472)
| greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) != multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))
| greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)),multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))) ),[1],$fot(multiply(inverse(least_upper_bound(X_472,X_473)),X_472))]]) ).
cnf(refute_0_5081,plain,
( greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) != multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))
| greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472)),multiply(inverse(least_upper_bound(X_472,X_473)),X_472)) )],[refute_0_5079,refute_0_5080]) ).
cnf(refute_0_5082,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))) != multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))
| greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_473),X_472)),multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))) )],[refute_0_5070,refute_0_5081]) ).
cnf(refute_0_5083,plain,
greatest_lower_bound(identity,multiply(inverse(X_473),X_472)) = multiply(inverse(least_upper_bound(X_472,X_473)),X_472),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(inverse(X_473),X_472)),identity))),multiply(multiply(inverse(least_upper_bound(X_472,X_473)),X_473),multiply(inverse(X_473),X_472))) )],[refute_0_5043,refute_0_5082]) ).
cnf(refute_0_5084,plain,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(least_upper_bound(c,b)),c),
inference(subst,[],[refute_0_5083:[bind(X_472,$fot(c)),bind(X_473,$fot(b))]]) ).
cnf(refute_0_5085,plain,
( multiply(inverse(least_upper_bound(c,b)),c) != multiply(inverse(least_upper_bound(b,c)),c)
| greatest_lower_bound(identity,multiply(inverse(b),c)) != multiply(inverse(least_upper_bound(c,b)),c)
| greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(least_upper_bound(b,c)),c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(b),c)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(c,b)),c))),bind(Z0,$fot(multiply(inverse(least_upper_bound(b,c)),c)))]]) ).
cnf(refute_0_5086,plain,
( multiply(inverse(least_upper_bound(c,b)),c) != multiply(inverse(least_upper_bound(b,c)),c)
| greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(least_upper_bound(b,c)),c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(least_upper_bound(c,b)),c)) )],[refute_0_5084,refute_0_5085]) ).
cnf(refute_0_5087,plain,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(least_upper_bound(b,c)),c),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(c,b)),c),multiply(inverse(least_upper_bound(b,c)),c)) )],[refute_0_5038,refute_0_5086]) ).
cnf(refute_0_5088,plain,
( multiply(inverse(least_upper_bound(b,c)),c) != multiply(inverse(least_upper_bound(a,c)),c)
| greatest_lower_bound(identity,multiply(inverse(b),c)) != multiply(inverse(least_upper_bound(b,c)),c)
| greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(least_upper_bound(a,c)),c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(b),c)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(b,c)),c))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,c)),c)))]]) ).
cnf(refute_0_5089,plain,
( multiply(inverse(least_upper_bound(b,c)),c) != multiply(inverse(least_upper_bound(a,c)),c)
| greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(least_upper_bound(a,c)),c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(least_upper_bound(b,c)),c)) )],[refute_0_5087,refute_0_5088]) ).
cnf(refute_0_5090,plain,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(least_upper_bound(a,c)),c),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(b,c)),c),multiply(inverse(least_upper_bound(a,c)),c)) )],[refute_0_4855,refute_0_5089]) ).
cnf(refute_0_5091,plain,
( multiply(inverse(b),greatest_lower_bound(a,c)) != greatest_lower_bound(identity,multiply(inverse(b),c))
| greatest_lower_bound(identity,multiply(inverse(b),c)) != multiply(inverse(least_upper_bound(a,c)),c)
| multiply(inverse(b),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),c) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(b),greatest_lower_bound(a,c)),multiply(inverse(least_upper_bound(a,c)),c)) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(b),c)))]]) ).
cnf(refute_0_5092,plain,
( multiply(inverse(b),greatest_lower_bound(a,c)) != greatest_lower_bound(identity,multiply(inverse(b),c))
| multiply(inverse(b),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(least_upper_bound(a,c)),c)) )],[refute_0_5090,refute_0_5091]) ).
cnf(refute_0_5093,plain,
multiply(inverse(b),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),c),
inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,c)),greatest_lower_bound(identity,multiply(inverse(b),c))) )],[refute_0_4847,refute_0_5092]) ).
cnf(refute_0_5094,plain,
( multiply(inverse(b),greatest_lower_bound(a,c)) != multiply(inverse(least_upper_bound(a,c)),c)
| multiply(inverse(least_upper_bound(a,c)),c) = multiply(inverse(b),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(b),greatest_lower_bound(a,c)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),c)))]]) ).
cnf(refute_0_5095,plain,
multiply(inverse(least_upper_bound(a,c)),c) = multiply(inverse(b),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,c)),multiply(inverse(least_upper_bound(a,c)),c)) )],[refute_0_5093,refute_0_5094]) ).
cnf(refute_0_5096,plain,
( multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c)))
| multiply(inverse(least_upper_bound(a,c)),c) != multiply(inverse(b),greatest_lower_bound(a,c))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c)))) ),[1,0,1],$fot(multiply(inverse(b),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5097,plain,
( multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c)))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),c),multiply(inverse(b),greatest_lower_bound(a,c))) )],[refute_0_5095,refute_0_5096]) ).
cnf(refute_0_5098,plain,
multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c)))) )],[refute_0_4787,refute_0_5097]) ).
cnf(refute_0_5099,plain,
least_upper_bound(a,least_upper_bound(c,c)) = least_upper_bound(a,least_upper_bound(c,c)),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(c,c)))]]) ).
cnf(refute_0_5100,plain,
( least_upper_bound(a,least_upper_bound(c,c)) != least_upper_bound(a,least_upper_bound(c,c))
| least_upper_bound(c,c) != c
| least_upper_bound(a,least_upper_bound(c,c)) = least_upper_bound(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,c)),least_upper_bound(a,least_upper_bound(c,c))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_5101,plain,
( least_upper_bound(c,c) != c
| least_upper_bound(a,least_upper_bound(c,c)) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,c)),least_upper_bound(a,least_upper_bound(c,c))) )],[refute_0_5099,refute_0_5100]) ).
cnf(refute_0_5102,plain,
least_upper_bound(a,least_upper_bound(c,c)) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(c,c),c) )],[refute_0_3569,refute_0_5101]) ).
cnf(refute_0_5103,plain,
multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),
introduced(tautology,[refl,[$fot(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))))]]) ).
cnf(refute_0_5104,plain,
( multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| least_upper_bound(a,least_upper_bound(c,c)) != least_upper_bound(a,c)
| multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) = multiply(inverse(c),least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))) ),[1,1],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_5105,plain,
( least_upper_bound(a,least_upper_bound(c,c)) != least_upper_bound(a,c)
| multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) = multiply(inverse(c),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5103,refute_0_5104]) ).
cnf(refute_0_5106,plain,
multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) = multiply(inverse(c),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,c)),least_upper_bound(a,c)) )],[refute_0_5102,refute_0_5105]) ).
cnf(refute_0_5107,plain,
multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))) = least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_82)),bind(Y,$fot(a)),bind(Z,$fot(least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_5108,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))) != least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33)))
| least_upper_bound(a,least_upper_bound(c,X_33)) != least_upper_bound(a,least_upper_bound(X_33,c))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))),least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33)))) ),[0,1],$fot(least_upper_bound(a,least_upper_bound(X_33,c)))]]) ).
cnf(refute_0_5109,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))) != least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33)))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_33)),least_upper_bound(a,least_upper_bound(X_33,c))) )],[refute_0_3505,refute_0_5108]) ).
cnf(refute_0_5110,plain,
multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))),least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33)))) )],[refute_0_5107,refute_0_5109]) ).
cnf(refute_0_5111,plain,
least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))) = multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))),
inference(subst,[],[refute_0_286:[bind(X,$fot(X_82)),bind(Y,$fot(a)),bind(Z,$fot(least_upper_bound(c,X_33)))]]) ).
cnf(refute_0_5112,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) != least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33)))
| least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))) != multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33)))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33)))) ),[0],$fot(least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))))]]) ).
cnf(refute_0_5113,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) != least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33)))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33))),multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33)))) )],[refute_0_5111,refute_0_5112]) ).
cnf(refute_0_5114,plain,
multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33))),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),least_upper_bound(multiply(X_82,a),multiply(X_82,least_upper_bound(c,X_33)))) )],[refute_0_5110,refute_0_5113]) ).
cnf(refute_0_5115,plain,
least_upper_bound(a,least_upper_bound(c,X_33)) = least_upper_bound(X_33,least_upper_bound(c,a)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(X_33)),bind(X_30,$fot(a)),bind(X_31,$fot(c))]]) ).
cnf(refute_0_5116,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) != multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33)))
| least_upper_bound(a,least_upper_bound(c,X_33)) != least_upper_bound(X_33,least_upper_bound(c,a))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33)))) ),[1,1],$fot(least_upper_bound(X_33,least_upper_bound(c,a)))]]) ).
cnf(refute_0_5117,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) != multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33)))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_33)),least_upper_bound(X_33,least_upper_bound(c,a))) )],[refute_0_5115,refute_0_5116]) ).
cnf(refute_0_5118,plain,
multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),multiply(X_82,least_upper_bound(a,least_upper_bound(c,X_33)))) )],[refute_0_5114,refute_0_5117]) ).
cnf(refute_0_5119,plain,
least_upper_bound(X_33,least_upper_bound(c,a)) = least_upper_bound(X_33,least_upper_bound(a,c)),
inference(subst,[],[refute_0_967:[bind(X_295,$fot(a)),bind(X_296,$fot(X_33)),bind(X_297,$fot(c))]]) ).
cnf(refute_0_5120,plain,
multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))),
introduced(tautology,[refl,[$fot(multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))))]]) ).
cnf(refute_0_5121,plain,
( multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) != multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a)))
| least_upper_bound(X_33,least_upper_bound(c,a)) != least_upper_bound(X_33,least_upper_bound(a,c))
| multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))),multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a)))) ),[1,1],$fot(least_upper_bound(X_33,least_upper_bound(a,c)))]]) ).
cnf(refute_0_5122,plain,
( least_upper_bound(X_33,least_upper_bound(c,a)) != least_upper_bound(X_33,least_upper_bound(a,c))
| multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))),multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a)))) )],[refute_0_5120,refute_0_5121]) ).
cnf(refute_0_5123,plain,
multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_33,least_upper_bound(c,a)),least_upper_bound(X_33,least_upper_bound(a,c))) )],[refute_0_5119,refute_0_5122]) ).
cnf(refute_0_5124,plain,
( multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))) != multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c)))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) != multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a)))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a)))) ),[1],$fot(multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))))]]) ).
cnf(refute_0_5125,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) != multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a)))
| multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a))),multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c)))) )],[refute_0_5123,refute_0_5124]) ).
cnf(refute_0_5126,plain,
multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) = multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),multiply(X_82,least_upper_bound(X_33,least_upper_bound(c,a)))) )],[refute_0_5118,refute_0_5125]) ).
cnf(refute_0_5127,plain,
( multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) != multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c)))
| multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))) = multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))))),bind(Y0,$fot(multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_5128,plain,
multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c))) = multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),
inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(a,least_upper_bound(X_33,c))),multiply(X_82,least_upper_bound(X_33,least_upper_bound(a,c)))) )],[refute_0_5126,refute_0_5127]) ).
cnf(refute_0_5129,plain,
multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),
inference(subst,[],[refute_0_5128:[bind(X_33,$fot(c)),bind(X_82,$fot(inverse(c)))]]) ).
cnf(refute_0_5130,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_83)),
inference(subst,[],[refute_0_67:[bind(X_84,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_5131,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_83))
| inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != inverse(c)
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = least_upper_bound(identity,multiply(inverse(c),X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_83))) ),[1,1,0],$fot(inverse(c))]]) ).
cnf(refute_0_5132,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_83))
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = least_upper_bound(identity,multiply(inverse(c),X_83)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),inverse(c)) )],[refute_0_4949,refute_0_5131]) ).
cnf(refute_0_5133,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = least_upper_bound(identity,multiply(inverse(c),X_83)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),X_83))) )],[refute_0_5130,refute_0_5132]) ).
cnf(refute_0_5134,plain,
multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),
inference(subst,[],[refute_0_2646:[bind(X_475,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),bind(X_50,$fot(X_83))]]) ).
cnf(refute_0_5135,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))
| multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != least_upper_bound(identity,multiply(inverse(c),X_83))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = least_upper_bound(identity,multiply(inverse(c),X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),least_upper_bound(identity,multiply(inverse(c),X_83))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))))]]) ).
cnf(refute_0_5136,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != least_upper_bound(identity,multiply(inverse(c),X_83))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = least_upper_bound(identity,multiply(inverse(c),X_83)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))) )],[refute_0_5134,refute_0_5135]) ).
cnf(refute_0_5137,plain,
least_upper_bound(identity,multiply(inverse(c),X_83)) = multiply(inverse(c),least_upper_bound(X_83,c)),
inference(subst,[],[refute_0_2042:[bind(X_84,$fot(c))]]) ).
cnf(refute_0_5138,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) != least_upper_bound(identity,multiply(inverse(c),X_83))
| least_upper_bound(identity,multiply(inverse(c),X_83)) != multiply(inverse(c),least_upper_bound(X_83,c))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = multiply(inverse(c),least_upper_bound(X_83,c)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),multiply(inverse(c),least_upper_bound(X_83,c))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(c),X_83)))]]) ).
cnf(refute_0_5139,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) != least_upper_bound(identity,multiply(inverse(c),X_83))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = multiply(inverse(c),least_upper_bound(X_83,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(c),X_83)),multiply(inverse(c),least_upper_bound(X_83,c))) )],[refute_0_5137,refute_0_5138]) ).
cnf(refute_0_5140,plain,
( multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != least_upper_bound(identity,multiply(inverse(c),X_83))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = multiply(inverse(c),least_upper_bound(X_83,c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),least_upper_bound(identity,multiply(inverse(c),X_83))) )],[refute_0_5136,refute_0_5139]) ).
cnf(refute_0_5141,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = multiply(inverse(c),least_upper_bound(X_83,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),least_upper_bound(X_83,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),least_upper_bound(identity,multiply(inverse(c),X_83))) )],[refute_0_5133,refute_0_5140]) ).
cnf(refute_0_5142,plain,
inverse(multiply(inverse(least_upper_bound(c,X_83)),c)) = multiply(inverse(c),least_upper_bound(c,X_83)),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(least_upper_bound(c,X_83))),bind(X_74,$fot(c))]]) ).
cnf(refute_0_5143,plain,
greatest_lower_bound(identity,multiply(inverse(X_83),c)) = multiply(inverse(least_upper_bound(c,X_83)),c),
inference(subst,[],[refute_0_5083:[bind(X_472,$fot(c)),bind(X_473,$fot(X_83))]]) ).
cnf(refute_0_5144,plain,
inverse(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),
inference(subst,[],[refute_0_88:[bind(X_50,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_5145,plain,
( inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != inverse(c)
| inverse(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| inverse(inverse(c)) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),[0,0],$fot(inverse(c))]]) ).
cnf(refute_0_5146,plain,
( inverse(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| inverse(inverse(c)) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),inverse(c)) )],[refute_0_4949,refute_0_5145]) ).
cnf(refute_0_5147,plain,
inverse(inverse(c)) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) )],[refute_0_5144,refute_0_5146]) ).
cnf(refute_0_5148,plain,
inverse(inverse(c)) = c,
inference(subst,[],[refute_0_88:[bind(X_50,$fot(c))]]) ).
cnf(refute_0_5149,plain,
( inverse(inverse(c)) != c
| inverse(inverse(c)) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| c = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(c)),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) ),[0],$fot(c)]]) ).
cnf(refute_0_5150,plain,
( inverse(inverse(c)) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| c = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(c)),c) )],[refute_0_5148,refute_0_5149]) ).
cnf(refute_0_5151,plain,
c = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),
inference(resolve,[$cnf( $equal(inverse(inverse(c)),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) )],[refute_0_5147,refute_0_5150]) ).
cnf(refute_0_5152,plain,
( c != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))
| greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) = c ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(c)),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_5153,plain,
greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) = c,
inference(resolve,[$cnf( $equal(c,greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) )],[refute_0_5151,refute_0_5152]) ).
cnf(refute_0_5154,plain,
multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))]]) ).
cnf(refute_0_5155,plain,
( multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))
| greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) != c
| multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = multiply(inverse(X_83),c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_5156,plain,
( greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))) != c
| multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = multiply(inverse(X_83),c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) )],[refute_0_5154,refute_0_5155]) ).
cnf(refute_0_5157,plain,
multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) = multiply(inverse(X_83),c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))),c) )],[refute_0_5153,refute_0_5156]) ).
cnf(refute_0_5158,plain,
greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))]]) ).
cnf(refute_0_5159,plain,
( multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != multiply(inverse(X_83),c)
| greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))
| greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = greatest_lower_bound(identity,multiply(inverse(X_83),c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) ),[1,1],$fot(multiply(inverse(X_83),c))]]) ).
cnf(refute_0_5160,plain,
( multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))) != multiply(inverse(X_83),c)
| greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = greatest_lower_bound(identity,multiply(inverse(X_83),c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) )],[refute_0_5158,refute_0_5159]) ).
cnf(refute_0_5161,plain,
greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = greatest_lower_bound(identity,multiply(inverse(X_83),c)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))),multiply(inverse(X_83),c)) )],[refute_0_5157,refute_0_5160]) ).
cnf(refute_0_5162,plain,
( greatest_lower_bound(identity,multiply(inverse(X_83),c)) != multiply(inverse(least_upper_bound(c,X_83)),c)
| greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != greatest_lower_bound(identity,multiply(inverse(X_83),c))
| greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = multiply(inverse(least_upper_bound(c,X_83)),c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_83),c)))),bind(Z0,$fot(multiply(inverse(least_upper_bound(c,X_83)),c)))]]) ).
cnf(refute_0_5163,plain,
( greatest_lower_bound(identity,multiply(inverse(X_83),c)) != multiply(inverse(least_upper_bound(c,X_83)),c)
| greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = multiply(inverse(least_upper_bound(c,X_83)),c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),greatest_lower_bound(identity,multiply(inverse(X_83),c))) )],[refute_0_5161,refute_0_5162]) ).
cnf(refute_0_5164,plain,
greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) = multiply(inverse(least_upper_bound(c,X_83)),c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_83),c)),multiply(inverse(least_upper_bound(c,X_83)),c)) )],[refute_0_5143,refute_0_5163]) ).
cnf(refute_0_5165,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))))]]) ).
cnf(refute_0_5166,plain,
( greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != multiply(inverse(least_upper_bound(c,X_83)),c)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = inverse(multiply(inverse(least_upper_bound(c,X_83)),c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))) ),[1,0],$fot(multiply(inverse(least_upper_bound(c,X_83)),c))]]) ).
cnf(refute_0_5167,plain,
( greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))) != multiply(inverse(least_upper_bound(c,X_83)),c)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = inverse(multiply(inverse(least_upper_bound(c,X_83)),c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))))) )],[refute_0_5165,refute_0_5166]) ).
cnf(refute_0_5168,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = inverse(multiply(inverse(least_upper_bound(c,X_83)),c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c))))),multiply(inverse(least_upper_bound(c,X_83)),c)) )],[refute_0_5164,refute_0_5167]) ).
cnf(refute_0_5169,plain,
( inverse(multiply(inverse(least_upper_bound(c,X_83)),c)) != multiply(inverse(c),least_upper_bound(c,X_83))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) != inverse(multiply(inverse(least_upper_bound(c,X_83)),c))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = multiply(inverse(c),least_upper_bound(c,X_83)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))))),bind(Y0,$fot(inverse(multiply(inverse(least_upper_bound(c,X_83)),c)))),bind(Z0,$fot(multiply(inverse(c),least_upper_bound(c,X_83))))]]) ).
cnf(refute_0_5170,plain,
( inverse(multiply(inverse(least_upper_bound(c,X_83)),c)) != multiply(inverse(c),least_upper_bound(c,X_83))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = multiply(inverse(c),least_upper_bound(c,X_83)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),inverse(multiply(inverse(least_upper_bound(c,X_83)),c))) )],[refute_0_5168,refute_0_5169]) ).
cnf(refute_0_5171,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) = multiply(inverse(c),least_upper_bound(c,X_83)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(c,X_83)),c)),multiply(inverse(c),least_upper_bound(c,X_83))) )],[refute_0_5142,refute_0_5170]) ).
cnf(refute_0_5172,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) != multiply(inverse(c),least_upper_bound(X_83,c))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) != multiply(inverse(c),least_upper_bound(c,X_83))
| multiply(inverse(c),least_upper_bound(c,X_83)) = multiply(inverse(c),least_upper_bound(X_83,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),multiply(inverse(c),least_upper_bound(X_83,c))) ),[0],$fot(multiply(inverse(c),least_upper_bound(c,X_83)))]]) ).
cnf(refute_0_5173,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))) != multiply(inverse(c),least_upper_bound(X_83,c))
| multiply(inverse(c),least_upper_bound(c,X_83)) = multiply(inverse(c),least_upper_bound(X_83,c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),multiply(inverse(c),least_upper_bound(c,X_83))) )],[refute_0_5171,refute_0_5172]) ).
cnf(refute_0_5174,plain,
multiply(inverse(c),least_upper_bound(c,X_83)) = multiply(inverse(c),least_upper_bound(X_83,c)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_83),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,b),multiply(inverse(b),c)))))),multiply(inverse(c),least_upper_bound(X_83,c))) )],[refute_0_5141,refute_0_5173]) ).
cnf(refute_0_5175,plain,
( multiply(inverse(c),least_upper_bound(c,X_83)) != multiply(inverse(c),least_upper_bound(X_83,c))
| multiply(inverse(c),least_upper_bound(X_83,c)) = multiply(inverse(c),least_upper_bound(c,X_83)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(c),least_upper_bound(c,X_83)))),bind(Y0,$fot(multiply(inverse(c),least_upper_bound(X_83,c))))]]) ).
cnf(refute_0_5176,plain,
multiply(inverse(c),least_upper_bound(X_83,c)) = multiply(inverse(c),least_upper_bound(c,X_83)),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(c,X_83)),multiply(inverse(c),least_upper_bound(X_83,c))) )],[refute_0_5174,refute_0_5175]) ).
cnf(refute_0_5177,plain,
multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)) = multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c))),
inference(subst,[],[refute_0_5176:[bind(X_83,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5178,plain,
( multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c))) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)) != multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c)))
| multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)))),bind(Y0,$fot(multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c))))),bind(Z0,$fot(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))))]]) ).
cnf(refute_0_5179,plain,
( multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c))) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)),multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c)))) )],[refute_0_5177,refute_0_5178]) ).
cnf(refute_0_5180,plain,
multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(c,least_upper_bound(a,c))),multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5129,refute_0_5179]) ).
cnf(refute_0_5181,plain,
( multiply(inverse(X_475),least_upper_bound(X_50,X_475)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475))) = multiply(inverse(X_475),least_upper_bound(X_50,X_475)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(X_475),least_upper_bound(X_50,X_475)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475)))))]]) ).
cnf(refute_0_5182,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475))) = multiply(inverse(X_475),least_upper_bound(X_50,X_475)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_475),least_upper_bound(X_50,X_475)),inverse(greatest_lower_bound(identity,multiply(inverse(X_50),X_475)))) )],[refute_0_2646,refute_0_5181]) ).
cnf(refute_0_5183,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))) = multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)),
inference(subst,[],[refute_0_5182:[bind(X_475,$fot(c)),bind(X_50,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5184,plain,
( multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))) != multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c))
| inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))))),bind(Y0,$fot(multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)))),bind(Z0,$fot(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))))]]) ).
cnf(refute_0_5185,plain,
( multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))),multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c))) )],[refute_0_5183,refute_0_5184]) ).
cnf(refute_0_5186,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(least_upper_bound(a,c),c)),multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5180,refute_0_5185]) ).
cnf(refute_0_5187,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84))),
inference(subst,[],[refute_0_67:[bind(X_83,$fot(least_upper_bound(inverse(X_474),X_84)))]]) ).
cnf(refute_0_5188,plain,
multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84)) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))),
inference(subst,[],[refute_0_1146:[bind(X_45,$fot(X_474)),bind(X_86,$fot(X_84))]]) ).
cnf(refute_0_5189,plain,
( multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84)) != inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) != least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))]]) ).
cnf(refute_0_5190,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) != least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84)),inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) )],[refute_0_5188,refute_0_5189]) ).
cnf(refute_0_5191,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)),least_upper_bound(identity,multiply(inverse(X_84),least_upper_bound(inverse(X_474),X_84)))) )],[refute_0_5187,refute_0_5190]) ).
cnf(refute_0_5192,plain,
least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)) = least_upper_bound(X_84,inverse(X_474)),
inference(subst,[],[refute_0_279:[bind(Y,$fot(inverse(X_474))),bind(X_13,$fot(X_84))]]) ).
cnf(refute_0_5193,plain,
multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))))]]) ).
cnf(refute_0_5194,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))) != multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)))
| least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)) != least_upper_bound(X_84,inverse(X_474))
| multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))),multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)))) ),[1,1],$fot(least_upper_bound(X_84,inverse(X_474)))]]) ).
cnf(refute_0_5195,plain,
( least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)) != least_upper_bound(X_84,inverse(X_474))
| multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))),multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)))) )],[refute_0_5193,refute_0_5194]) ).
cnf(refute_0_5196,plain,
multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))) = multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)),least_upper_bound(X_84,inverse(X_474))) )],[refute_0_5192,refute_0_5195]) ).
cnf(refute_0_5197,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))),
inference(subst,[],[refute_0_318:[bind(X,$fot(inverse(X_84))),bind(Y,$fot(least_upper_bound(inverse(X_474),X_84))),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_5198,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))) != multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) != multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)))),bind(Y0,$fot(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))))),bind(Z0,$fot(multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474)))))]]) ).
cnf(refute_0_5199,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))) != multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)),multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84)))) )],[refute_0_5197,refute_0_5198]) ).
cnf(refute_0_5200,plain,
multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) = multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,least_upper_bound(inverse(X_474),X_84))),multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474)))) )],[refute_0_5196,refute_0_5199]) ).
cnf(refute_0_5201,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) != multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474)))
| multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))
| multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))) ),[0],$fot(multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))))]]) ).
cnf(refute_0_5202,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))
| multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)),multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474)))) )],[refute_0_5200,refute_0_5201]) ).
cnf(refute_0_5203,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))) = greatest_lower_bound(identity,multiply(X_474,X_84)),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(multiply(X_474,X_84))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_5204,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))))]]) ).
cnf(refute_0_5205,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))) != greatest_lower_bound(identity,multiply(X_474,X_84))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_474,X_84)))]]) ).
cnf(refute_0_5206,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))) != greatest_lower_bound(identity,multiply(X_474,X_84))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))) )],[refute_0_5204,refute_0_5205]) ).
cnf(refute_0_5207,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))),greatest_lower_bound(identity,multiply(X_474,X_84))) )],[refute_0_5203,refute_0_5206]) ).
cnf(refute_0_5208,plain,
inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))),
inference(subst,[],[refute_0_2354:[bind(X_11,$fot(greatest_lower_bound(identity,multiply(X_474,X_84)))),bind(X_16,$fot(identity))]]) ).
cnf(refute_0_5209,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity)),
inference(subst,[],[refute_0_1139:[bind(X_364,$fot(greatest_lower_bound(identity,multiply(X_474,X_84))))]]) ).
cnf(refute_0_5210,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) != inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))))]]) ).
cnf(refute_0_5211,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))),inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity))) )],[refute_0_5209,refute_0_5210]) ).
cnf(refute_0_5212,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_474,X_84)),identity)),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))) )],[refute_0_5208,refute_0_5211]) ).
cnf(refute_0_5213,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))))]]) ).
cnf(refute_0_5214,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84))))) )],[refute_0_5212,refute_0_5213]) ).
cnf(refute_0_5215,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_474,X_84)))),inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) )],[refute_0_5207,refute_0_5214]) ).
cnf(refute_0_5216,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) != inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))
| multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))),inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))))]]) ).
cnf(refute_0_5217,plain,
( multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))
| multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))),inverse(greatest_lower_bound(identity,multiply(X_474,X_84)))) )],[refute_0_5215,refute_0_5216]) ).
cnf(refute_0_5218,plain,
( multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))
| multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))) )],[refute_0_5202,refute_0_5217]) ).
cnf(refute_0_5219,plain,
multiply(inverse(X_84),least_upper_bound(X_84,inverse(X_474))) = inverse(greatest_lower_bound(identity,multiply(X_474,X_84))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(least_upper_bound(inverse(X_474),X_84),X_84)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_474,X_84))))) )],[refute_0_5191,refute_0_5218]) ).
cnf(refute_0_5220,plain,
multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))) = inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))),
inference(subst,[],[refute_0_5219:[bind(X_474,$fot(inverse(least_upper_bound(a,c)))),bind(X_84,$fot(c))]]) ).
cnf(refute_0_5221,plain,
( multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))) != inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c)))
| inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))))),bind(Z0,$fot(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))))]]) ).
cnf(refute_0_5222,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))),inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c)))) )],[refute_0_5220,refute_0_5221]) ).
cnf(refute_0_5223,plain,
multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(a,c)),c))),multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5186,refute_0_5222]) ).
cnf(refute_0_5224,plain,
multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))),
inference(subst,[],[refute_0_5176:[bind(X_83,$fot(inverse(inverse(least_upper_bound(a,c)))))]]) ).
cnf(refute_0_5225,plain,
( multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c)))))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)))),bind(Y0,$fot(multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))))),bind(Z0,$fot(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))))]]) ).
cnf(refute_0_5226,plain,
( multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)),multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c)))))) )],[refute_0_5224,refute_0_5225]) ).
cnf(refute_0_5227,plain,
multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(c,inverse(inverse(least_upper_bound(a,c))))),multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5223,refute_0_5226]) ).
cnf(refute_0_5228,plain,
( multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) != multiply(inverse(c),least_upper_bound(a,c))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = multiply(inverse(c),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)))),bind(Y0,$fot(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))))),bind(Z0,$fot(multiply(inverse(c),least_upper_bound(a,c))))]]) ).
cnf(refute_0_5229,plain,
( multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))) != multiply(inverse(c),least_upper_bound(a,c))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = multiply(inverse(c),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)),multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5227,refute_0_5228]) ).
cnf(refute_0_5230,plain,
multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) = multiply(inverse(c),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(a,least_upper_bound(c,c))),multiply(inverse(c),least_upper_bound(a,c))) )],[refute_0_5106,refute_0_5229]) ).
cnf(refute_0_5231,plain,
( multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != multiply(inverse(c),least_upper_bound(a,c))
| multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))
| multiply(inverse(c),least_upper_bound(a,c)) = inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)),inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))) ),[0],$fot(multiply(inverse(c),least_upper_bound(a,c)))]]) ).
cnf(refute_0_5232,plain,
( multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))
| multiply(inverse(c),least_upper_bound(a,c)) = inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)),multiply(inverse(c),least_upper_bound(a,c))) )],[refute_0_5230,refute_0_5231]) ).
cnf(refute_0_5233,plain,
greatest_lower_bound(a,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(subst,[],[refute_0_2202:[bind(X_16,$fot(c)),bind(X_17,$fot(a))]]) ).
cnf(refute_0_5234,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,greatest_lower_bound(b,c)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(b,c)))]]) ).
cnf(refute_0_5235,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,greatest_lower_bound(b,c))
| greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,greatest_lower_bound(b,c))) ),[1,1],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_5236,plain,
( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,greatest_lower_bound(b,c))) )],[refute_0_5234,refute_0_5235]) ).
cnf(refute_0_5237,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_176,refute_0_5236]) ).
cnf(refute_0_5238,plain,
( greatest_lower_bound(a,greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,greatest_lower_bound(a,c))
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(b,c)))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(a,c)))),bind(Z0,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5239,plain,
( greatest_lower_bound(a,greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
| greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,greatest_lower_bound(a,c))) )],[refute_0_5237,refute_0_5238]) ).
cnf(refute_0_5240,plain,
greatest_lower_bound(a,greatest_lower_bound(b,c)) = greatest_lower_bound(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) )],[refute_0_5233,refute_0_5239]) ).
cnf(refute_0_5241,plain,
inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))))]]) ).
cnf(refute_0_5242,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
| inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))
| inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) = inverse(greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).
cnf(refute_0_5243,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(a,c)
| inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) = inverse(greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))) )],[refute_0_5241,refute_0_5242]) ).
cnf(refute_0_5244,plain,
inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) = inverse(greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,c)),greatest_lower_bound(a,c)) )],[refute_0_5240,refute_0_5243]) ).
cnf(refute_0_5245,plain,
inverse(greatest_lower_bound(b,X_461)) = least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))),
inference(subst,[],[refute_0_4154:[bind(X_59,$fot(X_461))]]) ).
cnf(refute_0_5246,plain,
greatest_lower_bound(X_461,b) = greatest_lower_bound(b,X_461),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_461)),bind(Y,$fot(b))]]) ).
cnf(refute_0_5247,plain,
( greatest_lower_bound(X_461,b) != greatest_lower_bound(b,X_461)
| greatest_lower_bound(b,X_461) = greatest_lower_bound(X_461,b) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_461,b))),bind(Y0,$fot(greatest_lower_bound(b,X_461)))]]) ).
cnf(refute_0_5248,plain,
greatest_lower_bound(b,X_461) = greatest_lower_bound(X_461,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_461,b),greatest_lower_bound(b,X_461)) )],[refute_0_5246,refute_0_5247]) ).
cnf(refute_0_5249,plain,
( greatest_lower_bound(b,X_461) != greatest_lower_bound(X_461,b)
| inverse(greatest_lower_bound(b,X_461)) != least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461)))
| inverse(greatest_lower_bound(X_461,b)) = least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,X_461)),least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461)))) ),[0,0],$fot(greatest_lower_bound(X_461,b))]]) ).
cnf(refute_0_5250,plain,
( inverse(greatest_lower_bound(b,X_461)) != least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461)))
| inverse(greatest_lower_bound(X_461,b)) = least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,X_461),greatest_lower_bound(X_461,b)) )],[refute_0_5248,refute_0_5249]) ).
cnf(refute_0_5251,plain,
inverse(greatest_lower_bound(X_461,b)) = least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,X_461)),least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461)))) )],[refute_0_5245,refute_0_5250]) ).
cnf(refute_0_5252,plain,
least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))) = inverse(greatest_lower_bound(b,X_461)),
inference(subst,[],[refute_0_4163:[bind(X_59,$fot(X_461))]]) ).
cnf(refute_0_5253,plain,
( inverse(greatest_lower_bound(X_461,b)) != least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461)))
| least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))) != inverse(greatest_lower_bound(b,X_461))
| inverse(greatest_lower_bound(X_461,b)) = inverse(greatest_lower_bound(b,X_461)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_461,b)),inverse(greatest_lower_bound(b,X_461))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))))]]) ).
cnf(refute_0_5254,plain,
( inverse(greatest_lower_bound(X_461,b)) != least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461)))
| inverse(greatest_lower_bound(X_461,b)) = inverse(greatest_lower_bound(b,X_461)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461))),inverse(greatest_lower_bound(b,X_461))) )],[refute_0_5252,refute_0_5253]) ).
cnf(refute_0_5255,plain,
inverse(greatest_lower_bound(X_461,b)) = inverse(greatest_lower_bound(b,X_461)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_461,b)),least_upper_bound(inverse(greatest_lower_bound(b,X_461)),inverse(greatest_lower_bound(least_upper_bound(a,c),X_461)))) )],[refute_0_5251,refute_0_5254]) ).
cnf(refute_0_5256,plain,
inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58))),
inference(subst,[],[refute_0_5255:[bind(X_461,$fot(greatest_lower_bound(Y,X_58)))]]) ).
cnf(refute_0_5257,plain,
greatest_lower_bound(Y,greatest_lower_bound(b,X_58)) = greatest_lower_bound(b,greatest_lower_bound(Y,X_58)),
inference(subst,[],[refute_0_1548:[bind(X_56,$fot(b))]]) ).
cnf(refute_0_5258,plain,
( greatest_lower_bound(Y,greatest_lower_bound(b,X_58)) != greatest_lower_bound(b,greatest_lower_bound(Y,X_58))
| greatest_lower_bound(b,greatest_lower_bound(Y,X_58)) = greatest_lower_bound(Y,greatest_lower_bound(b,X_58)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(b,X_58)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(Y,X_58))))]]) ).
cnf(refute_0_5259,plain,
greatest_lower_bound(b,greatest_lower_bound(Y,X_58)) = greatest_lower_bound(Y,greatest_lower_bound(b,X_58)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(b,X_58)),greatest_lower_bound(b,greatest_lower_bound(Y,X_58))) )],[refute_0_5257,refute_0_5258]) ).
cnf(refute_0_5260,plain,
( greatest_lower_bound(b,greatest_lower_bound(Y,X_58)) != greatest_lower_bound(Y,greatest_lower_bound(b,X_58))
| inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58)))
| inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58)))) ),[1,0],$fot(greatest_lower_bound(Y,greatest_lower_bound(b,X_58)))]]) ).
cnf(refute_0_5261,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58)))
| inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(Y,X_58)),greatest_lower_bound(Y,greatest_lower_bound(b,X_58))) )],[refute_0_5259,refute_0_5260]) ).
cnf(refute_0_5262,plain,
inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58)))) )],[refute_0_5256,refute_0_5261]) ).
cnf(refute_0_5263,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) != inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58)))
| inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58)))
| inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)),inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58)))) ),[0],$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58))))]]) ).
cnf(refute_0_5264,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)) != inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58)))
| inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58)))) )],[refute_0_5256,refute_0_5263]) ).
cnf(refute_0_5265,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(Y,X_58))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(Y,X_58),b)),inverse(greatest_lower_bound(Y,greatest_lower_bound(b,X_58)))) )],[refute_0_5262,refute_0_5264]) ).
cnf(refute_0_5266,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),
inference(subst,[],[refute_0_5265:[bind(Y,$fot(a)),bind(X_58,$fot(c))]]) ).
cnf(refute_0_5267,plain,
( inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) != inverse(greatest_lower_bound(a,c))
| inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))
| inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5268,plain,
( inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) != inverse(greatest_lower_bound(a,c))
| inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))) )],[refute_0_5266,refute_0_5267]) ).
cnf(refute_0_5269,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),inverse(greatest_lower_bound(a,c))) )],[refute_0_5244,refute_0_5268]) ).
cnf(refute_0_5270,plain,
multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b) = multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b))]]) ).
cnf(refute_0_5271,plain,
( multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b) != multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b)
| inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,c))
| multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b),multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b)) ),[1,0],$fot(inverse(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5272,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,c))
| multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b),multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b)) )],[refute_0_5270,refute_0_5271]) ).
cnf(refute_0_5273,plain,
multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b) = multiply(inverse(greatest_lower_bound(a,c)),b),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),inverse(greatest_lower_bound(a,c))) )],[refute_0_5269,refute_0_5272]) ).
cnf(refute_0_5274,plain,
inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))),
inference(subst,[],[refute_0_238:[bind(X_45,$fot(inverse(X_518))),bind(X_46,$fot(greatest_lower_bound(X_518,X_519)))]]) ).
cnf(refute_0_5275,plain,
multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)) = greatest_lower_bound(identity,multiply(inverse(X_518),X_519)),
inference(subst,[],[refute_0_4843:[bind(X_155,$fot(X_518)),bind(X_162,$fot(X_519))]]) ).
cnf(refute_0_5276,plain,
( multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)) != greatest_lower_bound(identity,multiply(inverse(X_518),X_519))
| inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_518),X_519)))]]) ).
cnf(refute_0_5277,plain,
( inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) )],[refute_0_5275,refute_0_5276]) ).
cnf(refute_0_5278,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))) )],[refute_0_5274,refute_0_5277]) ).
cnf(refute_0_5279,plain,
inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518),
inference(subst,[],[refute_0_242:[bind(X_50,$fot(X_518)),bind(X_74,$fot(greatest_lower_bound(X_518,X_519)))]]) ).
cnf(refute_0_5280,plain,
multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) = inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),
inference(subst,[],[refute_0_391:[bind(X_45,$fot(inverse(X_518))),bind(X_46,$fot(greatest_lower_bound(X_518,X_519)))]]) ).
cnf(refute_0_5281,plain,
( multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) != inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)))
| inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518)
| multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))))),bind(Y0,$fot(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518)))]]) ).
cnf(refute_0_5282,plain,
( inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518)
| multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))),inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)))) )],[refute_0_5280,refute_0_5281]) ).
cnf(refute_0_5283,plain,
multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518)) )],[refute_0_5279,refute_0_5282]) ).
cnf(refute_0_5284,plain,
( multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))) != multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) != multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518))]]) ).
cnf(refute_0_5285,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) != multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518))),multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518)) )],[refute_0_5283,refute_0_5284]) ).
cnf(refute_0_5286,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(greatest_lower_bound(X_518,X_519)),X_518),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),multiply(inverse(greatest_lower_bound(X_518,X_519)),inverse(inverse(X_518)))) )],[refute_0_5278,refute_0_5285]) ).
cnf(refute_0_5287,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) = multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b),
inference(subst,[],[refute_0_5286:[bind(X_518,$fot(b)),bind(X_519,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5288,plain,
( multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b) != multiply(inverse(greatest_lower_bound(a,c)),b)
| inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) != multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b)
| inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(a,c)),b)))]]) ).
cnf(refute_0_5289,plain,
( multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b) != multiply(inverse(greatest_lower_bound(a,c)),b)
| inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))),multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b)) )],[refute_0_5287,refute_0_5288]) ).
cnf(refute_0_5290,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) = multiply(inverse(greatest_lower_bound(a,c)),b),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),b),multiply(inverse(greatest_lower_bound(a,c)),b)) )],[refute_0_5273,refute_0_5289]) ).
cnf(refute_0_5291,plain,
( multiply(inverse(c),least_upper_bound(a,c)) != inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))
| inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))) != multiply(inverse(greatest_lower_bound(a,c)),b)
| multiply(inverse(c),least_upper_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(c),least_upper_bound(a,c)),multiply(inverse(greatest_lower_bound(a,c)),b)) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_5292,plain,
( multiply(inverse(c),least_upper_bound(a,c)) != inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))
| multiply(inverse(c),least_upper_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))),multiply(inverse(greatest_lower_bound(a,c)),b)) )],[refute_0_5290,refute_0_5291]) ).
cnf(refute_0_5293,plain,
( multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)) != inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))
| multiply(inverse(c),least_upper_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))) )],[refute_0_5232,refute_0_5292]) ).
cnf(refute_0_5294,plain,
multiply(inverse(c),least_upper_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,c)),b),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(inverse(inverse(least_upper_bound(a,c))),c)),inverse(greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))))) )],[refute_0_5098,refute_0_5293]) ).
cnf(refute_0_5295,plain,
( multiply(inverse(c),least_upper_bound(a,c)) != multiply(inverse(greatest_lower_bound(a,c)),b)
| multiply(inverse(greatest_lower_bound(a,c)),b) = multiply(inverse(c),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(c),least_upper_bound(a,c)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(a,c)),b)))]]) ).
cnf(refute_0_5296,plain,
multiply(inverse(greatest_lower_bound(a,c)),b) = multiply(inverse(c),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(c),least_upper_bound(a,c)),multiply(inverse(greatest_lower_bound(a,c)),b)) )],[refute_0_5294,refute_0_5295]) ).
cnf(refute_0_5297,plain,
( multiply(inverse(greatest_lower_bound(a,c)),b) != multiply(inverse(c),least_upper_bound(a,c))
| inverse(b) != multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))
| inverse(b) = multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) ),[1,0,0,1],$fot(multiply(inverse(c),least_upper_bound(a,c)))]]) ).
cnf(refute_0_5298,plain,
( inverse(b) != multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))
| inverse(b) = multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),b),multiply(inverse(c),least_upper_bound(a,c))) )],[refute_0_5296,refute_0_5297]) ).
cnf(refute_0_5299,plain,
inverse(b) = multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),b))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) )],[refute_0_4786,refute_0_5298]) ).
cnf(refute_0_5300,plain,
multiply(inverse(a),identity) = inverse(a),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(a)))]]) ).
cnf(refute_0_5301,plain,
multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))) = identity,
inference(subst,[],[refute_0_28:[bind(X_50,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5302,plain,
multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_5303,plain,
( multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))) != identity
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = multiply(inverse(a),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_5304,plain,
( multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))) != identity
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = multiply(inverse(a),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_5302,refute_0_5303]) ).
cnf(refute_0_5305,plain,
multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = multiply(inverse(a),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))),identity) )],[refute_0_5301,refute_0_5304]) ).
cnf(refute_0_5306,plain,
( multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != multiply(inverse(a),identity)
| multiply(inverse(a),identity) != inverse(a)
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = inverse(a) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(inverse(a),identity))),bind(Z0,$fot(inverse(a)))]]) ).
cnf(refute_0_5307,plain,
( multiply(inverse(a),identity) != inverse(a)
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),multiply(inverse(a),identity)) )],[refute_0_5305,refute_0_5306]) ).
cnf(refute_0_5308,plain,
multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = inverse(a),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),inverse(a)) )],[refute_0_5300,refute_0_5307]) ).
cnf(refute_0_5309,plain,
multiply(multiply(inverse(least_upper_bound(a,c)),c),Z) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(least_upper_bound(a,c)))),bind(Y,$fot(c))]]) ).
cnf(refute_0_5310,plain,
( multiply(multiply(inverse(least_upper_bound(a,c)),c),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(least_upper_bound(a,c)),c) != multiply(inverse(b),greatest_lower_bound(a,c))
| multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(a,c)),c),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) ),[0,0],$fot(multiply(inverse(b),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5311,plain,
( multiply(multiply(inverse(least_upper_bound(a,c)),c),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),c),multiply(inverse(b),greatest_lower_bound(a,c))) )],[refute_0_5095,refute_0_5310]) ).
cnf(refute_0_5312,plain,
multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(a,c)),c),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5309,refute_0_5311]) ).
cnf(refute_0_5313,plain,
multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z) = multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(b))),bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5314,plain,
( multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z) != multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))
| multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) ),[0],$fot(multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)))]]) ).
cnf(refute_0_5315,plain,
( multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z),multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))) )],[refute_0_5313,refute_0_5314]) ).
cnf(refute_0_5316,plain,
multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b),greatest_lower_bound(a,c)),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5312,refute_0_5315]) ).
cnf(refute_0_5317,plain,
inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(least_upper_bound(a,c)),c),
inference(subst,[],[refute_0_4866:[bind(X_85,$fot(a)),bind(X_86,$fot(c))]]) ).
cnf(refute_0_5318,plain,
( multiply(inverse(least_upper_bound(a,c)),c) != multiply(inverse(b),greatest_lower_bound(a,c))
| inverse(least_upper_bound(identity,multiply(inverse(c),a))) != multiply(inverse(least_upper_bound(a,c)),c)
| inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(b),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),a))),multiply(inverse(least_upper_bound(a,c)),c)) ),[1],$fot(multiply(inverse(b),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5319,plain,
( inverse(least_upper_bound(identity,multiply(inverse(c),a))) != multiply(inverse(least_upper_bound(a,c)),c)
| inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(b),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),c),multiply(inverse(b),greatest_lower_bound(a,c))) )],[refute_0_5095,refute_0_5318]) ).
cnf(refute_0_5320,plain,
inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(b),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),a))),multiply(inverse(least_upper_bound(a,c)),c)) )],[refute_0_5317,refute_0_5319]) ).
cnf(refute_0_5321,plain,
multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)) = greatest_lower_bound(identity,multiply(inverse(X_155),X_154)),
inference(subst,[],[refute_0_4843:[bind(X_162,$fot(X_154))]]) ).
cnf(refute_0_5322,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)) != greatest_lower_bound(identity,multiply(inverse(X_155),X_154))
| greatest_lower_bound(identity,multiply(inverse(X_155),X_154)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_155),X_154))))]]) ).
cnf(refute_0_5323,plain,
greatest_lower_bound(identity,multiply(inverse(X_155),X_154)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)),greatest_lower_bound(identity,multiply(inverse(X_155),X_154))) )],[refute_0_5321,refute_0_5322]) ).
cnf(refute_0_5324,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(identity,multiply(inverse(X_155),X_154))
| greatest_lower_bound(identity,multiply(inverse(X_155),X_154)) != multiply(inverse(X_155),greatest_lower_bound(X_155,X_154))
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)),multiply(inverse(X_155),greatest_lower_bound(X_155,X_154))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)))]]) ).
cnf(refute_0_5325,plain,
( multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) != greatest_lower_bound(identity,multiply(inverse(X_155),X_154))
| multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_155),X_154)),multiply(inverse(X_155),greatest_lower_bound(X_155,X_154))) )],[refute_0_5323,refute_0_5324]) ).
cnf(refute_0_5326,plain,
multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)) = multiply(inverse(X_155),greatest_lower_bound(X_155,X_154)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_155),greatest_lower_bound(X_154,X_155)),greatest_lower_bound(identity,multiply(inverse(X_155),X_154))) )],[refute_0_110,refute_0_5325]) ).
cnf(refute_0_5327,plain,
multiply(inverse(a),greatest_lower_bound(c,a)) = multiply(inverse(a),greatest_lower_bound(a,c)),
inference(subst,[],[refute_0_5326:[bind(X_154,$fot(c)),bind(X_155,$fot(a))]]) ).
cnf(refute_0_5328,plain,
multiply(inverse(multiply(inverse(X_518),X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)),
inference(subst,[],[refute_0_110:[bind(X_154,$fot(identity)),bind(X_155,$fot(multiply(inverse(X_518),X_519)))]]) ).
cnf(refute_0_5329,plain,
( multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)) != greatest_lower_bound(identity,multiply(inverse(X_518),X_519))
| greatest_lower_bound(identity,multiply(inverse(X_518),X_519)) = multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))))]]) ).
cnf(refute_0_5330,plain,
greatest_lower_bound(identity,multiply(inverse(X_518),X_519)) = multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) )],[refute_0_5275,refute_0_5329]) ).
cnf(refute_0_5331,plain,
( multiply(inverse(multiply(inverse(X_518),X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))
| greatest_lower_bound(identity,multiply(inverse(X_518),X_519)) != multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))
| multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_518),X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))) ),[0,1],$fot(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)))]]) ).
cnf(refute_0_5332,plain,
( multiply(inverse(multiply(inverse(X_518),X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))
| multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) )],[refute_0_5330,refute_0_5331]) ).
cnf(refute_0_5333,plain,
multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_518),X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))) )],[refute_0_5328,refute_0_5332]) ).
cnf(refute_0_5334,plain,
multiply(X_518,multiply(inverse(X_518),X_519)) = X_519,
inference(subst,[],[refute_0_3743:[bind(X_46,$fot(X_519)),bind(X_50,$fot(X_518))]]) ).
cnf(refute_0_5335,plain,
inverse(multiply(X_518,multiply(inverse(X_518),X_519))) = inverse(multiply(X_518,multiply(inverse(X_518),X_519))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_518,multiply(inverse(X_518),X_519))))]]) ).
cnf(refute_0_5336,plain,
( multiply(X_518,multiply(inverse(X_518),X_519)) != X_519
| inverse(multiply(X_518,multiply(inverse(X_518),X_519))) != inverse(multiply(X_518,multiply(inverse(X_518),X_519)))
| inverse(multiply(X_518,multiply(inverse(X_518),X_519))) = inverse(X_519) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),inverse(multiply(X_518,multiply(inverse(X_518),X_519)))) ),[1,0],$fot(X_519)]]) ).
cnf(refute_0_5337,plain,
( multiply(X_518,multiply(inverse(X_518),X_519)) != X_519
| inverse(multiply(X_518,multiply(inverse(X_518),X_519))) = inverse(X_519) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),inverse(multiply(X_518,multiply(inverse(X_518),X_519)))) )],[refute_0_5335,refute_0_5336]) ).
cnf(refute_0_5338,plain,
inverse(multiply(X_518,multiply(inverse(X_518),X_519))) = inverse(X_519),
inference(resolve,[$cnf( $equal(multiply(X_518,multiply(inverse(X_518),X_519)),X_519) )],[refute_0_5334,refute_0_5337]) ).
cnf(refute_0_5339,plain,
multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)) = multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)))]]) ).
cnf(refute_0_5340,plain,
( multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)) != multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519))
| inverse(multiply(X_518,multiply(inverse(X_518),X_519))) != inverse(X_519)
| multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)),multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519))) ),[1,0],$fot(inverse(X_519))]]) ).
cnf(refute_0_5341,plain,
( inverse(multiply(X_518,multiply(inverse(X_518),X_519))) != inverse(X_519)
| multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)),multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519))) )],[refute_0_5339,refute_0_5340]) ).
cnf(refute_0_5342,plain,
multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),inverse(X_519)) )],[refute_0_5338,refute_0_5341]) ).
cnf(refute_0_5343,plain,
multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)),
inference(subst,[],[refute_0_3761:[bind(Z,$fot(greatest_lower_bound(X_518,X_519))),bind(X_73,$fot(X_518)),bind(X_74,$fot(multiply(inverse(X_518),X_519)))]]) ).
cnf(refute_0_5344,plain,
( multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)) != multiply(inverse(X_519),greatest_lower_bound(X_518,X_519))
| multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519))
| multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))))),bind(Y0,$fot(multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)))),bind(Z0,$fot(multiply(inverse(X_519),greatest_lower_bound(X_518,X_519))))]]) ).
cnf(refute_0_5345,plain,
( multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)) != multiply(inverse(X_519),greatest_lower_bound(X_518,X_519))
| multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519))) )],[refute_0_5343,refute_0_5344]) ).
cnf(refute_0_5346,plain,
multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_518,multiply(inverse(X_518),X_519))),greatest_lower_bound(X_518,X_519)),multiply(inverse(X_519),greatest_lower_bound(X_518,X_519))) )],[refute_0_5342,refute_0_5345]) ).
cnf(refute_0_5347,plain,
( multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != multiply(inverse(X_519),greatest_lower_bound(X_518,X_519))
| multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))
| multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))) ),[0],$fot(multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)))]]) ).
cnf(refute_0_5348,plain,
( multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))
| multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),multiply(inverse(X_519),greatest_lower_bound(X_518,X_519))) )],[refute_0_5346,refute_0_5347]) ).
cnf(refute_0_5349,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))))]]) ).
cnf(refute_0_5350,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity),
inference(subst,[],[refute_0_5083:[bind(X_472,$fot(identity)),bind(X_473,$fot(multiply(inverse(X_518),X_519)))]]) ).
cnf(refute_0_5351,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity) != inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity)
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))))]]) ).
cnf(refute_0_5352,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity) != inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)),multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity)) )],[refute_0_5350,refute_0_5351]) ).
cnf(refute_0_5353,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),identity),inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))) )],[refute_0_5349,refute_0_5352]) ).
cnf(refute_0_5354,plain,
( multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)) != inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))
| multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)),inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)))]]) ).
cnf(refute_0_5355,plain,
( multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))
| multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity)),inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))) )],[refute_0_5353,refute_0_5354]) ).
cnf(refute_0_5356,plain,
( multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))
| multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))) )],[refute_0_5348,refute_0_5355]) ).
cnf(refute_0_5357,plain,
multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) = inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_518),X_519)),multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_518),X_519)),identity))) )],[refute_0_5333,refute_0_5356]) ).
cnf(refute_0_5358,plain,
( multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) != inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))
| inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))))]]) ).
cnf(refute_0_5359,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519))) = multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_519),greatest_lower_bound(X_518,X_519)),inverse(least_upper_bound(identity,multiply(inverse(X_518),X_519)))) )],[refute_0_5357,refute_0_5358]) ).
cnf(refute_0_5360,plain,
inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(a),greatest_lower_bound(c,a)),
inference(subst,[],[refute_0_5359:[bind(X_518,$fot(c)),bind(X_519,$fot(a))]]) ).
cnf(refute_0_5361,plain,
( multiply(inverse(a),greatest_lower_bound(c,a)) != multiply(inverse(a),greatest_lower_bound(a,c))
| inverse(least_upper_bound(identity,multiply(inverse(c),a))) != multiply(inverse(a),greatest_lower_bound(c,a))
| inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(a),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(c),a))))),bind(Y0,$fot(multiply(inverse(a),greatest_lower_bound(c,a)))),bind(Z0,$fot(multiply(inverse(a),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5362,plain,
( multiply(inverse(a),greatest_lower_bound(c,a)) != multiply(inverse(a),greatest_lower_bound(a,c))
| inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(a),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),a))),multiply(inverse(a),greatest_lower_bound(c,a))) )],[refute_0_5360,refute_0_5361]) ).
cnf(refute_0_5363,plain,
inverse(least_upper_bound(identity,multiply(inverse(c),a))) = multiply(inverse(a),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(c,a)),multiply(inverse(a),greatest_lower_bound(a,c))) )],[refute_0_5327,refute_0_5362]) ).
cnf(refute_0_5364,plain,
( inverse(least_upper_bound(identity,multiply(inverse(c),a))) != multiply(inverse(a),greatest_lower_bound(a,c))
| inverse(least_upper_bound(identity,multiply(inverse(c),a))) != multiply(inverse(b),greatest_lower_bound(a,c))
| multiply(inverse(a),greatest_lower_bound(a,c)) = multiply(inverse(b),greatest_lower_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),a))),multiply(inverse(b),greatest_lower_bound(a,c))) ),[0],$fot(multiply(inverse(a),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5365,plain,
( inverse(least_upper_bound(identity,multiply(inverse(c),a))) != multiply(inverse(b),greatest_lower_bound(a,c))
| multiply(inverse(a),greatest_lower_bound(a,c)) = multiply(inverse(b),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),a))),multiply(inverse(a),greatest_lower_bound(a,c))) )],[refute_0_5363,refute_0_5364]) ).
cnf(refute_0_5366,plain,
multiply(inverse(a),greatest_lower_bound(a,c)) = multiply(inverse(b),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(c),a))),multiply(inverse(b),greatest_lower_bound(a,c))) )],[refute_0_5320,refute_0_5365]) ).
cnf(refute_0_5367,plain,
( multiply(inverse(a),greatest_lower_bound(a,c)) != multiply(inverse(b),greatest_lower_bound(a,c))
| multiply(inverse(b),greatest_lower_bound(a,c)) = multiply(inverse(a),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(a),greatest_lower_bound(a,c)))),bind(Y0,$fot(multiply(inverse(b),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5368,plain,
multiply(inverse(b),greatest_lower_bound(a,c)) = multiply(inverse(a),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,c)),multiply(inverse(b),greatest_lower_bound(a,c))) )],[refute_0_5366,refute_0_5367]) ).
cnf(refute_0_5369,plain,
( multiply(inverse(b),greatest_lower_bound(a,c)) != multiply(inverse(a),greatest_lower_bound(a,c))
| multiply(inverse(b),greatest_lower_bound(a,c)) != multiply(inverse(least_upper_bound(a,c)),c)
| multiply(inverse(a),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,c)),multiply(inverse(least_upper_bound(a,c)),c)) ),[0],$fot(multiply(inverse(a),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5370,plain,
( multiply(inverse(b),greatest_lower_bound(a,c)) != multiply(inverse(least_upper_bound(a,c)),c)
| multiply(inverse(a),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,c)),multiply(inverse(a),greatest_lower_bound(a,c))) )],[refute_0_5368,refute_0_5369]) ).
cnf(refute_0_5371,plain,
multiply(inverse(a),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),c),
inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,c)),multiply(inverse(least_upper_bound(a,c)),c)) )],[refute_0_5093,refute_0_5370]) ).
cnf(refute_0_5372,plain,
( multiply(inverse(a),greatest_lower_bound(a,c)) != multiply(inverse(least_upper_bound(a,c)),c)
| multiply(inverse(least_upper_bound(a,c)),c) = multiply(inverse(a),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(a),greatest_lower_bound(a,c)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),c)))]]) ).
cnf(refute_0_5373,plain,
multiply(inverse(least_upper_bound(a,c)),c) = multiply(inverse(a),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),greatest_lower_bound(a,c)),multiply(inverse(least_upper_bound(a,c)),c)) )],[refute_0_5371,refute_0_5372]) ).
cnf(refute_0_5374,plain,
( multiply(multiply(inverse(least_upper_bound(a,c)),c),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(least_upper_bound(a,c)),c) != multiply(inverse(a),greatest_lower_bound(a,c))
| multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(a,c)),c),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) ),[0,0],$fot(multiply(inverse(a),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5375,plain,
( multiply(multiply(inverse(least_upper_bound(a,c)),c),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),c),multiply(inverse(a),greatest_lower_bound(a,c))) )],[refute_0_5373,refute_0_5374]) ).
cnf(refute_0_5376,plain,
multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(a,c)),c),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5309,refute_0_5375]) ).
cnf(refute_0_5377,plain,
multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) = multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(a))),bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5378,plain,
( multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) != multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z))
| multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) ),[0],$fot(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)))]]) ).
cnf(refute_0_5379,plain,
( multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z),multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z))) )],[refute_0_5377,refute_0_5378]) ).
cnf(refute_0_5380,plain,
( multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) = multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))))]]) ).
cnf(refute_0_5381,plain,
multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) = multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5316,refute_0_5380]) ).
cnf(refute_0_5382,plain,
( multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) != multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))) ),[0],$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)))]]) ).
cnf(refute_0_5383,plain,
( multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)),multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))) )],[refute_0_5381,refute_0_5382]) ).
cnf(refute_0_5384,plain,
( multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5379,refute_0_5383]) ).
cnf(refute_0_5385,plain,
multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(a),greatest_lower_bound(a,c)),Z),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5376,refute_0_5384]) ).
cnf(refute_0_5386,plain,
( multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))
| multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)))),bind(Y0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))))]]) ).
cnf(refute_0_5387,plain,
multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z))) )],[refute_0_5385,refute_0_5386]) ).
cnf(refute_0_5388,plain,
( multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z))
| multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) ),[0],$fot(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)))]]) ).
cnf(refute_0_5389,plain,
( multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z))) )],[refute_0_5387,refute_0_5388]) ).
cnf(refute_0_5390,plain,
multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) = multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5316,refute_0_5389]) ).
cnf(refute_0_5391,plain,
( multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) != multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))
| multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) = multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))))]]) ).
cnf(refute_0_5392,plain,
multiply(inverse(least_upper_bound(a,c)),multiply(c,Z)) = multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),Z)),multiply(inverse(least_upper_bound(a,c)),multiply(c,Z))) )],[refute_0_5390,refute_0_5391]) ).
cnf(refute_0_5393,plain,
multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_5392:[bind(Z,$fot(inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5394,plain,
( multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != inverse(a)
| multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
| multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(a) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(a)))]]) ).
cnf(refute_0_5395,plain,
( multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != inverse(a)
| multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_5393,refute_0_5394]) ).
cnf(refute_0_5396,plain,
multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(a),
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),inverse(a)) )],[refute_0_5308,refute_0_5395]) ).
cnf(refute_0_5397,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))),
inference(subst,[],[refute_0_4154:[bind(X_59,$fot(greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))]]) ).
cnf(refute_0_5398,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) = greatest_lower_bound(X_78,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33)))),
inference(subst,[],[refute_0_1521:[bind(X,$fot(least_upper_bound(a,least_upper_bound(c,X_33)))),bind(X_56,$fot(X_78)),bind(X_57,$fot(b))]]) ).
cnf(refute_0_5399,plain,
( greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))) != b
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) != greatest_lower_bound(X_78,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) = greatest_lower_bound(X_78,b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)),greatest_lower_bound(X_78,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_5400,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) != greatest_lower_bound(X_78,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) = greatest_lower_bound(X_78,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))),b) )],[refute_0_139,refute_0_5399]) ).
cnf(refute_0_5401,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) = greatest_lower_bound(X_78,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)),greatest_lower_bound(X_78,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_33))))) )],[refute_0_5398,refute_0_5400]) ).
cnf(refute_0_5402,plain,
greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) = greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))),
inference(subst,[],[refute_0_1648:[bind(Y,$fot(least_upper_bound(a,least_upper_bound(c,X_33)))),bind(X_77,$fot(b))]]) ).
cnf(refute_0_5403,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) != greatest_lower_bound(X_78,b)
| greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) != greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))
| greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) = greatest_lower_bound(X_78,b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)),greatest_lower_bound(X_78,b)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))]]) ).
cnf(refute_0_5404,plain,
( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)) != greatest_lower_bound(X_78,b)
| greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) = greatest_lower_bound(X_78,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)),greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) )],[refute_0_5402,refute_0_5403]) ).
cnf(refute_0_5405,plain,
greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) = greatest_lower_bound(X_78,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_33)),greatest_lower_bound(X_78,b)),greatest_lower_bound(X_78,b)) )],[refute_0_5401,refute_0_5404]) ).
cnf(refute_0_5406,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) != greatest_lower_bound(X_78,b)
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))) ),[1,0,0],$fot(greatest_lower_bound(X_78,b))]]) ).
cnf(refute_0_5407,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))),greatest_lower_bound(X_78,b)) )],[refute_0_5405,refute_0_5406]) ).
cnf(refute_0_5408,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),least_upper_bound(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))) )],[refute_0_5397,refute_0_5407]) ).
cnf(refute_0_5409,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))]]) ).
cnf(refute_0_5410,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) != greatest_lower_bound(X_78,b)
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(X_78,b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) ),[1,0],$fot(greatest_lower_bound(X_78,b))]]) ).
cnf(refute_0_5411,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) != greatest_lower_bound(X_78,b)
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(X_78,b)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) )],[refute_0_5409,refute_0_5410]) ).
cnf(refute_0_5412,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(X_78,b)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))),greatest_lower_bound(X_78,b)) )],[refute_0_5405,refute_0_5411]) ).
cnf(refute_0_5413,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != inverse(greatest_lower_bound(X_78,b))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| inverse(greatest_lower_bound(X_78,b)) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))) ),[0],$fot(inverse(greatest_lower_bound(X_78,b)))]]) ).
cnf(refute_0_5414,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| inverse(greatest_lower_bound(X_78,b)) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(X_78,b))) )],[refute_0_5412,refute_0_5413]) ).
cnf(refute_0_5415,plain,
greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) = greatest_lower_bound(X_78,least_upper_bound(a,c)),
inference(subst,[],[refute_0_1666:[bind(X_290,$fot(X_33)),bind(X_291,$fot(a)),bind(X_292,$fot(c)),bind(X_56,$fot(X_78))]]) ).
cnf(refute_0_5416,plain,
inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))]]) ).
cnf(refute_0_5417,plain,
( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) != greatest_lower_bound(X_78,least_upper_bound(a,c))
| inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))
| inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) ),[1,0],$fot(greatest_lower_bound(X_78,least_upper_bound(a,c)))]]) ).
cnf(refute_0_5418,plain,
( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))) != greatest_lower_bound(X_78,least_upper_bound(a,c))
| inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) )],[refute_0_5416,refute_0_5417]) ).
cnf(refute_0_5419,plain,
inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) = inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))),greatest_lower_bound(X_78,least_upper_bound(a,c))) )],[refute_0_5415,refute_0_5418]) ).
cnf(refute_0_5420,plain,
least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))))]]) ).
cnf(refute_0_5421,plain,
( inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))))]]) ).
cnf(refute_0_5422,plain,
( inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))) )],[refute_0_5420,refute_0_5421]) ).
cnf(refute_0_5423,plain,
least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) )],[refute_0_5419,refute_0_5422]) ).
cnf(refute_0_5424,plain,
( inverse(greatest_lower_bound(X_78,b)) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))))
| inverse(greatest_lower_bound(X_78,b)) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_78,b)),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))))]]) ).
cnf(refute_0_5425,plain,
( inverse(greatest_lower_bound(X_78,b)) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| inverse(greatest_lower_bound(X_78,b)) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33)))))),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))))) )],[refute_0_5423,refute_0_5424]) ).
cnf(refute_0_5426,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))
| inverse(greatest_lower_bound(X_78,b)) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_78,b)),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))) )],[refute_0_5414,refute_0_5425]) ).
cnf(refute_0_5427,plain,
inverse(greatest_lower_bound(X_78,b)) = least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_78,least_upper_bound(a,least_upper_bound(c,X_33))))))) )],[refute_0_5408,refute_0_5426]) ).
cnf(refute_0_5428,plain,
greatest_lower_bound(X_78,X_78) = X_78,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_78))]]) ).
cnf(refute_0_5429,plain,
greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)) = greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)))]]) ).
cnf(refute_0_5430,plain,
( greatest_lower_bound(X_78,X_78) != X_78
| greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)) != greatest_lower_bound(b,greatest_lower_bound(X_78,X_78))
| greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)) = greatest_lower_bound(b,X_78) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)),greatest_lower_bound(b,greatest_lower_bound(X_78,X_78))) ),[1,1],$fot(X_78)]]) ).
cnf(refute_0_5431,plain,
( greatest_lower_bound(X_78,X_78) != X_78
| greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)) = greatest_lower_bound(b,X_78) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)),greatest_lower_bound(b,greatest_lower_bound(X_78,X_78))) )],[refute_0_5429,refute_0_5430]) ).
cnf(refute_0_5432,plain,
greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)) = greatest_lower_bound(b,X_78),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_78,X_78),X_78) )],[refute_0_5428,refute_0_5431]) ).
cnf(refute_0_5433,plain,
greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))) = greatest_lower_bound(b,greatest_lower_bound(X,Y)),
inference(subst,[],[refute_0_1571:[bind(X_59,$fot(greatest_lower_bound(X,Y)))]]) ).
cnf(refute_0_5434,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c)),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5435,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))
| greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c)) = greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c))))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))))]]) ).
cnf(refute_0_5436,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c)) = greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))) )],[refute_0_5434,refute_0_5435]) ).
cnf(refute_0_5437,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))) != greatest_lower_bound(b,greatest_lower_bound(X,Y))
| greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c)) != greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c)))
| greatest_lower_bound(b,greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c)))) = greatest_lower_bound(b,greatest_lower_bound(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))),greatest_lower_bound(b,greatest_lower_bound(X,Y))) ),[0,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c))))]]) ).
cnf(refute_0_5438,plain,
( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))) != greatest_lower_bound(b,greatest_lower_bound(X,Y))
| greatest_lower_bound(b,greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c)))) = greatest_lower_bound(b,greatest_lower_bound(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c)),greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c)))) )],[refute_0_5436,refute_0_5437]) ).
cnf(refute_0_5439,plain,
greatest_lower_bound(b,greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(a,c)))) = greatest_lower_bound(b,greatest_lower_bound(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X,Y),least_upper_bound(a,c))),greatest_lower_bound(b,greatest_lower_bound(X,Y))) )],[refute_0_5433,refute_0_5438]) ).
cnf(refute_0_5440,plain,
greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))) = greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)),
inference(subst,[],[refute_0_5439:[bind(X,$fot(X_78)),bind(Y,$fot(X_78))]]) ).
cnf(refute_0_5441,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)) != greatest_lower_bound(b,X_78)
| greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))) != greatest_lower_bound(b,greatest_lower_bound(X_78,X_78))
| greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))) = greatest_lower_bound(b,X_78) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)))),bind(Z0,$fot(greatest_lower_bound(b,X_78)))]]) ).
cnf(refute_0_5442,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)) != greatest_lower_bound(b,X_78)
| greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))) = greatest_lower_bound(b,X_78) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))),greatest_lower_bound(b,greatest_lower_bound(X_78,X_78))) )],[refute_0_5440,refute_0_5441]) ).
cnf(refute_0_5443,plain,
greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))) = greatest_lower_bound(b,X_78),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_78,X_78)),greatest_lower_bound(b,X_78)) )],[refute_0_5432,refute_0_5442]) ).
cnf(refute_0_5444,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_5445,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))) != greatest_lower_bound(b,X_78)
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,X_78)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))) ),[1,0],$fot(greatest_lower_bound(b,X_78))]]) ).
cnf(refute_0_5446,plain,
( greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))) != greatest_lower_bound(b,X_78)
| inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,X_78)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))) )],[refute_0_5444,refute_0_5445]) ).
cnf(refute_0_5447,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) = inverse(greatest_lower_bound(b,X_78)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))),greatest_lower_bound(b,X_78)) )],[refute_0_5443,refute_0_5446]) ).
cnf(refute_0_5448,plain,
inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))),
inference(subst,[],[refute_0_4167:[bind(Y,$fot(greatest_lower_bound(X_78,least_upper_bound(a,c)))),bind(X_111,$fot(X_78))]]) ).
cnf(refute_0_5449,plain,
inverse(greatest_lower_bound(greatest_lower_bound(X,Y),b)) = inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y))),
inference(subst,[],[refute_0_5255:[bind(X_461,$fot(greatest_lower_bound(X,Y)))]]) ).
cnf(refute_0_5450,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,b)) = greatest_lower_bound(greatest_lower_bound(X,Y),b),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(b))]]) ).
cnf(refute_0_5451,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,b)) != greatest_lower_bound(greatest_lower_bound(X,Y),b)
| greatest_lower_bound(greatest_lower_bound(X,Y),b) = greatest_lower_bound(X,greatest_lower_bound(Y,b)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,b)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),b)))]]) ).
cnf(refute_0_5452,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),b) = greatest_lower_bound(X,greatest_lower_bound(Y,b)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,b)),greatest_lower_bound(greatest_lower_bound(X,Y),b)) )],[refute_0_5450,refute_0_5451]) ).
cnf(refute_0_5453,plain,
( greatest_lower_bound(greatest_lower_bound(X,Y),b) != greatest_lower_bound(X,greatest_lower_bound(Y,b))
| inverse(greatest_lower_bound(greatest_lower_bound(X,Y),b)) != inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y)))
| inverse(greatest_lower_bound(X,greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X,Y),b)),inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y)))) ),[0,0],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,b)))]]) ).
cnf(refute_0_5454,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(X,Y),b)) != inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y)))
| inverse(greatest_lower_bound(X,greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),b),greatest_lower_bound(X,greatest_lower_bound(Y,b))) )],[refute_0_5452,refute_0_5453]) ).
cnf(refute_0_5455,plain,
inverse(greatest_lower_bound(X,greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X,Y),b)),inverse(greatest_lower_bound(b,greatest_lower_bound(X,Y)))) )],[refute_0_5449,refute_0_5454]) ).
cnf(refute_0_5456,plain,
inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78))),
inference(subst,[],[refute_0_5455:[bind(X,$fot(greatest_lower_bound(X_78,least_upper_bound(a,c)))),bind(Y,$fot(X_78))]]) ).
cnf(refute_0_5457,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78)))
| inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))))),bind(Y0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_5458,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))
| inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))),inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78)))) )],[refute_0_5456,refute_0_5457]) ).
cnf(refute_0_5459,plain,
inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),X_78))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))) )],[refute_0_5448,refute_0_5458]) ).
cnf(refute_0_5460,plain,
inverse(greatest_lower_bound(X_518,X_519)) = multiply(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),inverse(X_518)),
inference(subst,[],[refute_0_234:[bind(X_68,$fot(inverse(X_518))),bind(X_69,$fot(greatest_lower_bound(X_518,X_519)))]]) ).
cnf(refute_0_5461,plain,
( multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)) != greatest_lower_bound(identity,multiply(inverse(X_518),X_519))
| inverse(greatest_lower_bound(X_518,X_519)) != multiply(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),inverse(X_518))
| inverse(greatest_lower_bound(X_518,X_519)) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_518,X_519)),multiply(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),inverse(X_518))) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_518),X_519)))]]) ).
cnf(refute_0_5462,plain,
( inverse(greatest_lower_bound(X_518,X_519)) != multiply(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),inverse(X_518))
| inverse(greatest_lower_bound(X_518,X_519)) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519)),greatest_lower_bound(identity,multiply(inverse(X_518),X_519))) )],[refute_0_5275,refute_0_5461]) ).
cnf(refute_0_5463,plain,
inverse(greatest_lower_bound(X_518,X_519)) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_518,X_519)),multiply(inverse(multiply(inverse(X_518),greatest_lower_bound(X_518,X_519))),inverse(X_518))) )],[refute_0_5460,refute_0_5462]) ).
cnf(refute_0_5464,plain,
inverse(greatest_lower_bound(X_159,inverse(X_68))) = multiply(inverse(multiply(X_68,greatest_lower_bound(X_159,inverse(X_68)))),X_68),
inference(subst,[],[refute_0_234:[bind(X_69,$fot(greatest_lower_bound(X_159,inverse(X_68))))]]) ).
cnf(refute_0_5465,plain,
multiply(X_68,greatest_lower_bound(X_159,inverse(X_68))) = greatest_lower_bound(identity,multiply(X_68,X_159)),
inference(subst,[],[refute_0_1857:[bind(X_153,$fot(X_68)),bind(X_154,$fot(X_159))]]) ).
cnf(refute_0_5466,plain,
( multiply(X_68,greatest_lower_bound(X_159,inverse(X_68))) != greatest_lower_bound(identity,multiply(X_68,X_159))
| inverse(greatest_lower_bound(X_159,inverse(X_68))) != multiply(inverse(multiply(X_68,greatest_lower_bound(X_159,inverse(X_68)))),X_68)
| inverse(greatest_lower_bound(X_159,inverse(X_68))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_159,inverse(X_68))),multiply(inverse(multiply(X_68,greatest_lower_bound(X_159,inverse(X_68)))),X_68)) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_68,X_159)))]]) ).
cnf(refute_0_5467,plain,
( inverse(greatest_lower_bound(X_159,inverse(X_68))) != multiply(inverse(multiply(X_68,greatest_lower_bound(X_159,inverse(X_68)))),X_68)
| inverse(greatest_lower_bound(X_159,inverse(X_68))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68) ),
inference(resolve,[$cnf( $equal(multiply(X_68,greatest_lower_bound(X_159,inverse(X_68))),greatest_lower_bound(identity,multiply(X_68,X_159))) )],[refute_0_5465,refute_0_5466]) ).
cnf(refute_0_5468,plain,
inverse(greatest_lower_bound(X_159,inverse(X_68))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_159,inverse(X_68))),multiply(inverse(multiply(X_68,greatest_lower_bound(X_159,inverse(X_68)))),X_68)) )],[refute_0_5464,refute_0_5467]) ).
cnf(refute_0_5469,plain,
inverse(greatest_lower_bound(X_159,inverse(X_68))) = least_upper_bound(inverse(X_159),X_68),
inference(subst,[],[refute_0_4651:[bind(X_474,$fot(X_159)),bind(X_475,$fot(X_68))]]) ).
cnf(refute_0_5470,plain,
( inverse(greatest_lower_bound(X_159,inverse(X_68))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68)
| inverse(greatest_lower_bound(X_159,inverse(X_68))) != least_upper_bound(inverse(X_159),X_68)
| least_upper_bound(inverse(X_159),X_68) = multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_159,inverse(X_68))),multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68)) ),[0],$fot(least_upper_bound(inverse(X_159),X_68))]]) ).
cnf(refute_0_5471,plain,
( inverse(greatest_lower_bound(X_159,inverse(X_68))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68)
| least_upper_bound(inverse(X_159),X_68) = multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_159,inverse(X_68))),least_upper_bound(inverse(X_159),X_68)) )],[refute_0_5469,refute_0_5470]) ).
cnf(refute_0_5472,plain,
least_upper_bound(inverse(X_159),X_68) = multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_159,inverse(X_68))),multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68)) )],[refute_0_5468,refute_0_5471]) ).
cnf(refute_0_5473,plain,
( least_upper_bound(inverse(X_159),X_68) != multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68)
| multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68) = least_upper_bound(inverse(X_159),X_68) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(inverse(X_159),X_68))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68)))]]) ).
cnf(refute_0_5474,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68) = least_upper_bound(inverse(X_159),X_68),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_159),X_68),multiply(inverse(greatest_lower_bound(identity,multiply(X_68,X_159))),X_68)) )],[refute_0_5472,refute_0_5473]) ).
cnf(refute_0_5475,plain,
multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518)) = least_upper_bound(inverse(X_519),inverse(X_518)),
inference(subst,[],[refute_0_5474:[bind(X_159,$fot(X_519)),bind(X_68,$fot(inverse(X_518)))]]) ).
cnf(refute_0_5476,plain,
( multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518)) != least_upper_bound(inverse(X_519),inverse(X_518))
| inverse(greatest_lower_bound(X_518,X_519)) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518))
| inverse(greatest_lower_bound(X_518,X_519)) = least_upper_bound(inverse(X_519),inverse(X_518)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_518,X_519)),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518))) ),[1],$fot(least_upper_bound(inverse(X_519),inverse(X_518)))]]) ).
cnf(refute_0_5477,plain,
( inverse(greatest_lower_bound(X_518,X_519)) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518))
| inverse(greatest_lower_bound(X_518,X_519)) = least_upper_bound(inverse(X_519),inverse(X_518)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518)),least_upper_bound(inverse(X_519),inverse(X_518))) )],[refute_0_5475,refute_0_5476]) ).
cnf(refute_0_5478,plain,
inverse(greatest_lower_bound(X_518,X_519)) = least_upper_bound(inverse(X_519),inverse(X_518)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_518,X_519)),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_518),X_519))),inverse(X_518))) )],[refute_0_5463,refute_0_5477]) ).
cnf(refute_0_5479,plain,
( inverse(greatest_lower_bound(X_518,X_519)) != least_upper_bound(inverse(X_519),inverse(X_518))
| least_upper_bound(inverse(X_519),inverse(X_518)) = inverse(greatest_lower_bound(X_518,X_519)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(greatest_lower_bound(X_518,X_519)))),bind(Y0,$fot(least_upper_bound(inverse(X_519),inverse(X_518))))]]) ).
cnf(refute_0_5480,plain,
least_upper_bound(inverse(X_519),inverse(X_518)) = inverse(greatest_lower_bound(X_518,X_519)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_518,X_519)),least_upper_bound(inverse(X_519),inverse(X_518))) )],[refute_0_5478,refute_0_5479]) ).
cnf(refute_0_5481,plain,
least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) = inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))),
inference(subst,[],[refute_0_5480:[bind(X_518,$fot(greatest_lower_bound(X_78,least_upper_bound(a,c)))),bind(X_519,$fot(greatest_lower_bound(X_78,b)))]]) ).
cnf(refute_0_5482,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) != inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b)))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_5483,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))),inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b)))) )],[refute_0_5481,refute_0_5482]) ).
cnf(refute_0_5484,plain,
least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) = inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_78,least_upper_bound(a,c)),greatest_lower_bound(X_78,b))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))) )],[refute_0_5459,refute_0_5483]) ).
cnf(refute_0_5485,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,X_78))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) != inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) = inverse(greatest_lower_bound(b,X_78)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))))),bind(Y0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,X_78))))]]) ).
cnf(refute_0_5486,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))) != inverse(greatest_lower_bound(b,X_78))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) = inverse(greatest_lower_bound(b,X_78)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))),inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c)))))) )],[refute_0_5484,refute_0_5485]) ).
cnf(refute_0_5487,plain,
least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) = inverse(greatest_lower_bound(b,X_78)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(X_78,greatest_lower_bound(X_78,least_upper_bound(a,c))))),inverse(greatest_lower_bound(b,X_78))) )],[refute_0_5447,refute_0_5486]) ).
cnf(refute_0_5488,plain,
( inverse(greatest_lower_bound(X_78,b)) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))))
| least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))) != inverse(greatest_lower_bound(b,X_78))
| inverse(greatest_lower_bound(X_78,b)) = inverse(greatest_lower_bound(b,X_78)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(b,X_78))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))))]]) ).
cnf(refute_0_5489,plain,
( inverse(greatest_lower_bound(X_78,b)) != least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))))
| inverse(greatest_lower_bound(X_78,b)) = inverse(greatest_lower_bound(b,X_78)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c)))),inverse(greatest_lower_bound(b,X_78))) )],[refute_0_5487,refute_0_5488]) ).
cnf(refute_0_5490,plain,
inverse(greatest_lower_bound(X_78,b)) = inverse(greatest_lower_bound(b,X_78)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_78,b)),least_upper_bound(inverse(greatest_lower_bound(X_78,b)),inverse(greatest_lower_bound(X_78,least_upper_bound(a,c))))) )],[refute_0_5427,refute_0_5489]) ).
cnf(refute_0_5491,plain,
inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)) = inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),
inference(subst,[],[refute_0_5490:[bind(X_78,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5492,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))
| inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)) != inverse(greatest_lower_bound(b,greatest_lower_bound(a,c)))
| inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)))),bind(Y0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))))]]) ).
cnf(refute_0_5493,plain,
( inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))
| inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)),inverse(greatest_lower_bound(b,greatest_lower_bound(a,c)))) )],[refute_0_5491,refute_0_5492]) ).
cnf(refute_0_5494,plain,
inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(a,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))) )],[refute_0_5266,refute_0_5493]) ).
cnf(refute_0_5495,plain,
least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)),
inference(subst,[],[refute_0_5480:[bind(X_518,$fot(greatest_lower_bound(a,c))),bind(X_519,$fot(b))]]) ).
cnf(refute_0_5496,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)) != inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))
| least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(greatest_lower_bound(a,c),b))
| least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)))),bind(Z0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))))]]) ).
cnf(refute_0_5497,plain,
( inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)) != inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))
| least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))),inverse(greatest_lower_bound(greatest_lower_bound(a,c),b))) )],[refute_0_5495,refute_0_5496]) ).
cnf(refute_0_5498,plain,
least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,c),b)),inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))) )],[refute_0_5494,refute_0_5497]) ).
cnf(refute_0_5499,plain,
( inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) != inverse(greatest_lower_bound(a,c))
| least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))
| least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5500,plain,
( inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))) != inverse(greatest_lower_bound(a,c))
| least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(b,c)))) )],[refute_0_5498,refute_0_5499]) ).
cnf(refute_0_5501,plain,
least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(b,c))),inverse(greatest_lower_bound(a,c))) )],[refute_0_5244,refute_0_5500]) ).
cnf(refute_0_5502,plain,
multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))) = multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))),
introduced(tautology,[refl,[$fot(multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_5503,plain,
( multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))) != multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))))
| least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,c))
| multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))),multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))))) ),[1,1],$fot(inverse(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5504,plain,
( least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,c))
| multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))),multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))))) )],[refute_0_5502,refute_0_5503]) ).
cnf(refute_0_5505,plain,
multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))),inverse(greatest_lower_bound(a,c))) )],[refute_0_5501,refute_0_5504]) ).
cnf(refute_0_5506,plain,
multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))),
inference(subst,[],[refute_0_318:[bind(X,$fot(c)),bind(Y,$fot(inverse(greatest_lower_bound(a,c)))),bind(Z,$fot(inverse(b)))]]) ).
cnf(refute_0_5507,plain,
( multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
| multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) != multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))))
| multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))),bind(Y0,$fot(multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(multiply(c,inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_5508,plain,
( multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
| multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))),multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c))))) )],[refute_0_5506,refute_0_5507]) ).
cnf(refute_0_5509,plain,
multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = multiply(c,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(inverse(b),inverse(greatest_lower_bound(a,c)))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_5505,refute_0_5508]) ).
cnf(refute_0_5510,plain,
multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))))]]) ).
cnf(refute_0_5511,plain,
( multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) != multiply(c,inverse(greatest_lower_bound(a,c)))
| multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))
| multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))) ),[1,1],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5512,plain,
( multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) != multiply(c,inverse(greatest_lower_bound(a,c)))
| multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))) )],[refute_0_5510,refute_0_5511]) ).
cnf(refute_0_5513,plain,
multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_5509,refute_0_5512]) ).
cnf(refute_0_5514,plain,
inverse(least_upper_bound(a,least_upper_bound(c,c))) = inverse(least_upper_bound(a,least_upper_bound(c,c))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(a,least_upper_bound(c,c))))]]) ).
cnf(refute_0_5515,plain,
( inverse(least_upper_bound(a,least_upper_bound(c,c))) != inverse(least_upper_bound(a,least_upper_bound(c,c)))
| least_upper_bound(a,least_upper_bound(c,c)) != least_upper_bound(a,c)
| inverse(least_upper_bound(a,least_upper_bound(c,c))) = inverse(least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,c))),inverse(least_upper_bound(a,least_upper_bound(c,c)))) ),[1,0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_5516,plain,
( least_upper_bound(a,least_upper_bound(c,c)) != least_upper_bound(a,c)
| inverse(least_upper_bound(a,least_upper_bound(c,c))) = inverse(least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,c))),inverse(least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5514,refute_0_5515]) ).
cnf(refute_0_5517,plain,
inverse(least_upper_bound(a,least_upper_bound(c,c))) = inverse(least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,c)),least_upper_bound(a,c)) )],[refute_0_5102,refute_0_5516]) ).
cnf(refute_0_5518,plain,
inverse(X_100) = multiply(inverse(least_upper_bound(X_100,X_101)),multiply(least_upper_bound(X_100,X_101),inverse(X_100))),
inference(subst,[],[refute_0_8:[bind(X_45,$fot(least_upper_bound(X_100,X_101))),bind(X_46,$fot(inverse(X_100)))]]) ).
cnf(refute_0_5519,plain,
( multiply(least_upper_bound(X_100,X_101),inverse(X_100)) != least_upper_bound(identity,multiply(X_101,inverse(X_100)))
| inverse(X_100) != multiply(inverse(least_upper_bound(X_100,X_101)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))
| inverse(X_100) = multiply(inverse(least_upper_bound(X_100,X_101)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_100),multiply(inverse(least_upper_bound(X_100,X_101)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_101,inverse(X_100))))]]) ).
cnf(refute_0_5520,plain,
( inverse(X_100) != multiply(inverse(least_upper_bound(X_100,X_101)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))
| inverse(X_100) = multiply(inverse(least_upper_bound(X_100,X_101)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_100,X_101),inverse(X_100)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))) )],[refute_0_2502,refute_0_5519]) ).
cnf(refute_0_5521,plain,
inverse(X_100) = multiply(inverse(least_upper_bound(X_100,X_101)),least_upper_bound(identity,multiply(X_101,inverse(X_100)))),
inference(resolve,[$cnf( $equal(inverse(X_100),multiply(inverse(least_upper_bound(X_100,X_101)),multiply(least_upper_bound(X_100,X_101),inverse(X_100)))) )],[refute_0_5518,refute_0_5520]) ).
cnf(refute_0_5522,plain,
inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c)))))),
inference(subst,[],[refute_0_5521:[bind(X_100,$fot(least_upper_bound(X_257,least_upper_bound(a,c)))),bind(X_101,$fot(least_upper_bound(a,least_upper_bound(c,X_257))))]]) ).
cnf(refute_0_5523,plain,
( multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c)))) != identity
| inverse(least_upper_bound(X_257,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c))))))
| inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_257,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c))))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_5524,plain,
( inverse(least_upper_bound(X_257,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c))))))
| inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c)))),identity) )],[refute_0_3557,refute_0_5523]) ).
cnf(refute_0_5525,plain,
inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_257,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,multiply(least_upper_bound(a,least_upper_bound(c,X_257)),inverse(least_upper_bound(X_257,least_upper_bound(a,c))))))) )],[refute_0_5522,refute_0_5524]) ).
cnf(refute_0_5526,plain,
multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))),
inference(subst,[],[refute_0_51:[bind(X_48,$fot(inverse(least_upper_bound(a,least_upper_bound(X_257,c)))))]]) ).
cnf(refute_0_5527,plain,
multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_5528,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity))
| least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_5529,plain,
( least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity))) )],[refute_0_5527,refute_0_5528]) ).
cnf(refute_0_5530,plain,
multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_3563,refute_0_5529]) ).
cnf(refute_0_5531,plain,
least_upper_bound(X_257,least_upper_bound(c,X_257)) = least_upper_bound(X_257,c),
inference(subst,[],[refute_0_279:[bind(Y,$fot(c)),bind(X_13,$fot(X_257))]]) ).
cnf(refute_0_5532,plain,
least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))) = least_upper_bound(X_257,least_upper_bound(c,X_257)),
inference(subst,[],[refute_0_731:[bind(Y,$fot(X_257)),bind(X_20,$fot(X_257)),bind(X_21,$fot(c))]]) ).
cnf(refute_0_5533,plain,
( least_upper_bound(X_257,least_upper_bound(c,X_257)) != least_upper_bound(X_257,c)
| least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))) != least_upper_bound(X_257,least_upper_bound(c,X_257))
| least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))) = least_upper_bound(X_257,c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))),bind(Y0,$fot(least_upper_bound(X_257,least_upper_bound(c,X_257)))),bind(Z0,$fot(least_upper_bound(X_257,c)))]]) ).
cnf(refute_0_5534,plain,
( least_upper_bound(X_257,least_upper_bound(c,X_257)) != least_upper_bound(X_257,c)
| least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))) = least_upper_bound(X_257,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))),least_upper_bound(X_257,least_upper_bound(c,X_257))) )],[refute_0_5532,refute_0_5533]) ).
cnf(refute_0_5535,plain,
least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))) = least_upper_bound(X_257,c),
inference(resolve,[$cnf( $equal(least_upper_bound(X_257,least_upper_bound(c,X_257)),least_upper_bound(X_257,c)) )],[refute_0_5531,refute_0_5534]) ).
cnf(refute_0_5536,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))))]]) ).
cnf(refute_0_5537,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))) != least_upper_bound(X_257,c)
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) = least_upper_bound(a,least_upper_bound(X_257,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) ),[1,1],$fot(least_upper_bound(X_257,c))]]) ).
cnf(refute_0_5538,plain,
( least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))) != least_upper_bound(X_257,c)
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) = least_upper_bound(a,least_upper_bound(X_257,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) )],[refute_0_5536,refute_0_5537]) ).
cnf(refute_0_5539,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) = least_upper_bound(a,least_upper_bound(X_257,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))),least_upper_bound(X_257,c)) )],[refute_0_5535,refute_0_5538]) ).
cnf(refute_0_5540,plain,
least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))),bind(X_19,$fot(a))]]) ).
cnf(refute_0_5541,plain,
least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))))) = least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(least_upper_bound(c,least_upper_bound(X_463,X_462)))),bind(X_21,$fot(a))]]) ).
cnf(refute_0_5542,plain,
least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))),
inference(subst,[],[refute_0_4268:[bind(X_139,$fot(X_462)),bind(X_22,$fot(X_463))]]) ).
cnf(refute_0_5543,plain,
( least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462)))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))) = least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462)))))]]) ).
cnf(refute_0_5544,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))) = least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462)))) )],[refute_0_5542,refute_0_5543]) ).
cnf(refute_0_5545,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))) != least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c)))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))))) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))))),least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))) ),[0,1,1],$fot(least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))]]) ).
cnf(refute_0_5546,plain,
( least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))))) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))),least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c)))) )],[refute_0_5544,refute_0_5545]) ).
cnf(refute_0_5547,plain,
least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_462))))),least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))) )],[refute_0_5541,refute_0_5546]) ).
cnf(refute_0_5548,plain,
least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))) = least_upper_bound(c,least_upper_bound(X_462,X_463)),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(c)),bind(X_20,$fot(X_462)),bind(X_21,$fot(X_463))]]) ).
cnf(refute_0_5549,plain,
least_upper_bound(X_463,least_upper_bound(X_463,c)) = least_upper_bound(X_463,c),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(c)),bind(X_19,$fot(X_463))]]) ).
cnf(refute_0_5550,plain,
least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) = least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))))]]) ).
cnf(refute_0_5551,plain,
( least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) != least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))
| least_upper_bound(X_463,least_upper_bound(X_463,c)) != least_upper_bound(X_463,c)
| least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) = least_upper_bound(X_462,least_upper_bound(X_463,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))),least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))) ),[1,1],$fot(least_upper_bound(X_463,c))]]) ).
cnf(refute_0_5552,plain,
( least_upper_bound(X_463,least_upper_bound(X_463,c)) != least_upper_bound(X_463,c)
| least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) = least_upper_bound(X_462,least_upper_bound(X_463,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))),least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))) )],[refute_0_5550,refute_0_5551]) ).
cnf(refute_0_5553,plain,
least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) = least_upper_bound(X_462,least_upper_bound(X_463,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_463,least_upper_bound(X_463,c)),least_upper_bound(X_463,c)) )],[refute_0_5549,refute_0_5552]) ).
cnf(refute_0_5554,plain,
least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))),
inference(subst,[],[refute_0_944:[bind(X_13,$fot(X_462)),bind(X_20,$fot(X_463)),bind(X_21,$fot(least_upper_bound(X_463,c)))]]) ).
cnf(refute_0_5555,plain,
least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_356,X_354))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)),
inference(subst,[],[refute_0_680:[bind(X_21,$fot(least_upper_bound(X_356,X_354)))]]) ).
cnf(refute_0_5556,plain,
least_upper_bound(X_20,least_upper_bound(X_356,X_354)) = least_upper_bound(X_354,least_upper_bound(X_356,X_20)),
inference(subst,[],[refute_0_927:[bind(Y,$fot(X_354)),bind(X_30,$fot(X_20)),bind(X_31,$fot(X_356))]]) ).
cnf(refute_0_5557,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_356,X_354))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))
| least_upper_bound(X_20,least_upper_bound(X_356,X_354)) != least_upper_bound(X_354,least_upper_bound(X_356,X_20))
| least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_356,X_354))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))) ),[0,1],$fot(least_upper_bound(X_354,least_upper_bound(X_356,X_20)))]]) ).
cnf(refute_0_5558,plain,
( least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_356,X_354))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))
| least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_356,X_354)),least_upper_bound(X_354,least_upper_bound(X_356,X_20))) )],[refute_0_5556,refute_0_5557]) ).
cnf(refute_0_5559,plain,
least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_20,least_upper_bound(X_356,X_354))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))) )],[refute_0_5555,refute_0_5558]) ).
cnf(refute_0_5560,plain,
least_upper_bound(least_upper_bound(X_356,X_354),X) = least_upper_bound(X_356,least_upper_bound(X_354,X)),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_356)),bind(Y,$fot(X_354)),bind(Z,$fot(X))]]) ).
cnf(refute_0_5561,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)))]]) ).
cnf(refute_0_5562,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))
| least_upper_bound(least_upper_bound(X_356,X_354),X) != least_upper_bound(X_356,least_upper_bound(X_354,X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))) ),[1,1],$fot(least_upper_bound(X_356,least_upper_bound(X_354,X)))]]) ).
cnf(refute_0_5563,plain,
( least_upper_bound(least_upper_bound(X_356,X_354),X) != least_upper_bound(X_356,least_upper_bound(X_354,X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))) )],[refute_0_5561,refute_0_5562]) ).
cnf(refute_0_5564,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_356,X_354),X),least_upper_bound(X_356,least_upper_bound(X_354,X))) )],[refute_0_5560,refute_0_5563]) ).
cnf(refute_0_5565,plain,
( least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X)))
| least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X)))) ),[0],$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)))]]) ).
cnf(refute_0_5566,plain,
( least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))
| least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X)),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X)))) )],[refute_0_5564,refute_0_5565]) ).
cnf(refute_0_5567,plain,
least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) = least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_356,X_354),X))) )],[refute_0_5559,refute_0_5566]) ).
cnf(refute_0_5568,plain,
( least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) != least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X)))
| least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))) = least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X)))))]]) ).
cnf(refute_0_5569,plain,
least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X))) = least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_354,least_upper_bound(X_356,X_20))),least_upper_bound(X_20,least_upper_bound(X_356,least_upper_bound(X_354,X)))) )],[refute_0_5567,refute_0_5568]) ).
cnf(refute_0_5570,plain,
least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462))),
inference(subst,[],[refute_0_5569:[bind(X,$fot(X_462)),bind(X_20,$fot(X_462)),bind(X_354,$fot(X_463)),bind(X_356,$fot(least_upper_bound(X_463,c)))]]) ).
cnf(refute_0_5571,plain,
( least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462))) != least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))
| least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) != least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462)))
| least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))))),bind(Y0,$fot(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462))))),bind(Z0,$fot(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))))]]) ).
cnf(refute_0_5572,plain,
( least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462))) != least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))
| least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))),least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462)))) )],[refute_0_5570,refute_0_5571]) ).
cnf(refute_0_5573,plain,
least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(least_upper_bound(X_463,c),X_462))),least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))) )],[refute_0_5554,refute_0_5572]) ).
cnf(refute_0_5574,plain,
( least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) != least_upper_bound(X_462,least_upper_bound(X_463,c))
| least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) != least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))
| least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))))),bind(Y0,$fot(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))))),bind(Z0,$fot(least_upper_bound(X_462,least_upper_bound(X_463,c))))]]) ).
cnf(refute_0_5575,plain,
( least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))) != least_upper_bound(X_462,least_upper_bound(X_463,c))
| least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))),least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c)))) )],[refute_0_5573,refute_0_5574]) ).
cnf(refute_0_5576,plain,
least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) = least_upper_bound(X_462,least_upper_bound(X_463,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_462,least_upper_bound(X_463,least_upper_bound(X_463,c))),least_upper_bound(X_462,least_upper_bound(X_463,c))) )],[refute_0_5553,refute_0_5575]) ).
cnf(refute_0_5577,plain,
least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))),
introduced(tautology,[refl,[$fot(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))))]]) ).
cnf(refute_0_5578,plain,
( least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) != least_upper_bound(X_462,least_upper_bound(X_463,c))
| least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) != least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))))
| least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))),least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))))) ),[1,1],$fot(least_upper_bound(X_462,least_upper_bound(X_463,c)))]]) ).
cnf(refute_0_5579,plain,
( least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))) != least_upper_bound(X_462,least_upper_bound(X_463,c))
| least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))),least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))))) )],[refute_0_5577,refute_0_5578]) ).
cnf(refute_0_5580,plain,
least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))),least_upper_bound(X_462,least_upper_bound(X_463,c))) )],[refute_0_5576,refute_0_5579]) ).
cnf(refute_0_5581,plain,
( least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))) != least_upper_bound(c,least_upper_bound(X_462,X_463))
| least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) != least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c)))
| least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,X_463)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))))),bind(Z0,$fot(least_upper_bound(c,least_upper_bound(X_462,X_463))))]]) ).
cnf(refute_0_5582,plain,
( least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))) != least_upper_bound(c,least_upper_bound(X_462,X_463))
| least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,X_463)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))),least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c)))) )],[refute_0_5580,refute_0_5581]) ).
cnf(refute_0_5583,plain,
least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,X_463)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(X_463,c))),least_upper_bound(c,least_upper_bound(X_462,X_463))) )],[refute_0_5548,refute_0_5582]) ).
cnf(refute_0_5584,plain,
least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))),
inference(subst,[],[refute_0_3637:[bind(X_20,$fot(c)),bind(X_21,$fot(least_upper_bound(X_463,X_462))),bind(X_354,$fot(X_462)),bind(X_356,$fot(least_upper_bound(X_463,c)))]]) ).
cnf(refute_0_5585,plain,
( least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) != least_upper_bound(c,least_upper_bound(X_462,X_463))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))) != least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,X_463)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))))),bind(Z0,$fot(least_upper_bound(c,least_upper_bound(X_462,X_463))))]]) ).
cnf(refute_0_5586,plain,
( least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))) != least_upper_bound(c,least_upper_bound(X_462,X_463))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,X_463)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))),least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462))))) )],[refute_0_5584,refute_0_5585]) ).
cnf(refute_0_5587,plain,
least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))) = least_upper_bound(c,least_upper_bound(X_462,X_463)),
inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_462,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_463,X_462)))),least_upper_bound(c,least_upper_bound(X_462,X_463))) )],[refute_0_5583,refute_0_5586]) ).
cnf(refute_0_5588,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))))]]) ).
cnf(refute_0_5589,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))))
| least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))) != least_upper_bound(c,least_upper_bound(X_462,X_463))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))) = least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))))) ),[1,1],$fot(least_upper_bound(c,least_upper_bound(X_462,X_463)))]]) ).
cnf(refute_0_5590,plain,
( least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))) != least_upper_bound(c,least_upper_bound(X_462,X_463))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))) = least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))))) )],[refute_0_5588,refute_0_5589]) ).
cnf(refute_0_5591,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))) = least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))),least_upper_bound(c,least_upper_bound(X_462,X_463))) )],[refute_0_5587,refute_0_5590]) ).
cnf(refute_0_5592,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))
| least_upper_bound(X_21,least_upper_bound(X_356,X_354)) != least_upper_bound(X_354,least_upper_bound(X_356,X_21))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))) ),[0,1],$fot(least_upper_bound(X_354,least_upper_bound(X_356,X_21)))]]) ).
cnf(refute_0_5593,plain,
( least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_356,X_354)),least_upper_bound(X_354,least_upper_bound(X_356,X_21))) )],[refute_0_3579,refute_0_5592]) ).
cnf(refute_0_5594,plain,
least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))) )],[refute_0_3592,refute_0_5593]) ).
cnf(refute_0_5595,plain,
least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),
inference(subst,[],[refute_0_731:[bind(Y,$fot(least_upper_bound(X_356,X_354)))]]) ).
cnf(refute_0_5596,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))
| least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) != least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) ),[0],$fot(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))))]]) ).
cnf(refute_0_5597,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) != least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))
| least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) )],[refute_0_5595,refute_0_5596]) ).
cnf(refute_0_5598,plain,
least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) = least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),least_upper_bound(X_21,least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))))) )],[refute_0_5594,refute_0_5597]) ).
cnf(refute_0_5599,plain,
( least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) != least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))
| least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))))]]) ).
cnf(refute_0_5600,plain,
least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354))) = least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_354,least_upper_bound(X_356,X_21))),least_upper_bound(X_20,least_upper_bound(X_21,least_upper_bound(X_356,X_354)))) )],[refute_0_5598,refute_0_5599]) ).
cnf(refute_0_5601,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))) = least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))),
inference(subst,[],[refute_0_5600:[bind(X_21,$fot(least_upper_bound(c,least_upper_bound(X_463,X_462)))),bind(X_354,$fot(least_upper_bound(X_463,c))),bind(X_356,$fot(X_462))]]) ).
cnf(refute_0_5602,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))) != least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))) != least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))) = least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))))),bind(Z0,$fot(least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))))]]) ).
cnf(refute_0_5603,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))) != least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))
| least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))) = least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))),least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462)))))) )],[refute_0_5601,refute_0_5602]) ).
cnf(refute_0_5604,plain,
least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))) = least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(X_463,c),least_upper_bound(X_462,least_upper_bound(c,least_upper_bound(X_463,X_462))))),least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) )],[refute_0_5591,refute_0_5603]) ).
cnf(refute_0_5605,plain,
least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))))]]) ).
cnf(refute_0_5606,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))) != least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))))) ),[1,1],$fot(least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))))]]) ).
cnf(refute_0_5607,plain,
( least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))) != least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))))) )],[refute_0_5605,refute_0_5606]) ).
cnf(refute_0_5608,plain,
least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))),least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) )],[refute_0_5604,refute_0_5607]) ).
cnf(refute_0_5609,plain,
least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))),
inference(subst,[],[refute_0_3637:[bind(X_20,$fot(a)),bind(X_21,$fot(least_upper_bound(X_462,least_upper_bound(X_463,c)))),bind(X_354,$fot(X_20)),bind(X_356,$fot(least_upper_bound(c,least_upper_bound(X_463,X_462))))]]) ).
cnf(refute_0_5610,plain,
( least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))))))]]) ).
cnf(refute_0_5611,plain,
( least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c)))))) )],[refute_0_5609,refute_0_5610]) ).
cnf(refute_0_5612,plain,
least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_462,least_upper_bound(X_463,c))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))))) )],[refute_0_5608,refute_0_5611]) ).
cnf(refute_0_5613,plain,
( least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) = least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))),least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))) ),[0],$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))))]]) ).
cnf(refute_0_5614,plain,
( least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) = least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463))))) )],[refute_0_5612,refute_0_5613]) ).
cnf(refute_0_5615,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y))),
inference(subst,[],[refute_0_549:[bind(Y,$fot(X_310)),bind(X_20,$fot(X_311)),bind(X_22,$fot(least_upper_bound(X_20,least_upper_bound(X_311,Y))))]]) ).
cnf(refute_0_5616,plain,
least_upper_bound(X_20,least_upper_bound(X_311,Y)) = least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y))),
inference(subst,[],[refute_0_729:[bind(X_21,$fot(X_311))]]) ).
cnf(refute_0_5617,plain,
( least_upper_bound(X_20,least_upper_bound(X_311,Y)) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y)))
| least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y))) = least_upper_bound(X_20,least_upper_bound(X_311,Y)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_20,least_upper_bound(X_311,Y)))),bind(Y0,$fot(least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y)))))]]) ).
cnf(refute_0_5618,plain,
least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y))) = least_upper_bound(X_20,least_upper_bound(X_311,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,least_upper_bound(X_311,Y)),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y)))) )],[refute_0_5616,refute_0_5617]) ).
cnf(refute_0_5619,plain,
( least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y))) != least_upper_bound(X_20,least_upper_bound(X_311,Y))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y)))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(X_20,least_upper_bound(X_311,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y)))) ),[1],$fot(least_upper_bound(X_20,least_upper_bound(X_311,Y)))]]) ).
cnf(refute_0_5620,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) != least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y)))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(X_20,least_upper_bound(X_311,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y))),least_upper_bound(X_20,least_upper_bound(X_311,Y))) )],[refute_0_5618,refute_0_5619]) ).
cnf(refute_0_5621,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(X_20,least_upper_bound(X_311,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))),least_upper_bound(X_311,least_upper_bound(X_20,least_upper_bound(X_311,Y)))) )],[refute_0_5615,refute_0_5620]) ).
cnf(refute_0_5622,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)) = least_upper_bound(X_311,X_20),
inference(subst,[],[refute_0_549:[bind(Y,$fot(X_310)),bind(X_20,$fot(X_311)),bind(X_22,$fot(X_20))]]) ).
cnf(refute_0_5623,plain,
least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))) = least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))))]]) ).
cnf(refute_0_5624,plain,
( least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))) != least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)) != least_upper_bound(X_311,X_20)
| least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))) = least_upper_bound(Y,least_upper_bound(X_311,X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))),least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)))) ),[1,1],$fot(least_upper_bound(X_311,X_20))]]) ).
cnf(refute_0_5625,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)) != least_upper_bound(X_311,X_20)
| least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))) = least_upper_bound(Y,least_upper_bound(X_311,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))),least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)))) )],[refute_0_5623,refute_0_5624]) ).
cnf(refute_0_5626,plain,
least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))) = least_upper_bound(Y,least_upper_bound(X_311,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)),least_upper_bound(X_311,X_20)) )],[refute_0_5622,refute_0_5625]) ).
cnf(refute_0_5627,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))),
inference(subst,[],[refute_0_1005:[bind(X,$fot(Y)),bind(X_139,$fot(greatest_lower_bound(X_311,X_310))),bind(X_140,$fot(X_20)),bind(X_20,$fot(X_311))]]) ).
cnf(refute_0_5628,plain,
( least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))) != least_upper_bound(Y,least_upper_bound(X_311,X_20))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) != least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(Y,least_upper_bound(X_311,X_20)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_311,X_20))))]]) ).
cnf(refute_0_5629,plain,
( least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))) != least_upper_bound(Y,least_upper_bound(X_311,X_20))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(Y,least_upper_bound(X_311,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))),least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20)))) )],[refute_0_5627,refute_0_5628]) ).
cnf(refute_0_5630,plain,
least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) = least_upper_bound(Y,least_upper_bound(X_311,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),X_20))),least_upper_bound(Y,least_upper_bound(X_311,X_20))) )],[refute_0_5626,refute_0_5629]) ).
cnf(refute_0_5631,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) != least_upper_bound(Y,least_upper_bound(X_311,X_20))
| least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) != least_upper_bound(X_20,least_upper_bound(X_311,Y))
| least_upper_bound(Y,least_upper_bound(X_311,X_20)) = least_upper_bound(X_20,least_upper_bound(X_311,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))),least_upper_bound(X_20,least_upper_bound(X_311,Y))) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_311,X_20)))]]) ).
cnf(refute_0_5632,plain,
( least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))) != least_upper_bound(X_20,least_upper_bound(X_311,Y))
| least_upper_bound(Y,least_upper_bound(X_311,X_20)) = least_upper_bound(X_20,least_upper_bound(X_311,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))),least_upper_bound(Y,least_upper_bound(X_311,X_20))) )],[refute_0_5630,refute_0_5631]) ).
cnf(refute_0_5633,plain,
least_upper_bound(Y,least_upper_bound(X_311,X_20)) = least_upper_bound(X_20,least_upper_bound(X_311,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_311,least_upper_bound(greatest_lower_bound(X_311,X_310),least_upper_bound(X_20,least_upper_bound(X_311,Y)))),least_upper_bound(X_20,least_upper_bound(X_311,Y))) )],[refute_0_5621,refute_0_5632]) ).
cnf(refute_0_5634,plain,
( least_upper_bound(Y,least_upper_bound(X_311,X_20)) != least_upper_bound(X_20,least_upper_bound(X_311,Y))
| least_upper_bound(X_20,least_upper_bound(X_311,Y)) = least_upper_bound(Y,least_upper_bound(X_311,X_20)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_311,X_20)))),bind(Y0,$fot(least_upper_bound(X_20,least_upper_bound(X_311,Y))))]]) ).
cnf(refute_0_5635,plain,
least_upper_bound(X_20,least_upper_bound(X_311,Y)) = least_upper_bound(Y,least_upper_bound(X_311,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_311,X_20)),least_upper_bound(X_20,least_upper_bound(X_311,Y))) )],[refute_0_5633,refute_0_5634]) ).
cnf(refute_0_5636,plain,
least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462)))),
inference(subst,[],[refute_0_5635:[bind(Y,$fot(a)),bind(X_20,$fot(least_upper_bound(c,least_upper_bound(X_463,X_462)))),bind(X_311,$fot(X_20))]]) ).
cnf(refute_0_5637,plain,
( least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))
| least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462))))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462))))) ),[0],$fot(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)))]]) ).
cnf(refute_0_5638,plain,
( least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a)),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462))))) )],[refute_0_5636,refute_0_5637]) ).
cnf(refute_0_5639,plain,
( least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))) != least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))),least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))) )],[refute_0_5614,refute_0_5638]) ).
cnf(refute_0_5640,plain,
least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,least_upper_bound(a,least_upper_bound(X_462,least_upper_bound(X_463,c))))),least_upper_bound(least_upper_bound(c,least_upper_bound(X_463,X_462)),least_upper_bound(X_20,a))) )],[refute_0_5547,refute_0_5639]) ).
cnf(refute_0_5641,plain,
( least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) != least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462))))
| least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462)))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462))))))]]) ).
cnf(refute_0_5642,plain,
least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462)))) = least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_462,X_463)))),least_upper_bound(a,least_upper_bound(X_20,least_upper_bound(c,least_upper_bound(X_463,X_462))))) )],[refute_0_5640,refute_0_5641]) ).
cnf(refute_0_5643,plain,
least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))),
inference(subst,[],[refute_0_5642:[bind(X_20,$fot(a)),bind(X_462,$fot(X_257)),bind(X_463,$fot(least_upper_bound(c,X_257)))]]) ).
cnf(refute_0_5644,plain,
( least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))) != least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))))
| least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))))]]) ).
cnf(refute_0_5645,plain,
( least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))),least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))))) )],[refute_0_5643,refute_0_5644]) ).
cnf(refute_0_5646,plain,
least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) )],[refute_0_5540,refute_0_5645]) ).
cnf(refute_0_5647,plain,
( least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))))]]) ).
cnf(refute_0_5648,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21))) = least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_463,least_upper_bound(c,X_21))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,X_21)))) )],[refute_0_4284,refute_0_5647]) ).
cnf(refute_0_5649,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))),
inference(subst,[],[refute_0_5648:[bind(X_21,$fot(least_upper_bound(least_upper_bound(c,X_257),X_257))),bind(X_463,$fot(a))]]) ).
cnf(refute_0_5650,plain,
( least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))) != least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))))]]) ).
cnf(refute_0_5651,plain,
( least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))),least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257))))) )],[refute_0_5649,refute_0_5650]) ).
cnf(refute_0_5652,plain,
least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,least_upper_bound(c,least_upper_bound(least_upper_bound(c,X_257),X_257)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) )],[refute_0_5646,refute_0_5651]) ).
cnf(refute_0_5653,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y)))),
inference(subst,[],[refute_0_4268:[bind(X_139,$fot(least_upper_bound(X,Y))),bind(X_22,$fot(X_463))]]) ).
cnf(refute_0_5654,plain,
least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c)),
inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_463,c)))]]) ).
cnf(refute_0_5655,plain,
( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c)) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))))]]) ).
cnf(refute_0_5656,plain,
least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c)) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))) )],[refute_0_5654,refute_0_5655]) ).
cnf(refute_0_5657,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y))))
| least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c)) != least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c)))
| least_upper_bound(a,least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y))))) ),[0,1],$fot(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c))))]]) ).
cnf(refute_0_5658,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y))))
| least_upper_bound(a,least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c)))) )],[refute_0_5656,refute_0_5657]) ).
cnf(refute_0_5659,plain,
least_upper_bound(a,least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_463,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_463,c))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_463,least_upper_bound(X,Y))))) )],[refute_0_5653,refute_0_5658]) ).
cnf(refute_0_5660,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))),
inference(subst,[],[refute_0_5659:[bind(X,$fot(least_upper_bound(c,X_257))),bind(Y,$fot(X_257)),bind(X_463,$fot(a))]]) ).
cnf(refute_0_5661,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257))))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))))]]) ).
cnf(refute_0_5662,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257))))) )],[refute_0_5660,refute_0_5661]) ).
cnf(refute_0_5663,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),X_257)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) )],[refute_0_5652,refute_0_5662]) ).
cnf(refute_0_5664,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) != least_upper_bound(a,least_upper_bound(X_257,c))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(X_257,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(X_257,c))))]]) ).
cnf(refute_0_5665,plain,
( least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))) != least_upper_bound(a,least_upper_bound(X_257,c))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(X_257,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257))))) )],[refute_0_5663,refute_0_5664]) ).
cnf(refute_0_5666,plain,
least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(X_257,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_257,least_upper_bound(c,X_257)))),least_upper_bound(a,least_upper_bound(X_257,c))) )],[refute_0_5539,refute_0_5665]) ).
cnf(refute_0_5667,plain,
inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) = inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))))]]) ).
cnf(refute_0_5668,plain,
( inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) != inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))
| least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) != least_upper_bound(a,least_upper_bound(X_257,c))
| inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))),inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))) ),[1,0],$fot(least_upper_bound(a,least_upper_bound(X_257,c)))]]) ).
cnf(refute_0_5669,plain,
( least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))) != least_upper_bound(a,least_upper_bound(X_257,c))
| inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))),inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))) )],[refute_0_5667,refute_0_5668]) ).
cnf(refute_0_5670,plain,
inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(X_257,c))) )],[refute_0_5666,refute_0_5669]) ).
cnf(refute_0_5671,plain,
inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))),
inference(subst,[],[refute_0_3491:[bind(Y,$fot(a)),bind(X_22,$fot(least_upper_bound(X_257,least_upper_bound(a,c)))),bind(X_375,$fot(least_upper_bound(c,X_257)))]]) ).
cnf(refute_0_5672,plain,
inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257)))),
inference(subst,[],[refute_0_1804:[bind(X_30,$fot(a)),bind(X_31,$fot(least_upper_bound(X_257,least_upper_bound(a,c)))),bind(X_375,$fot(least_upper_bound(c,X_257)))]]) ).
cnf(refute_0_5673,plain,
( inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257)))) != inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))
| inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) != inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257))))
| inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257)))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))))]]) ).
cnf(refute_0_5674,plain,
( inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257)))) != inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))
| inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257))))) )],[refute_0_5672,refute_0_5673]) ).
cnf(refute_0_5675,plain,
inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(c,X_257)))),inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))) )],[refute_0_5671,refute_0_5674]) ).
cnf(refute_0_5676,plain,
( inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) != inverse(least_upper_bound(a,least_upper_bound(X_257,c)))
| inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) != inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))
| inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(X_257,c)))))]]) ).
cnf(refute_0_5677,plain,
( inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))) != inverse(least_upper_bound(a,least_upper_bound(X_257,c)))
| inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c)))))) )],[refute_0_5675,refute_0_5676]) ).
cnf(refute_0_5678,plain,
inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(least_upper_bound(c,X_257),least_upper_bound(X_257,least_upper_bound(a,c))))),inverse(least_upper_bound(a,least_upper_bound(X_257,c)))) )],[refute_0_5670,refute_0_5677]) ).
cnf(refute_0_5679,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_5680,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) != inverse(least_upper_bound(a,least_upper_bound(X_257,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity))) ),[1,0],$fot(inverse(least_upper_bound(a,least_upper_bound(X_257,c))))]]) ).
cnf(refute_0_5681,plain,
( inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))) != inverse(least_upper_bound(a,least_upper_bound(X_257,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity))) )],[refute_0_5679,refute_0_5680]) ).
cnf(refute_0_5682,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),inverse(least_upper_bound(a,least_upper_bound(X_257,c)))) )],[refute_0_5678,refute_0_5681]) ).
cnf(refute_0_5683,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity))
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity)))]]) ).
cnf(refute_0_5684,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity))) )],[refute_0_5682,refute_0_5683]) ).
cnf(refute_0_5685,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity)) )],[refute_0_5530,refute_0_5684]) ).
cnf(refute_0_5686,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity) != inverse(least_upper_bound(a,least_upper_bound(X_257,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(X_257,c)))))]]) ).
cnf(refute_0_5687,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity) != inverse(least_upper_bound(a,least_upper_bound(X_257,c)))
| multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity)) )],[refute_0_5685,refute_0_5686]) ).
cnf(refute_0_5688,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(X_257,c))),identity),inverse(least_upper_bound(a,least_upper_bound(X_257,c)))) )],[refute_0_5526,refute_0_5687]) ).
cnf(refute_0_5689,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)) != inverse(least_upper_bound(a,least_upper_bound(X_257,c)))
| inverse(least_upper_bound(X_257,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_257,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity))) ),[1],$fot(inverse(least_upper_bound(a,least_upper_bound(X_257,c))))]]) ).
cnf(refute_0_5690,plain,
( inverse(least_upper_bound(X_257,least_upper_bound(a,c))) != multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity)),inverse(least_upper_bound(a,least_upper_bound(X_257,c)))) )],[refute_0_5688,refute_0_5689]) ).
cnf(refute_0_5691,plain,
inverse(least_upper_bound(X_257,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(X_257,c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_257,least_upper_bound(a,c))),multiply(inverse(least_upper_bound(least_upper_bound(X_257,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_257)))),least_upper_bound(identity,identity))) )],[refute_0_5525,refute_0_5690]) ).
cnf(refute_0_5692,plain,
inverse(least_upper_bound(c,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,c))),
inference(subst,[],[refute_0_5691:[bind(X_257,$fot(c))]]) ).
cnf(refute_0_5693,plain,
inverse(least_upper_bound(least_upper_bound(a,c),c)) = inverse(least_upper_bound(c,least_upper_bound(a,c))),
inference(subst,[],[refute_0_4994:[bind(X_323,$fot(c)),bind(X_324,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5694,plain,
( inverse(least_upper_bound(c,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,c)))
| inverse(least_upper_bound(least_upper_bound(a,c),c)) != inverse(least_upper_bound(c,least_upper_bound(a,c)))
| inverse(least_upper_bound(least_upper_bound(a,c),c)) = inverse(least_upper_bound(a,least_upper_bound(c,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(a,c),c)))),bind(Y0,$fot(inverse(least_upper_bound(c,least_upper_bound(a,c))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,c)))))]]) ).
cnf(refute_0_5695,plain,
( inverse(least_upper_bound(c,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,c)))
| inverse(least_upper_bound(least_upper_bound(a,c),c)) = inverse(least_upper_bound(a,least_upper_bound(c,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),c)),inverse(least_upper_bound(c,least_upper_bound(a,c)))) )],[refute_0_5693,refute_0_5694]) ).
cnf(refute_0_5696,plain,
inverse(least_upper_bound(least_upper_bound(a,c),c)) = inverse(least_upper_bound(a,least_upper_bound(c,c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(c,least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5692,refute_0_5695]) ).
cnf(refute_0_5697,plain,
( inverse(least_upper_bound(a,least_upper_bound(c,c))) != inverse(least_upper_bound(a,c))
| inverse(least_upper_bound(least_upper_bound(a,c),c)) != inverse(least_upper_bound(a,least_upper_bound(c,c)))
| inverse(least_upper_bound(least_upper_bound(a,c),c)) = inverse(least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(a,c),c)))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,c))))),bind(Z0,$fot(inverse(least_upper_bound(a,c))))]]) ).
cnf(refute_0_5698,plain,
( inverse(least_upper_bound(a,least_upper_bound(c,c))) != inverse(least_upper_bound(a,c))
| inverse(least_upper_bound(least_upper_bound(a,c),c)) = inverse(least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),c)),inverse(least_upper_bound(a,least_upper_bound(c,c)))) )],[refute_0_5696,refute_0_5697]) ).
cnf(refute_0_5699,plain,
inverse(least_upper_bound(least_upper_bound(a,c),c)) = inverse(least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,c))),inverse(least_upper_bound(a,c))) )],[refute_0_5517,refute_0_5698]) ).
cnf(refute_0_5700,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))))]]) ).
cnf(refute_0_5701,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))
| inverse(least_upper_bound(least_upper_bound(a,c),c)) != inverse(least_upper_bound(a,c))
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))) ),[1,0],$fot(inverse(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5702,plain,
( inverse(least_upper_bound(least_upper_bound(a,c),c)) != inverse(least_upper_bound(a,c))
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))) )],[refute_0_5700,refute_0_5701]) ).
cnf(refute_0_5703,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),c)),inverse(least_upper_bound(a,c))) )],[refute_0_5699,refute_0_5702]) ).
cnf(refute_0_5704,plain,
( multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))))]]) ).
cnf(refute_0_5705,plain,
( multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))) )],[refute_0_5703,refute_0_5704]) ).
cnf(refute_0_5706,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_5513,refute_0_5705]) ).
cnf(refute_0_5707,plain,
( multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != inverse(a)
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = inverse(a) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(a)))]]) ).
cnf(refute_0_5708,plain,
( multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != inverse(a)
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_5706,refute_0_5707]) ).
cnf(refute_0_5709,plain,
multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) = inverse(a),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),inverse(a)) )],[refute_0_5396,refute_0_5708]) ).
cnf(refute_0_5710,plain,
multiply(multiply(inverse(least_upper_bound(X_472,Y)),Y),Z) = multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(least_upper_bound(X_472,Y))))]]) ).
cnf(refute_0_5711,plain,
inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))) = multiply(inverse(least_upper_bound(X_472,Y)),Y),
inference(subst,[],[refute_0_4866:[bind(X_85,$fot(X_472)),bind(X_86,$fot(Y))]]) ).
cnf(refute_0_5712,plain,
( inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))) != multiply(inverse(least_upper_bound(X_472,Y)),Y)
| multiply(inverse(least_upper_bound(X_472,Y)),Y) = inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_472,Y)),Y)))]]) ).
cnf(refute_0_5713,plain,
multiply(inverse(least_upper_bound(X_472,Y)),Y) = inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))),multiply(inverse(least_upper_bound(X_472,Y)),Y)) )],[refute_0_5711,refute_0_5712]) ).
cnf(refute_0_5714,plain,
( multiply(multiply(inverse(least_upper_bound(X_472,Y)),Y),Z) != multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z))
| multiply(inverse(least_upper_bound(X_472,Y)),Y) != inverse(least_upper_bound(identity,multiply(inverse(Y),X_472)))
| multiply(inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))),Z) = multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_472,Y)),Y),Z),multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z))) ),[0,0],$fot(inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))))]]) ).
cnf(refute_0_5715,plain,
( multiply(multiply(inverse(least_upper_bound(X_472,Y)),Y),Z) != multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z))
| multiply(inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))),Z) = multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_472,Y)),Y),inverse(least_upper_bound(identity,multiply(inverse(Y),X_472)))) )],[refute_0_5713,refute_0_5714]) ).
cnf(refute_0_5716,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(Y),X_472))),Z) = multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_472,Y)),Y),Z),multiply(inverse(least_upper_bound(X_472,Y)),multiply(Y,Z))) )],[refute_0_5710,refute_0_5715]) ).
cnf(refute_0_5717,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),
inference(subst,[],[refute_0_5716:[bind(Y,$fot(c)),bind(Z,$fot(least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),bind(X_472,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5718,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) != multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))
| multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != inverse(a)
| multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = inverse(a) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))))),bind(Z0,$fot(inverse(a)))]]) ).
cnf(refute_0_5719,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) != inverse(a)
| multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))),multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))))) )],[refute_0_5717,refute_0_5718]) ).
cnf(refute_0_5720,plain,
multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) = inverse(a),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(a,c),c)),multiply(c,least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))),inverse(a)) )],[refute_0_5709,refute_0_5719]) ).
cnf(refute_0_5721,plain,
( multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))) != inverse(a)
| inverse(b) != multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))
| inverse(b) = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) ),[1],$fot(inverse(a))]]) ).
cnf(refute_0_5722,plain,
( inverse(b) != multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))
| inverse(b) = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b))),inverse(a)) )],[refute_0_5720,refute_0_5721]) ).
cnf(refute_0_5723,plain,
inverse(b) = inverse(a),
inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(least_upper_bound(identity,multiply(inverse(c),least_upper_bound(a,c)))),least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(b)))) )],[refute_0_5299,refute_0_5722]) ).
cnf(refute_0_5724,plain,
multiply(inverse(b),a) = multiply(inverse(b),a),
introduced(tautology,[refl,[$fot(multiply(inverse(b),a))]]) ).
cnf(refute_0_5725,plain,
( multiply(inverse(b),a) != multiply(inverse(b),a)
| inverse(b) != inverse(a)
| multiply(inverse(b),a) = multiply(inverse(a),a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),a),multiply(inverse(b),a)) ),[1,0],$fot(inverse(a))]]) ).
cnf(refute_0_5726,plain,
( inverse(b) != inverse(a)
| multiply(inverse(b),a) = multiply(inverse(a),a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),a),multiply(inverse(b),a)) )],[refute_0_5724,refute_0_5725]) ).
cnf(refute_0_5727,plain,
multiply(inverse(b),a) = multiply(inverse(a),a),
inference(resolve,[$cnf( $equal(inverse(b),inverse(a)) )],[refute_0_5723,refute_0_5726]) ).
cnf(refute_0_5728,plain,
( multiply(inverse(a),a) != identity
| multiply(inverse(b),a) != multiply(inverse(a),a)
| multiply(inverse(b),a) = identity ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(inverse(b),a))),bind(Y0,$fot(multiply(inverse(a),a))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_5729,plain,
( multiply(inverse(a),a) != identity
| multiply(inverse(b),a) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),a),multiply(inverse(a),a)) )],[refute_0_5727,refute_0_5728]) ).
cnf(refute_0_5730,plain,
multiply(inverse(b),a) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a),a),identity) )],[refute_0_3529,refute_0_5729]) ).
cnf(refute_0_5731,plain,
least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) = least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))]]) ).
cnf(refute_0_5732,plain,
( multiply(inverse(b),a) != identity
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) != least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) = least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))),least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_5733,plain,
( multiply(inverse(b),a) != identity
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) = least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))),least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) )],[refute_0_5731,refute_0_5732]) ).
cnf(refute_0_5734,plain,
least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) = least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(inverse(b),a),identity) )],[refute_0_5730,refute_0_5733]) ).
cnf(refute_0_5735,plain,
( least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) != least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c)))
| least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))) != multiply(inverse(a),least_upper_bound(a,c))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(a),least_upper_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))))),bind(Z0,$fot(multiply(inverse(a),least_upper_bound(a,c))))]]) ).
cnf(refute_0_5736,plain,
( least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))) != multiply(inverse(a),least_upper_bound(a,c))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(a),least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))),least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c)))) )],[refute_0_5734,refute_0_5735]) ).
cnf(refute_0_5737,plain,
least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) = multiply(inverse(a),least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(a,c))),multiply(inverse(a),least_upper_bound(a,c))) )],[refute_0_4785,refute_0_5736]) ).
cnf(refute_0_5738,plain,
inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) = inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_5739,plain,
( inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) != inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))
| least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) != multiply(inverse(a),least_upper_bound(a,c))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) = inverse(multiply(inverse(a),least_upper_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) ),[1,0],$fot(multiply(inverse(a),least_upper_bound(a,c)))]]) ).
cnf(refute_0_5740,plain,
( least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))) != multiply(inverse(a),least_upper_bound(a,c))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) = inverse(multiply(inverse(a),least_upper_bound(a,c))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) )],[refute_0_5738,refute_0_5739]) ).
cnf(refute_0_5741,plain,
inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) = inverse(multiply(inverse(a),least_upper_bound(a,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))),multiply(inverse(a),least_upper_bound(a,c))) )],[refute_0_5737,refute_0_5740]) ).
cnf(refute_0_5742,plain,
( inverse(multiply(inverse(a),least_upper_bound(a,c))) != multiply(inverse(c),greatest_lower_bound(a,c))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) != inverse(multiply(inverse(a),least_upper_bound(a,c)))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) = multiply(inverse(c),greatest_lower_bound(a,c)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))),bind(Y0,$fot(inverse(multiply(inverse(a),least_upper_bound(a,c))))),bind(Z0,$fot(multiply(inverse(c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5743,plain,
( inverse(multiply(inverse(a),least_upper_bound(a,c))) != multiply(inverse(c),greatest_lower_bound(a,c))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) = multiply(inverse(c),greatest_lower_bound(a,c)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))),inverse(multiply(inverse(a),least_upper_bound(a,c)))) )],[refute_0_5741,refute_0_5742]) ).
cnf(refute_0_5744,plain,
inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) = multiply(inverse(c),greatest_lower_bound(a,c)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(a),least_upper_bound(a,c))),multiply(inverse(c),greatest_lower_bound(a,c))) )],[refute_0_4748,refute_0_5743]) ).
cnf(refute_0_5745,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))))]]) ).
cnf(refute_0_5746,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))
| inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) != multiply(inverse(c),greatest_lower_bound(a,c))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))) ),[1,1],$fot(multiply(inverse(c),greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5747,plain,
( inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))) != multiply(inverse(c),greatest_lower_bound(a,c))
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))) )],[refute_0_5745,refute_0_5746]) ).
cnf(refute_0_5748,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) )],[refute_0_5744,refute_0_5747]) ).
cnf(refute_0_5749,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))
| b != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))
| b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))) ),[1],$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5750,plain,
( b != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))
| b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c))))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))) )],[refute_0_5748,refute_0_5749]) ).
cnf(refute_0_5751,plain,
b = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(b,multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),inverse(least_upper_bound(multiply(inverse(b),a),multiply(inverse(a),least_upper_bound(a,c)))))) )],[refute_0_4734,refute_0_5750]) ).
cnf(refute_0_5752,plain,
multiply(a,identity) = a,
inference(subst,[],[refute_0_51:[bind(X_48,$fot(a))]]) ).
cnf(refute_0_5753,plain,
multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5754,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))),
introduced(tautology,[refl,[$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5755,plain,
( multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)))
| multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) != identity
| multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) = multiply(a,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_5756,plain,
( multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) != identity
| multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) = multiply(a,identity) ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)))) )],[refute_0_5754,refute_0_5755]) ).
cnf(refute_0_5757,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) = multiply(a,identity),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)),identity) )],[refute_0_5753,refute_0_5756]) ).
cnf(refute_0_5758,plain,
( multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) != multiply(a,identity)
| multiply(a,identity) != a
| multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) = a ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))))),bind(Y0,$fot(multiply(a,identity))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_5759,plain,
( multiply(a,identity) != a
| multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) = a ),
inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))),multiply(a,identity)) )],[refute_0_5757,refute_0_5758]) ).
cnf(refute_0_5760,plain,
multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) = a,
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_5752,refute_0_5759]) ).
cnf(refute_0_5761,plain,
multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)),
inference(subst,[],[monotony_lub2:[bind(Y,$fot(identity)),bind(Z,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_5762,plain,
( multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) != least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != multiply(least_upper_bound(a,c),inverse(c))
| multiply(multiply(least_upper_bound(a,c),inverse(c)),X) = least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))) ),[0,0],$fot(multiply(least_upper_bound(a,c),inverse(c)))]]) ).
cnf(refute_0_5763,plain,
( multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) != least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))
| multiply(multiply(least_upper_bound(a,c),inverse(c)),X) = least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2659,refute_0_5762]) ).
cnf(refute_0_5764,plain,
multiply(multiply(least_upper_bound(a,c),inverse(c)),X) = least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))) )],[refute_0_5761,refute_0_5763]) ).
cnf(refute_0_5765,plain,
multiply(multiply(least_upper_bound(a,c),inverse(c)),X) = multiply(least_upper_bound(a,c),multiply(inverse(c),X)),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(inverse(c))),bind(Z,$fot(X))]]) ).
cnf(refute_0_5766,plain,
( multiply(multiply(least_upper_bound(a,c),inverse(c)),X) != multiply(least_upper_bound(a,c),multiply(inverse(c),X))
| multiply(multiply(least_upper_bound(a,c),inverse(c)),X) != least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))
| multiply(least_upper_bound(a,c),multiply(inverse(c),X)) = least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(a,c),inverse(c)),X),least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))) ),[0],$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),X)))]]) ).
cnf(refute_0_5767,plain,
( multiply(multiply(least_upper_bound(a,c),inverse(c)),X) != least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))
| multiply(least_upper_bound(a,c),multiply(inverse(c),X)) = least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,c),inverse(c)),X),multiply(least_upper_bound(a,c),multiply(inverse(c),X))) )],[refute_0_5765,refute_0_5766]) ).
cnf(refute_0_5768,plain,
multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)),
inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(inverse(greatest_lower_bound(a,c)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_5769,plain,
( multiply(least_upper_bound(a,c),inverse(c)) != multiply(a,inverse(greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != multiply(least_upper_bound(a,c),inverse(c))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),inverse(c)))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(a,c)))))]]) ).
cnf(refute_0_5770,plain,
( multiply(least_upper_bound(a,c),inverse(c)) != multiply(a,inverse(greatest_lower_bound(a,c)))
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = multiply(a,inverse(greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),multiply(least_upper_bound(a,c),inverse(c))) )],[refute_0_2659,refute_0_5769]) ).
cnf(refute_0_5771,plain,
least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) = multiply(a,inverse(greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(c)),multiply(a,inverse(greatest_lower_bound(a,c)))) )],[refute_0_4677,refute_0_5770]) ).
cnf(refute_0_5772,plain,
multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X))]]) ).
cnf(refute_0_5773,plain,
( multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) != multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X)
| least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != multiply(a,inverse(greatest_lower_bound(a,c)))
| multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X)) ),[1,0],$fot(multiply(a,inverse(greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5774,plain,
( least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))) != multiply(a,inverse(greatest_lower_bound(a,c)))
| multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X)) )],[refute_0_5772,refute_0_5773]) ).
cnf(refute_0_5775,plain,
multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),multiply(a,inverse(greatest_lower_bound(a,c)))) )],[refute_0_5771,refute_0_5774]) ).
cnf(refute_0_5776,plain,
( multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))
| multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) != multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X)
| multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X))),bind(Y0,$fot(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X))),bind(Z0,$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))))]]) ).
cnf(refute_0_5777,plain,
( multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))
| multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X)) )],[refute_0_5775,refute_0_5776]) ).
cnf(refute_0_5778,plain,
multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(greatest_lower_bound(a,c))),X),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))) )],[refute_0_5768,refute_0_5777]) ).
cnf(refute_0_5779,plain,
least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) = multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),
inference(subst,[],[refute_0_630:[bind(Y,$fot(identity)),bind(Z,$fot(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))))]]) ).
cnf(refute_0_5780,plain,
( multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))
| least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) != multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X)
| least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X))),bind(Z0,$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))))]]) ).
cnf(refute_0_5781,plain,
( multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))
| least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)),multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X)) )],[refute_0_5779,refute_0_5780]) ).
cnf(refute_0_5782,plain,
least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c))))),X),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))) )],[refute_0_5778,refute_0_5781]) ).
cnf(refute_0_5783,plain,
( multiply(least_upper_bound(a,c),multiply(inverse(c),X)) != least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))
| least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))
| multiply(least_upper_bound(a,c),multiply(inverse(c),X)) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,c),multiply(inverse(c),X)),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))) ),[0],$fot(least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)))]]) ).
cnf(refute_0_5784,plain,
( multiply(least_upper_bound(a,c),multiply(inverse(c),X)) != least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))
| multiply(least_upper_bound(a,c),multiply(inverse(c),X)) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X)),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X))) )],[refute_0_5782,refute_0_5783]) ).
cnf(refute_0_5785,plain,
( multiply(multiply(least_upper_bound(a,c),inverse(c)),X) != least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))
| multiply(least_upper_bound(a,c),multiply(inverse(c),X)) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(inverse(c),X)),least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))) )],[refute_0_5767,refute_0_5784]) ).
cnf(refute_0_5786,plain,
multiply(least_upper_bound(a,c),multiply(inverse(c),X)) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),X)),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(a,c),inverse(c)),X),least_upper_bound(multiply(identity,X),multiply(multiply(b,multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,c),inverse(c)))),X))) )],[refute_0_5764,refute_0_5785]) ).
cnf(refute_0_5787,plain,
multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) = multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))),
inference(subst,[],[refute_0_5786:[bind(X,$fot(greatest_lower_bound(a,c)))]]) ).
cnf(refute_0_5788,plain,
( multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) != a
| multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) != multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)))
| multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) = a ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))))),bind(Y0,$fot(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_5789,plain,
( multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))) != a
| multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) = a ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))),multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c)))) )],[refute_0_5787,refute_0_5788]) ).
cnf(refute_0_5790,plain,
multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) = a,
inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,c))),a) )],[refute_0_5760,refute_0_5789]) ).
cnf(refute_0_5791,plain,
least_upper_bound(a,least_upper_bound(a,c)) = least_upper_bound(a,c),
inference(subst,[],[refute_0_426:[bind(X_18,$fot(c)),bind(X_19,$fot(a))]]) ).
cnf(refute_0_5792,plain,
X_46 = multiply(b,multiply(inverse(b),X_46)),
inference(subst,[],[refute_0_823:[bind(X_50,$fot(b))]]) ).
cnf(refute_0_5793,plain,
( X_46 != multiply(b,multiply(inverse(b),X_46))
| inverse(b) != inverse(a)
| X_46 = multiply(b,multiply(inverse(a),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(X_46,multiply(b,multiply(inverse(b),X_46))) ),[1,1,0],$fot(inverse(a))]]) ).
cnf(refute_0_5794,plain,
( X_46 != multiply(b,multiply(inverse(b),X_46))
| X_46 = multiply(b,multiply(inverse(a),X_46)) ),
inference(resolve,[$cnf( $equal(inverse(b),inverse(a)) )],[refute_0_5723,refute_0_5793]) ).
cnf(refute_0_5795,plain,
X_46 = multiply(b,multiply(inverse(a),X_46)),
inference(resolve,[$cnf( $equal(X_46,multiply(b,multiply(inverse(b),X_46))) )],[refute_0_5792,refute_0_5794]) ).
cnf(refute_0_5796,plain,
( X_46 != multiply(b,multiply(inverse(a),X_46))
| multiply(b,multiply(inverse(a),X_46)) = X_46 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_46)),bind(Y0,$fot(multiply(b,multiply(inverse(a),X_46))))]]) ).
cnf(refute_0_5797,plain,
multiply(b,multiply(inverse(a),X_46)) = X_46,
inference(resolve,[$cnf( $equal(X_46,multiply(b,multiply(inverse(a),X_46))) )],[refute_0_5795,refute_0_5796]) ).
cnf(refute_0_5798,plain,
multiply(b,multiply(inverse(a),least_upper_bound(a,c))) = least_upper_bound(a,c),
inference(subst,[],[refute_0_5797:[bind(X_46,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5799,plain,
least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) = least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),
introduced(tautology,[refl,[$fot(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))))]]) ).
cnf(refute_0_5800,plain,
( multiply(b,multiply(inverse(a),least_upper_bound(a,c))) != least_upper_bound(a,c)
| least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) != least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c))))
| least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c))))) ),[1,1],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_5801,plain,
( multiply(b,multiply(inverse(a),least_upper_bound(a,c))) != least_upper_bound(a,c)
| least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(a,c)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c))))) )],[refute_0_5799,refute_0_5800]) ).
cnf(refute_0_5802,plain,
least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) = least_upper_bound(a,least_upper_bound(a,c)),
inference(resolve,[$cnf( $equal(multiply(b,multiply(inverse(a),least_upper_bound(a,c))),least_upper_bound(a,c)) )],[refute_0_5798,refute_0_5801]) ).
cnf(refute_0_5803,plain,
( least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) != least_upper_bound(a,least_upper_bound(a,c))
| least_upper_bound(a,least_upper_bound(a,c)) != least_upper_bound(a,c)
| least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) = least_upper_bound(a,c) ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(a,c)))),bind(Z0,$fot(least_upper_bound(a,c)))]]) ).
cnf(refute_0_5804,plain,
( least_upper_bound(a,least_upper_bound(a,c)) != least_upper_bound(a,c)
| least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) = least_upper_bound(a,c) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),least_upper_bound(a,least_upper_bound(a,c))) )],[refute_0_5802,refute_0_5803]) ).
cnf(refute_0_5805,plain,
least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) = least_upper_bound(a,c),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,c)),least_upper_bound(a,c)) )],[refute_0_5791,refute_0_5804]) ).
cnf(refute_0_5806,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) = multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))))]]) ).
cnf(refute_0_5807,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))
| least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) != least_upper_bound(a,c)
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) = multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))) ),[1,0],$fot(least_upper_bound(a,c))]]) ).
cnf(refute_0_5808,plain,
( least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))) != least_upper_bound(a,c)
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) = multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))),multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))) )],[refute_0_5806,refute_0_5807]) ).
cnf(refute_0_5809,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) = multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),least_upper_bound(a,c)) )],[refute_0_5805,refute_0_5808]) ).
cnf(refute_0_5810,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) != multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c)))
| multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) != a
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) = a ),
inference(subst,[],[refute_0_245:[bind(X0,$fot(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_5811,plain,
( multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))) != a
| multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) = a ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c)))) )],[refute_0_5809,refute_0_5810]) ).
cnf(refute_0_5812,plain,
multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) = a,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),multiply(inverse(c),greatest_lower_bound(a,c))),a) )],[refute_0_5790,refute_0_5811]) ).
cnf(refute_0_5813,plain,
( multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))) != a
| b != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))
| b = a ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))) ),[1],$fot(a)]]) ).
cnf(refute_0_5814,plain,
( b != multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))
| b = a ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c))),a) )],[refute_0_5812,refute_0_5813]) ).
cnf(refute_0_5815,plain,
b = a,
inference(resolve,[$cnf( $equal(b,multiply(least_upper_bound(a,multiply(b,multiply(inverse(a),least_upper_bound(a,c)))),multiply(inverse(c),greatest_lower_bound(a,c)))) )],[refute_0_5751,refute_0_5814]) ).
cnf(refute_0_5816,plain,
( a != a
| b != a
| a = b ),
introduced(tautology,[equality,[$cnf( ~ $equal(a,b) ),[1],$fot(a)]]) ).
cnf(refute_0_5817,plain,
( a != a
| a = b ),
inference(resolve,[$cnf( $equal(b,a) )],[refute_0_5815,refute_0_5816]) ).
cnf(refute_0_5818,plain,
a != a,
inference(resolve,[$cnf( $equal(a,b) )],[refute_0_5817,prove_p12]) ).
cnf(refute_0_5819,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_5820,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_5819,refute_0_5818]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP181-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 17:38:23 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 115.78/115.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 115.78/115.97
% 115.78/115.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 116.74/116.94
%------------------------------------------------------------------------------