TSTP Solution File: GRP179-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP179-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 10:37:21 EDT 2022
% Result : Unsatisfiable 222.73s 222.88s
% Output : CNFRefutation 222.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 297
% Syntax : Number of clauses : 1475 ( 768 unt; 0 nHn; 699 RR)
% Number of literals : 2485 (2484 equ;1012 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 2983 ( 35 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(prove_p10,negated_conjecture,
inverse(least_upper_bound(a,b)) != greatest_lower_bound(inverse(a),inverse(b)) ).
cnf(refute_0_0,plain,
multiply(multiply(inverse(X_30),X_30),X_31) = multiply(inverse(X_30),multiply(X_30,X_31)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_30))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_30),X_30) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(inverse(X_30),X_30),X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| multiply(inverse(X_30),X_30) != identity
| multiply(identity,X_31) = multiply(inverse(X_30),multiply(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_30),X_30),X_31),multiply(inverse(X_30),multiply(X_30,X_31))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_30),X_30),X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| multiply(identity,X_31) = multiply(inverse(X_30),multiply(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),X_30),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_31) = multiply(inverse(X_30),multiply(X_30,X_31)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_30),X_30),X_31),multiply(inverse(X_30),multiply(X_30,X_31))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_31) = X_31,
inference(subst,[],[left_identity:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_31) != X_31
| multiply(identity,X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| X_31 = multiply(inverse(X_30),multiply(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_31),multiply(inverse(X_30),multiply(X_30,X_31))) ),[0],$fot(X_31)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_31) != multiply(inverse(X_30),multiply(X_30,X_31))
| X_31 = multiply(inverse(X_30),multiply(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_31),X_31) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_31 = multiply(inverse(X_30),multiply(X_30,X_31)),
inference(resolve,[$cnf( $equal(multiply(identity,X_31),multiply(inverse(X_30),multiply(X_30,X_31))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
inverse(least_upper_bound(X_30,X_776)) = multiply(inverse(X_30),multiply(X_30,inverse(least_upper_bound(X_30,X_776)))),
inference(subst,[],[refute_0_8:[bind(X_31,$fot(inverse(least_upper_bound(X_30,X_776))))]]) ).
cnf(refute_0_10,plain,
X_33 = multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33)),
inference(subst,[],[refute_0_8:[bind(X_30,$fot(multiply(X,Y))),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(X,Y),X_33) = multiply(X,multiply(Y,X_33)),
inference(subst,[],[associativity:[bind(Z,$fot(X_33))]]) ).
cnf(refute_0_12,plain,
( X_33 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))
| multiply(multiply(X,Y),X_33) != multiply(X,multiply(Y,X_33))
| X_33 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(X_33,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))) ),[1,1],$fot(multiply(X,multiply(Y,X_33)))]]) ).
cnf(refute_0_13,plain,
( X_33 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))
| X_33 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_33))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_33),multiply(X,multiply(Y,X_33))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
X_33 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_33))),
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_33))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
inverse(X_49) = multiply(inverse(multiply(X_48,X_49)),multiply(X_48,multiply(X_49,inverse(X_49)))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_48)),bind(Y,$fot(X_49)),bind(X_33,$fot(inverse(X_49)))]]) ).
cnf(refute_0_16,plain,
multiply(inverse(inverse(X_35)),inverse(X_35)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_35)))]]) ).
cnf(refute_0_17,plain,
multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33))),
inference(subst,[],[refute_0_8:[bind(X_30,$fot(inverse(X_32))),bind(X_31,$fot(multiply(X_32,X_33)))]]) ).
cnf(refute_0_18,plain,
X_33 = multiply(inverse(X_32),multiply(X_32,X_33)),
inference(subst,[],[refute_0_8:[bind(X_30,$fot(X_32)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_19,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_20,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_21,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( X_33 != multiply(inverse(X_32),multiply(X_32,X_33))
| multiply(inverse(X_32),multiply(X_32,X_33)) = X_33 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_33)),bind(Y0,$fot(multiply(inverse(X_32),multiply(X_32,X_33))))]]) ).
cnf(refute_0_23,plain,
multiply(inverse(X_32),multiply(X_32,X_33)) = X_33,
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(X_32),multiply(X_32,X_33))) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( multiply(X_32,X_33) != multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))
| multiply(inverse(X_32),multiply(X_32,X_33)) != X_33
| multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_32,X_33),multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))) ),[1,1],$fot(X_33)]]) ).
cnf(refute_0_25,plain,
( multiply(X_32,X_33) != multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))
| multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),X_33) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_32),multiply(X_32,X_33)),X_33) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(X_32,X_33) = multiply(inverse(inverse(X_32)),X_33),
inference(resolve,[$cnf( $equal(multiply(X_32,X_33),multiply(inverse(inverse(X_32)),multiply(inverse(X_32),multiply(X_32,X_33)))) )],[refute_0_17,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_35,inverse(X_35)) = multiply(inverse(inverse(X_35)),inverse(X_35)),
inference(subst,[],[refute_0_26:[bind(X_32,$fot(X_35)),bind(X_33,$fot(inverse(X_35)))]]) ).
cnf(refute_0_28,plain,
( multiply(X_35,inverse(X_35)) != multiply(inverse(inverse(X_35)),inverse(X_35))
| multiply(inverse(inverse(X_35)),inverse(X_35)) = multiply(X_35,inverse(X_35)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_35,inverse(X_35)))),bind(Y0,$fot(multiply(inverse(inverse(X_35)),inverse(X_35))))]]) ).
cnf(refute_0_29,plain,
multiply(inverse(inverse(X_35)),inverse(X_35)) = multiply(X_35,inverse(X_35)),
inference(resolve,[$cnf( $equal(multiply(X_35,inverse(X_35)),multiply(inverse(inverse(X_35)),inverse(X_35))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiply(inverse(inverse(X_35)),inverse(X_35)) != multiply(X_35,inverse(X_35))
| multiply(inverse(inverse(X_35)),inverse(X_35)) != identity
| multiply(X_35,inverse(X_35)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_35)),inverse(X_35)),identity) ),[0],$fot(multiply(X_35,inverse(X_35)))]]) ).
cnf(refute_0_31,plain,
( multiply(inverse(inverse(X_35)),inverse(X_35)) != identity
| multiply(X_35,inverse(X_35)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),inverse(X_35)),multiply(X_35,inverse(X_35))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(X_35,inverse(X_35)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),inverse(X_35)),identity) )],[refute_0_16,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_49,inverse(X_49)) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_49))]]) ).
cnf(refute_0_34,plain,
( multiply(X_49,inverse(X_49)) != identity
| inverse(X_49) != multiply(inverse(multiply(X_48,X_49)),multiply(X_48,multiply(X_49,inverse(X_49))))
| inverse(X_49) = multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_49),multiply(inverse(multiply(X_48,X_49)),multiply(X_48,multiply(X_49,inverse(X_49))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_35,plain,
( inverse(X_49) != multiply(inverse(multiply(X_48,X_49)),multiply(X_48,multiply(X_49,inverse(X_49))))
| inverse(X_49) = multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_49,inverse(X_49)),identity) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
inverse(X_49) = multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)),
inference(resolve,[$cnf( $equal(inverse(X_49),multiply(inverse(multiply(X_48,X_49)),multiply(X_48,multiply(X_49,inverse(X_49))))) )],[refute_0_15,refute_0_35]) ).
cnf(refute_0_37,plain,
X_33 = multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33)),
inference(subst,[],[refute_0_8:[bind(X_30,$fot(inverse(X_33))),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_38,plain,
multiply(inverse(X_33),X_33) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_39,plain,
( X_33 != multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))
| multiply(inverse(X_33),X_33) != identity
| X_33 = multiply(inverse(inverse(X_33)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_33,multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_40,plain,
( X_33 != multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))
| X_33 = multiply(inverse(inverse(X_33)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),X_33),identity) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
X_33 = multiply(inverse(inverse(X_33)),identity),
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_33))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( multiply(X_32,X_33) != multiply(inverse(inverse(X_32)),X_33)
| multiply(inverse(inverse(X_32)),X_33) = multiply(X_32,X_33) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_32,X_33))),bind(Y0,$fot(multiply(inverse(inverse(X_32)),X_33)))]]) ).
cnf(refute_0_43,plain,
multiply(inverse(inverse(X_32)),X_33) = multiply(X_32,X_33),
inference(resolve,[$cnf( $equal(multiply(X_32,X_33),multiply(inverse(inverse(X_32)),X_33)) )],[refute_0_26,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(inverse(inverse(X_33)),identity) = multiply(X_33,identity),
inference(subst,[],[refute_0_43:[bind(X_32,$fot(X_33)),bind(X_33,$fot(identity))]]) ).
cnf(refute_0_45,plain,
( X_33 != multiply(inverse(inverse(X_33)),identity)
| multiply(inverse(inverse(X_33)),identity) != multiply(X_33,identity)
| X_33 = multiply(X_33,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_33,multiply(X_33,identity)) ),[0],$fot(multiply(inverse(inverse(X_33)),identity))]]) ).
cnf(refute_0_46,plain,
( X_33 != multiply(inverse(inverse(X_33)),identity)
| X_33 = multiply(X_33,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_33)),identity),multiply(X_33,identity)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
X_33 = multiply(X_33,identity),
inference(resolve,[$cnf( $equal(X_33,multiply(inverse(inverse(X_33)),identity)) )],[refute_0_41,refute_0_46]) ).
cnf(refute_0_48,plain,
( X_33 != multiply(X_33,identity)
| multiply(X_33,identity) = X_33 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_33)),bind(Y0,$fot(multiply(X_33,identity)))]]) ).
cnf(refute_0_49,plain,
multiply(X_33,identity) = X_33,
inference(resolve,[$cnf( $equal(X_33,multiply(X_33,identity)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(X_48,identity) = X_48,
inference(subst,[],[refute_0_49:[bind(X_33,$fot(X_48))]]) ).
cnf(refute_0_51,plain,
multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) = multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)))]]) ).
cnf(refute_0_52,plain,
( multiply(X_48,identity) != X_48
| multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) != multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity))
| multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) = multiply(inverse(multiply(X_48,X_49)),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)),multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity))) ),[1,1],$fot(X_48)]]) ).
cnf(refute_0_53,plain,
( multiply(X_48,identity) != X_48
| multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) = multiply(inverse(multiply(X_48,X_49)),X_48) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)),multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) = multiply(inverse(multiply(X_48,X_49)),X_48),
inference(resolve,[$cnf( $equal(multiply(X_48,identity),X_48) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)) != multiply(inverse(multiply(X_48,X_49)),X_48)
| inverse(X_49) != multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity))
| inverse(X_49) = multiply(inverse(multiply(X_48,X_49)),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_49),multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity))) ),[1],$fot(multiply(inverse(multiply(X_48,X_49)),X_48))]]) ).
cnf(refute_0_56,plain,
( inverse(X_49) != multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity))
| inverse(X_49) = multiply(inverse(multiply(X_48,X_49)),X_48) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity)),multiply(inverse(multiply(X_48,X_49)),X_48)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
inverse(X_49) = multiply(inverse(multiply(X_48,X_49)),X_48),
inference(resolve,[$cnf( $equal(inverse(X_49),multiply(inverse(multiply(X_48,X_49)),multiply(X_48,identity))) )],[refute_0_36,refute_0_56]) ).
cnf(refute_0_58,plain,
inverse(inverse(X_65)) = multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_65))),least_upper_bound(X_64,X_65)),
inference(subst,[],[refute_0_57:[bind(X_48,$fot(least_upper_bound(X_64,X_65))),bind(X_49,$fot(inverse(X_65)))]]) ).
cnf(refute_0_59,plain,
multiply(least_upper_bound(X_64,X_65),inverse(X_65)) = least_upper_bound(multiply(X_64,inverse(X_65)),multiply(X_65,inverse(X_65))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_65))),bind(Y,$fot(X_64)),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_60,plain,
multiply(X_65,inverse(X_65)) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_65))]]) ).
cnf(refute_0_61,plain,
( multiply(X_65,inverse(X_65)) != identity
| multiply(least_upper_bound(X_64,X_65),inverse(X_65)) != least_upper_bound(multiply(X_64,inverse(X_65)),multiply(X_65,inverse(X_65)))
| multiply(least_upper_bound(X_64,X_65),inverse(X_65)) = least_upper_bound(multiply(X_64,inverse(X_65)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_65)),least_upper_bound(multiply(X_64,inverse(X_65)),multiply(X_65,inverse(X_65)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_62,plain,
( multiply(least_upper_bound(X_64,X_65),inverse(X_65)) != least_upper_bound(multiply(X_64,inverse(X_65)),multiply(X_65,inverse(X_65)))
| multiply(least_upper_bound(X_64,X_65),inverse(X_65)) = least_upper_bound(multiply(X_64,inverse(X_65)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_65,inverse(X_65)),identity) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(least_upper_bound(X_64,X_65),inverse(X_65)) = least_upper_bound(multiply(X_64,inverse(X_65)),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_65)),least_upper_bound(multiply(X_64,inverse(X_65)),multiply(X_65,inverse(X_65)))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_65,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_64]) ).
cnf(refute_0_66,plain,
least_upper_bound(multiply(X_64,inverse(X_65)),identity) = least_upper_bound(identity,multiply(X_64,inverse(X_65))),
inference(subst,[],[refute_0_65:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_64,inverse(X_65))))]]) ).
cnf(refute_0_67,plain,
( multiply(least_upper_bound(X_64,X_65),inverse(X_65)) != least_upper_bound(multiply(X_64,inverse(X_65)),identity)
| least_upper_bound(multiply(X_64,inverse(X_65)),identity) != least_upper_bound(identity,multiply(X_64,inverse(X_65)))
| multiply(least_upper_bound(X_64,X_65),inverse(X_65)) = least_upper_bound(identity,multiply(X_64,inverse(X_65))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_65)),least_upper_bound(identity,multiply(X_64,inverse(X_65)))) ),[0],$fot(least_upper_bound(multiply(X_64,inverse(X_65)),identity))]]) ).
cnf(refute_0_68,plain,
( multiply(least_upper_bound(X_64,X_65),inverse(X_65)) != least_upper_bound(multiply(X_64,inverse(X_65)),identity)
| multiply(least_upper_bound(X_64,X_65),inverse(X_65)) = least_upper_bound(identity,multiply(X_64,inverse(X_65))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,inverse(X_65)),identity),least_upper_bound(identity,multiply(X_64,inverse(X_65)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
multiply(least_upper_bound(X_64,X_65),inverse(X_65)) = least_upper_bound(identity,multiply(X_64,inverse(X_65))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_65)),least_upper_bound(multiply(X_64,inverse(X_65)),identity)) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
( multiply(least_upper_bound(X_64,X_65),inverse(X_65)) != least_upper_bound(identity,multiply(X_64,inverse(X_65)))
| inverse(inverse(X_65)) != multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_65))),least_upper_bound(X_64,X_65))
| inverse(inverse(X_65)) = multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_65)),multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_65))),least_upper_bound(X_64,X_65))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_64,inverse(X_65))))]]) ).
cnf(refute_0_71,plain,
( inverse(inverse(X_65)) != multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_65))),least_upper_bound(X_64,X_65))
| inverse(inverse(X_65)) = multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_65)),least_upper_bound(identity,multiply(X_64,inverse(X_65)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
inverse(inverse(X_65)) = multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_65)),multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_65))),least_upper_bound(X_64,X_65))) )],[refute_0_58,refute_0_71]) ).
cnf(refute_0_73,plain,
inverse(inverse(X_35)) = multiply(inverse(inverse(X_35)),identity),
inference(subst,[],[refute_0_47:[bind(X_33,$fot(inverse(inverse(X_35))))]]) ).
cnf(refute_0_74,plain,
multiply(X_35,identity) = multiply(inverse(inverse(X_35)),identity),
inference(subst,[],[refute_0_26:[bind(X_32,$fot(X_35)),bind(X_33,$fot(identity))]]) ).
cnf(refute_0_75,plain,
( multiply(X_35,identity) != multiply(inverse(inverse(X_35)),identity)
| multiply(inverse(inverse(X_35)),identity) = multiply(X_35,identity) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_35,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_35)),identity)))]]) ).
cnf(refute_0_76,plain,
multiply(inverse(inverse(X_35)),identity) = multiply(X_35,identity),
inference(resolve,[$cnf( $equal(multiply(X_35,identity),multiply(inverse(inverse(X_35)),identity)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( multiply(inverse(inverse(X_35)),identity) != multiply(X_35,identity)
| inverse(inverse(X_35)) != multiply(inverse(inverse(X_35)),identity)
| inverse(inverse(X_35)) = multiply(X_35,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_35)),multiply(inverse(inverse(X_35)),identity)) ),[1],$fot(multiply(X_35,identity))]]) ).
cnf(refute_0_78,plain,
( inverse(inverse(X_35)) != multiply(inverse(inverse(X_35)),identity)
| inverse(inverse(X_35)) = multiply(X_35,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),identity),multiply(X_35,identity)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
inverse(inverse(X_35)) = multiply(X_35,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),multiply(inverse(inverse(X_35)),identity)) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(X_35,identity) = X_35,
inference(subst,[],[refute_0_49:[bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_81,plain,
( multiply(X_35,identity) != X_35
| inverse(inverse(X_35)) != multiply(X_35,identity)
| inverse(inverse(X_35)) = X_35 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_35)),multiply(X_35,identity)) ),[1],$fot(X_35)]]) ).
cnf(refute_0_82,plain,
( inverse(inverse(X_35)) != multiply(X_35,identity)
| inverse(inverse(X_35)) = X_35 ),
inference(resolve,[$cnf( $equal(multiply(X_35,identity),X_35) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
inverse(inverse(X_35)) = X_35,
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),multiply(X_35,identity)) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
inverse(inverse(X_65)) = X_65,
inference(subst,[],[refute_0_83:[bind(X_35,$fot(X_65))]]) ).
cnf(refute_0_85,plain,
( inverse(inverse(X_65)) != X_65
| inverse(inverse(X_65)) != multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65))
| X_65 = multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_65)),multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65))) ),[0],$fot(X_65)]]) ).
cnf(refute_0_86,plain,
( inverse(inverse(X_65)) != multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65))
| X_65 = multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_65)),X_65) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
X_65 = multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_65)),multiply(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),least_upper_bound(X_64,X_65))) )],[refute_0_72,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),
inference(subst,[],[refute_0_87:[bind(X_64,$fot(identity)),bind(X_65,$fot(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))]]) ).
cnf(refute_0_89,plain,
multiply(least_upper_bound(X_70,least_upper_bound(X_70,X_16)),inverse(least_upper_bound(X_70,X_16))) = least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))),
inference(subst,[],[refute_0_69:[bind(X_64,$fot(X_70)),bind(X_65,$fot(least_upper_bound(X_70,X_16)))]]) ).
cnf(refute_0_90,plain,
least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) = X_12,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_91,plain,
greatest_lower_bound(X_13,X_12) = greatest_lower_bound(X_12,X_13),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_92,plain,
( greatest_lower_bound(X_13,X_12) != greatest_lower_bound(X_12,X_13)
| greatest_lower_bound(X_12,X_13) = greatest_lower_bound(X_13,X_12) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_13,X_12))),bind(Y0,$fot(greatest_lower_bound(X_12,X_13)))]]) ).
cnf(refute_0_93,plain,
greatest_lower_bound(X_12,X_13) = greatest_lower_bound(X_13,X_12),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,X_12),greatest_lower_bound(X_12,X_13)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( greatest_lower_bound(X_12,X_13) != greatest_lower_bound(X_13,X_12)
| least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)),X_12) ),[0,1],$fot(greatest_lower_bound(X_13,X_12))]]) ).
cnf(refute_0_95,plain,
( least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,X_13),greatest_lower_bound(X_13,X_12)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12,
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)),X_12) )],[refute_0_90,refute_0_95]) ).
cnf(refute_0_97,plain,
least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) = least_upper_bound(X_15,Y),
inference(subst,[],[refute_0_96:[bind(X_12,$fot(least_upper_bound(X_15,Y))),bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_98,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_99,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) != X_15
| least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_100,plain,
( least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_103,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_102]) ).
cnf(refute_0_104,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_105,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(Y,X_15)))]]) ).
cnf(refute_0_106,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_101,refute_0_106]) ).
cnf(refute_0_108,plain,
least_upper_bound(X_17,least_upper_bound(X_16,X_17)) = least_upper_bound(X_17,X_16),
inference(subst,[],[refute_0_107:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_109,plain,
least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_110,plain,
( least_upper_bound(X_17,X_16) != least_upper_bound(X_16,X_17)
| least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_17,X_16))),bind(Y0,$fot(least_upper_bound(X_16,X_17)))]]) ).
cnf(refute_0_111,plain,
least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),least_upper_bound(X_16,X_17)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( least_upper_bound(X_16,X_17) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) ),[0,1],$fot(least_upper_bound(X_17,X_16))]]) ).
cnf(refute_0_113,plain,
( least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,X_17),least_upper_bound(X_17,X_16)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
least_upper_bound(X_70,least_upper_bound(X_70,X_16)) = least_upper_bound(X_70,X_16),
inference(subst,[],[refute_0_114:[bind(X_17,$fot(X_70))]]) ).
cnf(refute_0_116,plain,
( multiply(least_upper_bound(X_70,least_upper_bound(X_70,X_16)),inverse(least_upper_bound(X_70,X_16))) != least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))
| least_upper_bound(X_70,least_upper_bound(X_70,X_16)) != least_upper_bound(X_70,X_16)
| multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))) = least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_70,least_upper_bound(X_70,X_16)),inverse(least_upper_bound(X_70,X_16))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) ),[0,0],$fot(least_upper_bound(X_70,X_16))]]) ).
cnf(refute_0_117,plain,
( multiply(least_upper_bound(X_70,least_upper_bound(X_70,X_16)),inverse(least_upper_bound(X_70,X_16))) != least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))
| multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))) = least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_70,least_upper_bound(X_70,X_16)),least_upper_bound(X_70,X_16)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))) = least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_70,least_upper_bound(X_70,X_16)),inverse(least_upper_bound(X_70,X_16))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) )],[refute_0_89,refute_0_117]) ).
cnf(refute_0_119,plain,
multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(least_upper_bound(X_70,X_16)))]]) ).
cnf(refute_0_120,plain,
( multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))) != identity
| multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))) != least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))
| identity = least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_121,plain,
( multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))) != least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))
| identity = least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))),identity) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
identity = least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_70,X_16),inverse(least_upper_bound(X_70,X_16))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( identity != least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))
| least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) = identity ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))]]) ).
cnf(refute_0_124,plain,
least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
( multiply(X_70,inverse(least_upper_bound(X_70,X_16))) != multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))
| least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) != identity
| multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_70,inverse(least_upper_bound(X_70,X_16))),multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_126,plain,
( multiply(X_70,inverse(least_upper_bound(X_70,X_16))) != multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))
| multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))),identity) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity),
inference(resolve,[$cnf( $equal(multiply(X_70,inverse(least_upper_bound(X_70,X_16))),multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),least_upper_bound(identity,multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) )],[refute_0_88,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71))),
inference(subst,[],[refute_0_69:[bind(X_64,$fot(least_upper_bound(inverse(inverse(X_71)),X_65))),bind(X_65,$fot(X_71))]]) ).
cnf(refute_0_129,plain,
multiply(least_upper_bound(inverse(X_63),X_65),X_63) = least_upper_bound(multiply(inverse(X_63),X_63),multiply(X_65,X_63)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_63)),bind(Y,$fot(inverse(X_63))),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_130,plain,
multiply(inverse(X_63),X_63) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_131,plain,
( multiply(inverse(X_63),X_63) != identity
| multiply(least_upper_bound(inverse(X_63),X_65),X_63) != least_upper_bound(multiply(inverse(X_63),X_63),multiply(X_65,X_63))
| multiply(least_upper_bound(inverse(X_63),X_65),X_63) = least_upper_bound(identity,multiply(X_65,X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_63),X_65),X_63),least_upper_bound(multiply(inverse(X_63),X_63),multiply(X_65,X_63))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_132,plain,
( multiply(least_upper_bound(inverse(X_63),X_65),X_63) != least_upper_bound(multiply(inverse(X_63),X_63),multiply(X_65,X_63))
| multiply(least_upper_bound(inverse(X_63),X_65),X_63) = least_upper_bound(identity,multiply(X_65,X_63)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),X_63),identity) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
multiply(least_upper_bound(inverse(X_63),X_65),X_63) = least_upper_bound(identity,multiply(X_65,X_63)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_63),X_65),X_63),least_upper_bound(multiply(inverse(X_63),X_63),multiply(X_65,X_63))) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71)) = least_upper_bound(identity,multiply(X_65,inverse(X_71))),
inference(subst,[],[refute_0_133:[bind(X_63,$fot(inverse(X_71)))]]) ).
cnf(refute_0_135,plain,
( multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71)) != least_upper_bound(identity,multiply(X_65,inverse(X_71)))
| multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) != least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71)))
| multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)),least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_65,inverse(X_71))))]]) ).
cnf(refute_0_136,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) != least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71)))
| multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71)),least_upper_bound(identity,multiply(X_65,inverse(X_71)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)),least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_71)),X_65),inverse(X_71)))) )],[refute_0_128,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = least_upper_bound(multiply(least_upper_bound(X_67,inverse(X)),X),multiply(Z,X)),
inference(subst,[],[monotony_lub2:[bind(Y,$fot(least_upper_bound(X_67,inverse(X))))]]) ).
cnf(refute_0_139,plain,
multiply(least_upper_bound(X_64,inverse(X_63)),X_63) = least_upper_bound(multiply(X_64,X_63),multiply(inverse(X_63),X_63)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_63)),bind(Y,$fot(X_64)),bind(Z,$fot(inverse(X_63)))]]) ).
cnf(refute_0_140,plain,
( multiply(inverse(X_63),X_63) != identity
| multiply(least_upper_bound(X_64,inverse(X_63)),X_63) != least_upper_bound(multiply(X_64,X_63),multiply(inverse(X_63),X_63))
| multiply(least_upper_bound(X_64,inverse(X_63)),X_63) = least_upper_bound(multiply(X_64,X_63),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_64,inverse(X_63)),X_63),least_upper_bound(multiply(X_64,X_63),multiply(inverse(X_63),X_63))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_141,plain,
( multiply(least_upper_bound(X_64,inverse(X_63)),X_63) != least_upper_bound(multiply(X_64,X_63),multiply(inverse(X_63),X_63))
| multiply(least_upper_bound(X_64,inverse(X_63)),X_63) = least_upper_bound(multiply(X_64,X_63),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),X_63),identity) )],[refute_0_130,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(least_upper_bound(X_64,inverse(X_63)),X_63) = least_upper_bound(multiply(X_64,X_63),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,inverse(X_63)),X_63),least_upper_bound(multiply(X_64,X_63),multiply(inverse(X_63),X_63))) )],[refute_0_139,refute_0_141]) ).
cnf(refute_0_143,plain,
least_upper_bound(multiply(X_64,X_63),identity) = least_upper_bound(identity,multiply(X_64,X_63)),
inference(subst,[],[refute_0_65:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_64,X_63)))]]) ).
cnf(refute_0_144,plain,
( multiply(least_upper_bound(X_64,inverse(X_63)),X_63) != least_upper_bound(multiply(X_64,X_63),identity)
| least_upper_bound(multiply(X_64,X_63),identity) != least_upper_bound(identity,multiply(X_64,X_63))
| multiply(least_upper_bound(X_64,inverse(X_63)),X_63) = least_upper_bound(identity,multiply(X_64,X_63)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_64,inverse(X_63)),X_63),least_upper_bound(identity,multiply(X_64,X_63))) ),[0],$fot(least_upper_bound(multiply(X_64,X_63),identity))]]) ).
cnf(refute_0_145,plain,
( multiply(least_upper_bound(X_64,inverse(X_63)),X_63) != least_upper_bound(multiply(X_64,X_63),identity)
| multiply(least_upper_bound(X_64,inverse(X_63)),X_63) = least_upper_bound(identity,multiply(X_64,X_63)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),identity),least_upper_bound(identity,multiply(X_64,X_63))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(least_upper_bound(X_64,inverse(X_63)),X_63) = least_upper_bound(identity,multiply(X_64,X_63)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,inverse(X_63)),X_63),least_upper_bound(multiply(X_64,X_63),identity)) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(least_upper_bound(X_67,inverse(X)),X) = least_upper_bound(identity,multiply(X_67,X)),
inference(subst,[],[refute_0_146:[bind(X_63,$fot(X)),bind(X_64,$fot(X_67))]]) ).
cnf(refute_0_148,plain,
( multiply(least_upper_bound(X_67,inverse(X)),X) != least_upper_bound(identity,multiply(X_67,X))
| multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_67,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_67,inverse(X)),X),multiply(Z,X))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_67,X)))]]) ).
cnf(refute_0_149,plain,
( multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_67,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_67,inverse(X)),X),least_upper_bound(identity,multiply(X_67,X))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_67,inverse(X)),X),multiply(Z,X))) )],[refute_0_138,refute_0_149]) ).
cnf(refute_0_151,plain,
least_upper_bound(least_upper_bound(X_67,inverse(X)),Z) = least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_67)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_152,plain,
multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X))]]) ).
cnf(refute_0_153,plain,
( multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) != multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X)
| least_upper_bound(least_upper_bound(X_67,inverse(X)),Z) != least_upper_bound(X_67,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X)) ),[1,0],$fot(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_154,plain,
( least_upper_bound(least_upper_bound(X_67,inverse(X)),Z) != least_upper_bound(X_67,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) = multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),least_upper_bound(X_67,least_upper_bound(inverse(X),Z))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
( multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) != multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X)
| multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))
| multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))) ),[0],$fot(multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X))]]) ).
cnf(refute_0_157,plain,
( multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))
| multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_159,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_158]) ).
cnf(refute_0_160,plain,
least_upper_bound(multiply(X_67,X),multiply(Z,X)) = multiply(least_upper_bound(X_67,Z),X),
inference(subst,[],[refute_0_159:[bind(Y,$fot(X_67))]]) ).
cnf(refute_0_161,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))) = least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))))]]) ).
cnf(refute_0_162,plain,
( least_upper_bound(multiply(X_67,X),multiply(Z,X)) != multiply(least_upper_bound(X_67,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))) != least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X)))
| least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X)))) ),[1,1],$fot(multiply(least_upper_bound(X_67,Z),X))]]) ).
cnf(refute_0_163,plain,
( least_upper_bound(multiply(X_67,X),multiply(Z,X)) != multiply(least_upper_bound(X_67,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_67,X),multiply(Z,X)),multiply(least_upper_bound(X_67,Z),X)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) = least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))),
inference(subst,[],[refute_0_103:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_67,X))),bind(Z,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_166,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_167,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_21,refute_0_166]) ).
cnf(refute_0_168,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) != least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X)))
| least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X))))]]) ).
cnf(refute_0_169,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)),least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X)))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_67,X),multiply(Z,X))),least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X))) )],[refute_0_164,refute_0_169]) ).
cnf(refute_0_171,plain,
( multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))
| least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)) != least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X))
| multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X),least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)))]]) ).
cnf(refute_0_172,plain,
( multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))
| multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X)),least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))
| multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X),least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))) )],[refute_0_157,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(least_upper_bound(X_67,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_67,Z),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_67,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_67,X)),multiply(Z,X))) )],[refute_0_150,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71)) = least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))),
inference(subst,[],[refute_0_174:[bind(X,$fot(inverse(X_71))),bind(Z,$fot(X_65)),bind(X_67,$fot(X_71))]]) ).
cnf(refute_0_176,plain,
least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63)),
inference(subst,[],[refute_0_114:[bind(X_16,$fot(multiply(X_65,X_63))),bind(X_17,$fot(multiply(X_64,X_63)))]]) ).
cnf(refute_0_177,plain,
multiply(least_upper_bound(X_64,X_65),X_63) = least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_63)),bind(Y,$fot(X_64)),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_178,plain,
( multiply(least_upper_bound(X_64,X_65),X_63) != least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))
| least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63)) = multiply(least_upper_bound(X_64,X_65),X_63) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(X_64,X_65),X_63))),bind(Y0,$fot(least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))))]]) ).
cnf(refute_0_179,plain,
least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63)) = multiply(least_upper_bound(X_64,X_65),X_63),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63)) != multiply(least_upper_bound(X_64,X_65),X_63)
| least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) != least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))
| least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = multiply(least_upper_bound(X_64,X_65),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) ),[1],$fot(multiply(least_upper_bound(X_64,X_65),X_63))]]) ).
cnf(refute_0_181,plain,
( least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) != least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))
| least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = multiply(least_upper_bound(X_64,X_65),X_63) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63)),multiply(least_upper_bound(X_64,X_65),X_63)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = multiply(least_upper_bound(X_64,X_65),X_63),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) )],[refute_0_176,refute_0_181]) ).
cnf(refute_0_183,plain,
least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)) = multiply(least_upper_bound(X_65,X_64),X_63),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_63)),bind(Y,$fot(X_65)),bind(Z,$fot(X_64))]]) ).
cnf(refute_0_184,plain,
least_upper_bound(X_63,X_63) = X_63,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_185,plain,
multiply(X_64,least_upper_bound(X_63,X_63)) = multiply(X_64,least_upper_bound(X_63,X_63)),
introduced(tautology,[refl,[$fot(multiply(X_64,least_upper_bound(X_63,X_63)))]]) ).
cnf(refute_0_186,plain,
( multiply(X_64,least_upper_bound(X_63,X_63)) != multiply(X_64,least_upper_bound(X_63,X_63))
| least_upper_bound(X_63,X_63) != X_63
| multiply(X_64,least_upper_bound(X_63,X_63)) = multiply(X_64,X_63) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_64,least_upper_bound(X_63,X_63)),multiply(X_64,least_upper_bound(X_63,X_63))) ),[1,1],$fot(X_63)]]) ).
cnf(refute_0_187,plain,
( least_upper_bound(X_63,X_63) != X_63
| multiply(X_64,least_upper_bound(X_63,X_63)) = multiply(X_64,X_63) ),
inference(resolve,[$cnf( $equal(multiply(X_64,least_upper_bound(X_63,X_63)),multiply(X_64,least_upper_bound(X_63,X_63))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(X_64,least_upper_bound(X_63,X_63)) = multiply(X_64,X_63),
inference(resolve,[$cnf( $equal(least_upper_bound(X_63,X_63),X_63) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) = least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))))]]) ).
cnf(refute_0_190,plain,
( multiply(X_64,least_upper_bound(X_63,X_63)) != multiply(X_64,X_63)
| least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) != least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63)))
| least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) = least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))),least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63)))) ),[1,1],$fot(multiply(X_64,X_63))]]) ).
cnf(refute_0_191,plain,
( multiply(X_64,least_upper_bound(X_63,X_63)) != multiply(X_64,X_63)
| least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) = least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))),least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63)))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) = least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)),
inference(resolve,[$cnf( $equal(multiply(X_64,least_upper_bound(X_63,X_63)),multiply(X_64,X_63)) )],[refute_0_188,refute_0_191]) ).
cnf(refute_0_193,plain,
( least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)) != multiply(least_upper_bound(X_65,X_64),X_63)
| least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) != least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63))
| least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) = multiply(least_upper_bound(X_65,X_64),X_63) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))))),bind(Y0,$fot(least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)))),bind(Z0,$fot(multiply(least_upper_bound(X_65,X_64),X_63)))]]) ).
cnf(refute_0_194,plain,
( least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)) != multiply(least_upper_bound(X_65,X_64),X_63)
| least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) = multiply(least_upper_bound(X_65,X_64),X_63) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))),least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) = multiply(least_upper_bound(X_65,X_64),X_63),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_65,X_63),multiply(X_64,X_63)),multiply(least_upper_bound(X_65,X_64),X_63)) )],[refute_0_183,refute_0_194]) ).
cnf(refute_0_196,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_197,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X))]]) ).
cnf(refute_0_198,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),X)))]]) ).
cnf(refute_0_199,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),X))]]) ).
cnf(refute_0_201,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_196,refute_0_201]) ).
cnf(refute_0_203,plain,
least_upper_bound(X,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))) = least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X)),
inference(subst,[],[refute_0_202:[bind(X_18,$fot(multiply(X_51,X_52))),bind(X_19,$fot(multiply(X_51,X_53)))]]) ).
cnf(refute_0_204,plain,
multiply(X_51,least_upper_bound(X_52,X_53)) = least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_205,plain,
( multiply(X_51,least_upper_bound(X_52,X_53)) != least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))
| least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)) = multiply(X_51,least_upper_bound(X_52,X_53)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_51,least_upper_bound(X_52,X_53)))),bind(Y0,$fot(least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))))]]) ).
cnf(refute_0_206,plain,
least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)) = multiply(X_51,least_upper_bound(X_52,X_53)),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,X_53)),least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))) != least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X))
| least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)) != multiply(X_51,least_upper_bound(X_52,X_53))
| least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))) = least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))),least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X))) ),[0,1],$fot(multiply(X_51,least_upper_bound(X_52,X_53)))]]) ).
cnf(refute_0_208,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))) != least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X))
| least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))) = least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)),multiply(X_51,least_upper_bound(X_52,X_53))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))) = least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))),least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X))) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
( least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))) != least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X))
| least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X)) = least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))))),bind(Y0,$fot(least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X))))]]) ).
cnf(refute_0_211,plain,
least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X)) = least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X_51,least_upper_bound(X_52,X_53))),least_upper_bound(multiply(X_51,X_52),least_upper_bound(multiply(X_51,X_53),X))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))),
inference(subst,[],[refute_0_211:[bind(X,$fot(multiply(X_65,X_63))),bind(X_51,$fot(X_64)),bind(X_52,$fot(X_63)),bind(X_53,$fot(X_63))]]) ).
cnf(refute_0_213,plain,
( least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) != least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63)))
| least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) != multiply(least_upper_bound(X_65,X_64),X_63)
| least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = multiply(least_upper_bound(X_65,X_64),X_63) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))))),bind(Y0,$fot(least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))))),bind(Z0,$fot(multiply(least_upper_bound(X_65,X_64),X_63)))]]) ).
cnf(refute_0_214,plain,
( least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))) != multiply(least_upper_bound(X_65,X_64),X_63)
| least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = multiply(least_upper_bound(X_65,X_64),X_63) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))),least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63)))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) = multiply(least_upper_bound(X_65,X_64),X_63),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_65,X_63),multiply(X_64,least_upper_bound(X_63,X_63))),multiply(least_upper_bound(X_65,X_64),X_63)) )],[refute_0_195,refute_0_214]) ).
cnf(refute_0_216,plain,
( least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) != multiply(least_upper_bound(X_64,X_65),X_63)
| least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) != multiply(least_upper_bound(X_65,X_64),X_63)
| multiply(least_upper_bound(X_65,X_64),X_63) = multiply(least_upper_bound(X_64,X_65),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))),multiply(least_upper_bound(X_64,X_65),X_63)) ),[0],$fot(multiply(least_upper_bound(X_65,X_64),X_63))]]) ).
cnf(refute_0_217,plain,
( least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))) != multiply(least_upper_bound(X_64,X_65),X_63)
| multiply(least_upper_bound(X_65,X_64),X_63) = multiply(least_upper_bound(X_64,X_65),X_63) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))),multiply(least_upper_bound(X_65,X_64),X_63)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
multiply(least_upper_bound(X_65,X_64),X_63) = multiply(least_upper_bound(X_64,X_65),X_63),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),least_upper_bound(multiply(X_64,X_63),multiply(X_65,X_63))),multiply(least_upper_bound(X_64,X_65),X_63)) )],[refute_0_182,refute_0_217]) ).
cnf(refute_0_219,plain,
( multiply(least_upper_bound(X_65,X_64),X_63) != multiply(least_upper_bound(X_64,X_65),X_63)
| multiply(least_upper_bound(X_64,X_65),X_63) = multiply(least_upper_bound(X_65,X_64),X_63) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(X_65,X_64),X_63))),bind(Y0,$fot(multiply(least_upper_bound(X_64,X_65),X_63)))]]) ).
cnf(refute_0_220,plain,
multiply(least_upper_bound(X_64,X_65),X_63) = multiply(least_upper_bound(X_65,X_64),X_63),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_65,X_64),X_63),multiply(least_upper_bound(X_64,X_65),X_63)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71)),
inference(subst,[],[refute_0_220:[bind(X_63,$fot(inverse(X_71))),bind(X_64,$fot(least_upper_bound(inverse(inverse(X_71)),X_65))),bind(X_65,$fot(X_71))]]) ).
cnf(refute_0_222,plain,
( multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71)) != least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71)))
| multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) != multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71))
| multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)))),bind(Y0,$fot(multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71)))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71)))))]]) ).
cnf(refute_0_223,plain,
( multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71)) != least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71)))
| multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)),multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) = least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_71,least_upper_bound(inverse(inverse(X_71)),X_65)),inverse(X_71)),least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71)))) )],[refute_0_175,refute_0_223]) ).
cnf(refute_0_225,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) != least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71)))
| multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))
| least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))))]]) ).
cnf(refute_0_226,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))
| least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)),least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71)))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))) = least_upper_bound(identity,multiply(X_65,inverse(X_71))),
inference(subst,[],[refute_0_114:[bind(X_16,$fot(multiply(X_65,inverse(X_71)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_228,plain,
( least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))) != least_upper_bound(identity,multiply(X_65,inverse(X_71)))
| least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) = least_upper_bound(identity,multiply(X_65,inverse(X_71))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))),least_upper_bound(identity,multiply(X_65,inverse(X_71)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))))]]) ).
cnf(refute_0_229,plain,
( least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))
| least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) = least_upper_bound(identity,multiply(X_65,inverse(X_71))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71)))),least_upper_bound(identity,multiply(X_65,inverse(X_71)))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))
| least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) = least_upper_bound(identity,multiply(X_65,inverse(X_71))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_71,X_65),inverse(X_71))) = least_upper_bound(identity,multiply(X_65,inverse(X_71))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_71)),X_65),X_71),inverse(X_71)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_65,inverse(X_71))))) )],[refute_0_137,refute_0_230]) ).
cnf(refute_0_232,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))) = least_upper_bound(identity,multiply(X_16,inverse(X_70))),
inference(subst,[],[refute_0_231:[bind(X_65,$fot(X_16)),bind(X_71,$fot(X_70))]]) ).
cnf(refute_0_233,plain,
inverse(multiply(X_30,X_31)) = multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30)),
inference(subst,[],[refute_0_57:[bind(X_48,$fot(inverse(X_30))),bind(X_49,$fot(multiply(X_30,X_31)))]]) ).
cnf(refute_0_234,plain,
( X_31 != multiply(inverse(X_30),multiply(X_30,X_31))
| multiply(inverse(X_30),multiply(X_30,X_31)) = X_31 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(inverse(X_30),multiply(X_30,X_31))))]]) ).
cnf(refute_0_235,plain,
multiply(inverse(X_30),multiply(X_30,X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(X_30),multiply(X_30,X_31))) )],[refute_0_8,refute_0_234]) ).
cnf(refute_0_236,plain,
( multiply(inverse(X_30),multiply(X_30,X_31)) != X_31
| inverse(multiply(X_30,X_31)) != multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))
| inverse(multiply(X_30,X_31)) = multiply(inverse(X_31),inverse(X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_30,X_31)),multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))) ),[1,0,0],$fot(X_31)]]) ).
cnf(refute_0_237,plain,
( inverse(multiply(X_30,X_31)) != multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))
| inverse(multiply(X_30,X_31)) = multiply(inverse(X_31),inverse(X_30)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),multiply(X_30,X_31)),X_31) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
inverse(multiply(X_30,X_31)) = multiply(inverse(X_31),inverse(X_30)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,X_31)),multiply(inverse(multiply(inverse(X_30),multiply(X_30,X_31))),inverse(X_30))) )],[refute_0_233,refute_0_237]) ).
cnf(refute_0_239,plain,
inverse(multiply(X_152,inverse(X_35))) = multiply(inverse(inverse(X_35)),inverse(X_152)),
inference(subst,[],[refute_0_238:[bind(X_30,$fot(X_152)),bind(X_31,$fot(inverse(X_35)))]]) ).
cnf(refute_0_240,plain,
( inverse(multiply(X_152,inverse(X_35))) != multiply(inverse(inverse(X_35)),inverse(X_152))
| inverse(inverse(X_35)) != X_35
| inverse(multiply(X_152,inverse(X_35))) = multiply(X_35,inverse(X_152)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_152,inverse(X_35))),multiply(inverse(inverse(X_35)),inverse(X_152))) ),[1,0],$fot(X_35)]]) ).
cnf(refute_0_241,plain,
( inverse(multiply(X_152,inverse(X_35))) != multiply(inverse(inverse(X_35)),inverse(X_152))
| inverse(multiply(X_152,inverse(X_35))) = multiply(X_35,inverse(X_152)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),X_35) )],[refute_0_83,refute_0_240]) ).
cnf(refute_0_242,plain,
inverse(multiply(X_152,inverse(X_35))) = multiply(X_35,inverse(X_152)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_152,inverse(X_35))),multiply(inverse(inverse(X_35)),inverse(X_152))) )],[refute_0_239,refute_0_241]) ).
cnf(refute_0_243,plain,
inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) = multiply(least_upper_bound(X_70,X_16),inverse(X_70)),
inference(subst,[],[refute_0_242:[bind(X_152,$fot(X_70)),bind(X_35,$fot(least_upper_bound(X_70,X_16)))]]) ).
cnf(refute_0_244,plain,
least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))]]) ).
cnf(refute_0_245,plain,
( inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) != multiply(least_upper_bound(X_70,X_16),inverse(X_70))
| least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))
| least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) ),[1,1],$fot(multiply(least_upper_bound(X_70,X_16),inverse(X_70)))]]) ).
cnf(refute_0_246,plain,
( inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))) != multiply(least_upper_bound(X_70,X_16),inverse(X_70))
| least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))),multiply(least_upper_bound(X_70,X_16),inverse(X_70))) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(inverse(identity),identity) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_249,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_47:[bind(X_33,$fot(inverse(identity)))]]) ).
cnf(refute_0_250,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_251,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
( multiply(inverse(identity),identity) != identity
| multiply(inverse(identity),identity) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_253,plain,
( multiply(inverse(identity),identity) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_248,refute_0_253]) ).
cnf(refute_0_255,plain,
least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))]]) ).
cnf(refute_0_256,plain,
( inverse(identity) != identity
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_257,plain,
( inverse(identity) != identity
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
( least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70)))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70)))))]]) ).
cnf(refute_0_260,plain,
( least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70)))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70)))) )],[refute_0_247,refute_0_260]) ).
cnf(refute_0_262,plain,
( least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))) != least_upper_bound(identity,multiply(X_16,inverse(X_70)))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70)))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(X_16,inverse(X_70))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_16,inverse(X_70)))))]]) ).
cnf(refute_0_263,plain,
( least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))) != least_upper_bound(identity,multiply(X_16,inverse(X_70)))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(X_16,inverse(X_70))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) = least_upper_bound(identity,multiply(X_16,inverse(X_70))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_70,X_16),inverse(X_70))),least_upper_bound(identity,multiply(X_16,inverse(X_70)))) )],[refute_0_232,refute_0_263]) ).
cnf(refute_0_265,plain,
inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) = inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))))]]) ).
cnf(refute_0_266,plain,
( inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) != inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))
| least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(identity,multiply(X_16,inverse(X_70)))
| inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))),inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_16,inverse(X_70))))]]) ).
cnf(refute_0_267,plain,
( least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))) != least_upper_bound(identity,multiply(X_16,inverse(X_70)))
| inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))),inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))),least_upper_bound(identity,multiply(X_16,inverse(X_70)))) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
inverse(least_upper_bound(inverse(X_141),X_53)) = multiply(inverse(multiply(X_141,least_upper_bound(inverse(X_141),X_53))),X_141),
inference(subst,[],[refute_0_57:[bind(X_48,$fot(X_141)),bind(X_49,$fot(least_upper_bound(inverse(X_141),X_53)))]]) ).
cnf(refute_0_270,plain,
multiply(X_51,least_upper_bound(inverse(X_51),X_53)) = least_upper_bound(multiply(X_51,inverse(X_51)),multiply(X_51,X_53)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_51)),bind(Y,$fot(inverse(X_51))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_271,plain,
multiply(X_51,inverse(X_51)) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_51))]]) ).
cnf(refute_0_272,plain,
( multiply(X_51,inverse(X_51)) != identity
| multiply(X_51,least_upper_bound(inverse(X_51),X_53)) != least_upper_bound(multiply(X_51,inverse(X_51)),multiply(X_51,X_53))
| multiply(X_51,least_upper_bound(inverse(X_51),X_53)) = least_upper_bound(identity,multiply(X_51,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,least_upper_bound(inverse(X_51),X_53)),least_upper_bound(multiply(X_51,inverse(X_51)),multiply(X_51,X_53))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_273,plain,
( multiply(X_51,least_upper_bound(inverse(X_51),X_53)) != least_upper_bound(multiply(X_51,inverse(X_51)),multiply(X_51,X_53))
| multiply(X_51,least_upper_bound(inverse(X_51),X_53)) = least_upper_bound(identity,multiply(X_51,X_53)) ),
inference(resolve,[$cnf( $equal(multiply(X_51,inverse(X_51)),identity) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
multiply(X_51,least_upper_bound(inverse(X_51),X_53)) = least_upper_bound(identity,multiply(X_51,X_53)),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(inverse(X_51),X_53)),least_upper_bound(multiply(X_51,inverse(X_51)),multiply(X_51,X_53))) )],[refute_0_270,refute_0_273]) ).
cnf(refute_0_275,plain,
multiply(X_141,least_upper_bound(inverse(X_141),X_53)) = least_upper_bound(identity,multiply(X_141,X_53)),
inference(subst,[],[refute_0_274:[bind(X_51,$fot(X_141))]]) ).
cnf(refute_0_276,plain,
( multiply(X_141,least_upper_bound(inverse(X_141),X_53)) != least_upper_bound(identity,multiply(X_141,X_53))
| inverse(least_upper_bound(inverse(X_141),X_53)) != multiply(inverse(multiply(X_141,least_upper_bound(inverse(X_141),X_53))),X_141)
| inverse(least_upper_bound(inverse(X_141),X_53)) = multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_141),X_53)),multiply(inverse(multiply(X_141,least_upper_bound(inverse(X_141),X_53))),X_141)) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_141,X_53)))]]) ).
cnf(refute_0_277,plain,
( inverse(least_upper_bound(inverse(X_141),X_53)) != multiply(inverse(multiply(X_141,least_upper_bound(inverse(X_141),X_53))),X_141)
| inverse(least_upper_bound(inverse(X_141),X_53)) = multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141) ),
inference(resolve,[$cnf( $equal(multiply(X_141,least_upper_bound(inverse(X_141),X_53)),least_upper_bound(identity,multiply(X_141,X_53))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
inverse(least_upper_bound(inverse(X_141),X_53)) = multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_141),X_53)),multiply(inverse(multiply(X_141,least_upper_bound(inverse(X_141),X_53))),X_141)) )],[refute_0_269,refute_0_277]) ).
cnf(refute_0_279,plain,
( inverse(least_upper_bound(inverse(X_141),X_53)) != multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141)
| multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141) = inverse(least_upper_bound(inverse(X_141),X_53)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(inverse(X_141),X_53)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141)))]]) ).
cnf(refute_0_280,plain,
multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141) = inverse(least_upper_bound(inverse(X_141),X_53)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_141),X_53)),multiply(inverse(least_upper_bound(identity,multiply(X_141,X_53))),X_141)) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) = inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))),
inference(subst,[],[refute_0_280:[bind(X_141,$fot(identity)),bind(X_53,$fot(inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))]]) ).
cnf(refute_0_282,plain,
( multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) != inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))
| inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) != inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))
| multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity))),bind(Y0,$fot(inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))))]]) ).
cnf(refute_0_283,plain,
( inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))) != inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))
| multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity),inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(identity),inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16)))))),inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))) )],[refute_0_268,refute_0_283]) ).
cnf(refute_0_285,plain,
( multiply(X_70,inverse(least_upper_bound(X_70,X_16))) != multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity)
| multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity) != inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))
| multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_70,inverse(least_upper_bound(X_70,X_16))),inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))) ),[0],$fot(multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity))]]) ).
cnf(refute_0_286,plain,
( multiply(X_70,inverse(least_upper_bound(X_70,X_16))) != multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity)
| multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity),inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))),
inference(resolve,[$cnf( $equal(multiply(X_70,inverse(least_upper_bound(X_70,X_16))),multiply(inverse(least_upper_bound(identity,multiply(identity,inverse(multiply(X_70,inverse(least_upper_bound(X_70,X_16))))))),identity)) )],[refute_0_127,refute_0_286]) ).
cnf(refute_0_288,plain,
inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))),
inference(subst,[],[refute_0_238:[bind(X_30,$fot(inverse(X_59))),bind(X_31,$fot(least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_289,plain,
multiply(inverse(X_53),least_upper_bound(X_52,X_53)) = least_upper_bound(multiply(inverse(X_53),X_52),multiply(inverse(X_53),X_53)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_53))),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_290,plain,
multiply(inverse(X_53),X_53) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_53))]]) ).
cnf(refute_0_291,plain,
( multiply(inverse(X_53),X_53) != identity
| multiply(inverse(X_53),least_upper_bound(X_52,X_53)) != least_upper_bound(multiply(inverse(X_53),X_52),multiply(inverse(X_53),X_53))
| multiply(inverse(X_53),least_upper_bound(X_52,X_53)) = least_upper_bound(multiply(inverse(X_53),X_52),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_53),least_upper_bound(X_52,X_53)),least_upper_bound(multiply(inverse(X_53),X_52),multiply(inverse(X_53),X_53))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_292,plain,
( multiply(inverse(X_53),least_upper_bound(X_52,X_53)) != least_upper_bound(multiply(inverse(X_53),X_52),multiply(inverse(X_53),X_53))
| multiply(inverse(X_53),least_upper_bound(X_52,X_53)) = least_upper_bound(multiply(inverse(X_53),X_52),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_53),X_53),identity) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
multiply(inverse(X_53),least_upper_bound(X_52,X_53)) = least_upper_bound(multiply(inverse(X_53),X_52),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_53),least_upper_bound(X_52,X_53)),least_upper_bound(multiply(inverse(X_53),X_52),multiply(inverse(X_53),X_53))) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
least_upper_bound(multiply(inverse(X_53),X_52),identity) = least_upper_bound(identity,multiply(inverse(X_53),X_52)),
inference(subst,[],[refute_0_65:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_53),X_52)))]]) ).
cnf(refute_0_295,plain,
( multiply(inverse(X_53),least_upper_bound(X_52,X_53)) != least_upper_bound(multiply(inverse(X_53),X_52),identity)
| least_upper_bound(multiply(inverse(X_53),X_52),identity) != least_upper_bound(identity,multiply(inverse(X_53),X_52))
| multiply(inverse(X_53),least_upper_bound(X_52,X_53)) = least_upper_bound(identity,multiply(inverse(X_53),X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_53),least_upper_bound(X_52,X_53)),least_upper_bound(identity,multiply(inverse(X_53),X_52))) ),[0],$fot(least_upper_bound(multiply(inverse(X_53),X_52),identity))]]) ).
cnf(refute_0_296,plain,
( multiply(inverse(X_53),least_upper_bound(X_52,X_53)) != least_upper_bound(multiply(inverse(X_53),X_52),identity)
| multiply(inverse(X_53),least_upper_bound(X_52,X_53)) = least_upper_bound(identity,multiply(inverse(X_53),X_52)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_53),X_52),identity),least_upper_bound(identity,multiply(inverse(X_53),X_52))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
multiply(inverse(X_53),least_upper_bound(X_52,X_53)) = least_upper_bound(identity,multiply(inverse(X_53),X_52)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_53),least_upper_bound(X_52,X_53)),least_upper_bound(multiply(inverse(X_53),X_52),identity)) )],[refute_0_293,refute_0_296]) ).
cnf(refute_0_298,plain,
multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,multiply(inverse(X_59),identity)),
inference(subst,[],[refute_0_297:[bind(X_52,$fot(identity)),bind(X_53,$fot(X_59))]]) ).
cnf(refute_0_299,plain,
inverse(X_59) = multiply(inverse(X_59),identity),
inference(subst,[],[refute_0_47:[bind(X_33,$fot(inverse(X_59)))]]) ).
cnf(refute_0_300,plain,
( inverse(X_59) != multiply(inverse(X_59),identity)
| multiply(inverse(X_59),identity) = inverse(X_59) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(X_59))),bind(Y0,$fot(multiply(inverse(X_59),identity)))]]) ).
cnf(refute_0_301,plain,
multiply(inverse(X_59),identity) = inverse(X_59),
inference(resolve,[$cnf( $equal(inverse(X_59),multiply(inverse(X_59),identity)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
( multiply(inverse(X_59),identity) != inverse(X_59)
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(identity,multiply(inverse(X_59),identity))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,inverse(X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(identity,multiply(inverse(X_59),identity))) ),[1,1],$fot(inverse(X_59))]]) ).
cnf(refute_0_303,plain,
( multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(identity,multiply(inverse(X_59),identity))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,inverse(X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),identity),inverse(X_59)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,inverse(X_59)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(identity,multiply(inverse(X_59),identity))) )],[refute_0_298,refute_0_303]) ).
cnf(refute_0_305,plain,
( multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(identity,inverse(X_59))
| inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))
| inverse(least_upper_bound(identity,inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_59)))]]) ).
cnf(refute_0_306,plain,
( inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))
| inverse(least_upper_bound(identity,inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(identity,inverse(X_59))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
inverse(least_upper_bound(identity,inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))) )],[refute_0_288,refute_0_306]) ).
cnf(refute_0_308,plain,
inverse(multiply(inverse(X_141),X_31)) = multiply(inverse(multiply(X_141,multiply(inverse(X_141),X_31))),X_141),
inference(subst,[],[refute_0_57:[bind(X_48,$fot(X_141)),bind(X_49,$fot(multiply(inverse(X_141),X_31)))]]) ).
cnf(refute_0_309,plain,
X_31 = multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)),
inference(subst,[],[refute_0_8:[bind(X_30,$fot(inverse(X_35)))]]) ).
cnf(refute_0_310,plain,
multiply(X_35,multiply(inverse(X_35),X_31)) = multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)),
inference(subst,[],[refute_0_26:[bind(X_32,$fot(X_35)),bind(X_33,$fot(multiply(inverse(X_35),X_31)))]]) ).
cnf(refute_0_311,plain,
( multiply(X_35,multiply(inverse(X_35),X_31)) != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))
| multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)) = multiply(X_35,multiply(inverse(X_35),X_31)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_35,multiply(inverse(X_35),X_31)))),bind(Y0,$fot(multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))))]]) ).
cnf(refute_0_312,plain,
multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)) = multiply(X_35,multiply(inverse(X_35),X_31)),
inference(resolve,[$cnf( $equal(multiply(X_35,multiply(inverse(X_35),X_31)),multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
( X_31 != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))
| multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)) != multiply(X_35,multiply(inverse(X_35),X_31))
| X_31 = multiply(X_35,multiply(inverse(X_35),X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,multiply(X_35,multiply(inverse(X_35),X_31))) ),[0],$fot(multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)))]]) ).
cnf(refute_0_314,plain,
( X_31 != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))
| X_31 = multiply(X_35,multiply(inverse(X_35),X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31)),multiply(X_35,multiply(inverse(X_35),X_31))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
X_31 = multiply(X_35,multiply(inverse(X_35),X_31)),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(inverse(X_35)),multiply(inverse(X_35),X_31))) )],[refute_0_309,refute_0_314]) ).
cnf(refute_0_316,plain,
X_31 = multiply(X_141,multiply(inverse(X_141),X_31)),
inference(subst,[],[refute_0_315:[bind(X_35,$fot(X_141))]]) ).
cnf(refute_0_317,plain,
( X_31 != multiply(X_141,multiply(inverse(X_141),X_31))
| multiply(X_141,multiply(inverse(X_141),X_31)) = X_31 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(X_141,multiply(inverse(X_141),X_31))))]]) ).
cnf(refute_0_318,plain,
multiply(X_141,multiply(inverse(X_141),X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(X_141,multiply(inverse(X_141),X_31))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
( multiply(X_141,multiply(inverse(X_141),X_31)) != X_31
| inverse(multiply(inverse(X_141),X_31)) != multiply(inverse(multiply(X_141,multiply(inverse(X_141),X_31))),X_141)
| inverse(multiply(inverse(X_141),X_31)) = multiply(inverse(X_31),X_141) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_141),X_31)),multiply(inverse(multiply(X_141,multiply(inverse(X_141),X_31))),X_141)) ),[1,0,0],$fot(X_31)]]) ).
cnf(refute_0_320,plain,
( inverse(multiply(inverse(X_141),X_31)) != multiply(inverse(multiply(X_141,multiply(inverse(X_141),X_31))),X_141)
| inverse(multiply(inverse(X_141),X_31)) = multiply(inverse(X_31),X_141) ),
inference(resolve,[$cnf( $equal(multiply(X_141,multiply(inverse(X_141),X_31)),X_31) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
inverse(multiply(inverse(X_141),X_31)) = multiply(inverse(X_31),X_141),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_141),X_31)),multiply(inverse(multiply(X_141,multiply(inverse(X_141),X_31))),X_141)) )],[refute_0_308,refute_0_320]) ).
cnf(refute_0_322,plain,
inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),X_59),
inference(subst,[],[refute_0_321:[bind(X_141,$fot(X_59)),bind(X_31,$fot(least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_323,plain,
( inverse(multiply(X_30,X_31)) != multiply(inverse(X_31),inverse(X_30))
| multiply(inverse(X_31),inverse(X_30)) = inverse(multiply(X_30,X_31)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(multiply(X_30,X_31)))),bind(Y0,$fot(multiply(inverse(X_31),inverse(X_30))))]]) ).
cnf(refute_0_324,plain,
multiply(inverse(X_31),inverse(X_30)) = inverse(multiply(X_30,X_31)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,X_31)),multiply(inverse(X_31),inverse(X_30))) )],[refute_0_238,refute_0_323]) ).
cnf(refute_0_325,plain,
multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) = inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),
inference(subst,[],[refute_0_324:[bind(X_30,$fot(inverse(X_59))),bind(X_31,$fot(least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_326,plain,
( multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) != inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59)))
| inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),X_59)
| multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),X_59) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))))),bind(Y0,$fot(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,X_59)),X_59)))]]) ).
cnf(refute_0_327,plain,
( inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),X_59)
| multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),X_59) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))),inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59)))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),X_59),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),multiply(inverse(least_upper_bound(identity,X_59)),X_59)) )],[refute_0_322,refute_0_327]) ).
cnf(refute_0_329,plain,
( multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),X_59)
| inverse(least_upper_bound(identity,inverse(X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))
| inverse(least_upper_bound(identity,inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_59))),multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))) ),[1],$fot(multiply(inverse(least_upper_bound(identity,X_59)),X_59))]]) ).
cnf(refute_0_330,plain,
( inverse(least_upper_bound(identity,inverse(X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))
| inverse(least_upper_bound(identity,inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),X_59) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59))),multiply(inverse(least_upper_bound(identity,X_59)),X_59)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
inverse(least_upper_bound(identity,inverse(X_59))) = multiply(inverse(least_upper_bound(identity,X_59)),X_59),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_59))),multiply(inverse(least_upper_bound(identity,X_59)),inverse(inverse(X_59)))) )],[refute_0_307,refute_0_330]) ).
cnf(refute_0_332,plain,
multiply(least_upper_bound(X_64,identity),X_63) = least_upper_bound(multiply(X_64,X_63),multiply(identity,X_63)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_63)),bind(Y,$fot(X_64)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_333,plain,
multiply(identity,X_63) = X_63,
inference(subst,[],[left_identity:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_334,plain,
( multiply(identity,X_63) != X_63
| multiply(least_upper_bound(X_64,identity),X_63) != least_upper_bound(multiply(X_64,X_63),multiply(identity,X_63))
| multiply(least_upper_bound(X_64,identity),X_63) = least_upper_bound(multiply(X_64,X_63),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_64,identity),X_63),least_upper_bound(multiply(X_64,X_63),multiply(identity,X_63))) ),[1,1],$fot(X_63)]]) ).
cnf(refute_0_335,plain,
( multiply(least_upper_bound(X_64,identity),X_63) != least_upper_bound(multiply(X_64,X_63),multiply(identity,X_63))
| multiply(least_upper_bound(X_64,identity),X_63) = least_upper_bound(multiply(X_64,X_63),X_63) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_63),X_63) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
multiply(least_upper_bound(X_64,identity),X_63) = least_upper_bound(multiply(X_64,X_63),X_63),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,identity),X_63),least_upper_bound(multiply(X_64,X_63),multiply(identity,X_63))) )],[refute_0_332,refute_0_335]) ).
cnf(refute_0_337,plain,
least_upper_bound(multiply(X_64,X_63),X_63) = least_upper_bound(X_63,multiply(X_64,X_63)),
inference(subst,[],[refute_0_65:[bind(X,$fot(X_63)),bind(Y,$fot(multiply(X_64,X_63)))]]) ).
cnf(refute_0_338,plain,
( multiply(least_upper_bound(X_64,identity),X_63) != least_upper_bound(multiply(X_64,X_63),X_63)
| least_upper_bound(multiply(X_64,X_63),X_63) != least_upper_bound(X_63,multiply(X_64,X_63))
| multiply(least_upper_bound(X_64,identity),X_63) = least_upper_bound(X_63,multiply(X_64,X_63)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_64,identity),X_63),least_upper_bound(X_63,multiply(X_64,X_63))) ),[0],$fot(least_upper_bound(multiply(X_64,X_63),X_63))]]) ).
cnf(refute_0_339,plain,
( multiply(least_upper_bound(X_64,identity),X_63) != least_upper_bound(multiply(X_64,X_63),X_63)
| multiply(least_upper_bound(X_64,identity),X_63) = least_upper_bound(X_63,multiply(X_64,X_63)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_64,X_63),X_63),least_upper_bound(X_63,multiply(X_64,X_63))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
multiply(least_upper_bound(X_64,identity),X_63) = least_upper_bound(X_63,multiply(X_64,X_63)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,identity),X_63),least_upper_bound(multiply(X_64,X_63),X_63)) )],[refute_0_336,refute_0_339]) ).
cnf(refute_0_341,plain,
multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) = least_upper_bound(X_63,multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63)),
inference(subst,[],[refute_0_340:[bind(X_64,$fot(greatest_lower_bound(X_430,inverse(X_63))))]]) ).
cnf(refute_0_342,plain,
multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) = greatest_lower_bound(multiply(X_107,X_106),multiply(inverse(X_106),X_106)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_106)),bind(Y,$fot(X_107)),bind(Z,$fot(inverse(X_106)))]]) ).
cnf(refute_0_343,plain,
multiply(inverse(X_106),X_106) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_106))]]) ).
cnf(refute_0_344,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) != greatest_lower_bound(multiply(X_107,X_106),multiply(inverse(X_106),X_106))
| multiply(inverse(X_106),X_106) != identity
| multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) = greatest_lower_bound(multiply(X_107,X_106),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106),greatest_lower_bound(multiply(X_107,X_106),multiply(inverse(X_106),X_106))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_345,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) != greatest_lower_bound(multiply(X_107,X_106),multiply(inverse(X_106),X_106))
| multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) = greatest_lower_bound(multiply(X_107,X_106),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_106),X_106),identity) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) = greatest_lower_bound(multiply(X_107,X_106),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106),greatest_lower_bound(multiply(X_107,X_106),multiply(inverse(X_106),X_106))) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_348,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_347]) ).
cnf(refute_0_349,plain,
greatest_lower_bound(multiply(X_107,X_106),identity) = greatest_lower_bound(identity,multiply(X_107,X_106)),
inference(subst,[],[refute_0_348:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_107,X_106)))]]) ).
cnf(refute_0_350,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) != greatest_lower_bound(multiply(X_107,X_106),identity)
| greatest_lower_bound(multiply(X_107,X_106),identity) != greatest_lower_bound(identity,multiply(X_107,X_106))
| multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) = greatest_lower_bound(identity,multiply(X_107,X_106)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106),greatest_lower_bound(identity,multiply(X_107,X_106))) ),[0],$fot(greatest_lower_bound(multiply(X_107,X_106),identity))]]) ).
cnf(refute_0_351,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) != greatest_lower_bound(multiply(X_107,X_106),identity)
| multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) = greatest_lower_bound(identity,multiply(X_107,X_106)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_106),identity),greatest_lower_bound(identity,multiply(X_107,X_106))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106) = greatest_lower_bound(identity,multiply(X_107,X_106)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,inverse(X_106)),X_106),greatest_lower_bound(multiply(X_107,X_106),identity)) )],[refute_0_346,refute_0_351]) ).
cnf(refute_0_353,plain,
multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63) = greatest_lower_bound(identity,multiply(X_430,X_63)),
inference(subst,[],[refute_0_352:[bind(X_106,$fot(X_63)),bind(X_107,$fot(X_430))]]) ).
cnf(refute_0_354,plain,
( multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63) != greatest_lower_bound(identity,multiply(X_430,X_63))
| multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) != least_upper_bound(X_63,multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63))
| multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) = least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63),least_upper_bound(X_63,multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_430,X_63)))]]) ).
cnf(refute_0_355,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) != least_upper_bound(X_63,multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63))
| multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) = least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63),greatest_lower_bound(identity,multiply(X_430,X_63))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) = least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63),least_upper_bound(X_63,multiply(greatest_lower_bound(X_430,inverse(X_63)),X_63))) )],[refute_0_341,refute_0_355]) ).
cnf(refute_0_357,plain,
greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) = X_6,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_358,plain,
least_upper_bound(X_7,X_6) = least_upper_bound(X_6,X_7),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_7)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_359,plain,
( least_upper_bound(X_7,X_6) != least_upper_bound(X_6,X_7)
| least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_7,X_6))),bind(Y0,$fot(least_upper_bound(X_6,X_7)))]]) ).
cnf(refute_0_360,plain,
least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,X_6),least_upper_bound(X_6,X_7)) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| least_upper_bound(X_6,X_7) != least_upper_bound(X_7,X_6)
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) ),[0,1],$fot(least_upper_bound(X_7,X_6))]]) ).
cnf(refute_0_362,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_6,X_7),least_upper_bound(X_7,X_6)) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) )],[refute_0_357,refute_0_362]) ).
cnf(refute_0_364,plain,
greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))) = least_upper_bound(X_16,X_7),
inference(subst,[],[refute_0_363:[bind(X_6,$fot(least_upper_bound(X_16,X_7)))]]) ).
cnf(refute_0_365,plain,
least_upper_bound(X_7,least_upper_bound(X_16,X_7)) = least_upper_bound(X_7,X_16),
inference(subst,[],[refute_0_107:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_7))]]) ).
cnf(refute_0_366,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))) != least_upper_bound(X_16,X_7)
| least_upper_bound(X_7,least_upper_bound(X_16,X_7)) != least_upper_bound(X_7,X_16)
| greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) = least_upper_bound(X_16,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))),least_upper_bound(X_16,X_7)) ),[0,1],$fot(least_upper_bound(X_7,X_16))]]) ).
cnf(refute_0_367,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))) != least_upper_bound(X_16,X_7)
| greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) = least_upper_bound(X_16,X_7) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,least_upper_bound(X_16,X_7)),least_upper_bound(X_7,X_16)) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,X_16)) = least_upper_bound(X_16,X_7),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_7),least_upper_bound(X_7,least_upper_bound(X_16,X_7))),least_upper_bound(X_16,X_7)) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_368:[bind(X_16,$fot(multiply(Z,X))),bind(X_7,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_370,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_371,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_159,refute_0_370]) ).
cnf(refute_0_372,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_369,refute_0_371]) ).
cnf(refute_0_373,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_368:[bind(X_16,$fot(Y)),bind(X_7,$fot(Z))]]) ).
cnf(refute_0_374,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))]]) ).
cnf(refute_0_375,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) ),[1,0],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_376,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_379,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_378]) ).
cnf(refute_0_380,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
inference(subst,[],[refute_0_379:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_381,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_382,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_377,refute_0_382]) ).
cnf(refute_0_384,plain,
least_upper_bound(multiply(Z,X),multiply(Y,X)) = multiply(least_upper_bound(Z,Y),X),
inference(subst,[],[refute_0_159:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_385,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_386,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(least_upper_bound(Z,Y),X))]]) ).
cnf(refute_0_387,plain,
( least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_390,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_383,refute_0_390]) ).
cnf(refute_0_392,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_348:[bind(X,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y,$fot(least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_393,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_394,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_397,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),[0],$fot(least_upper_bound(multiply(Z,X),multiply(Y,X)))]]) ).
cnf(refute_0_399,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_384,refute_0_398]) ).
cnf(refute_0_400,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_397,refute_0_399]) ).
cnf(refute_0_401,plain,
multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_372,refute_0_400]) ).
cnf(refute_0_402,plain,
( multiply(least_upper_bound(Y,Z),X) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(multiply(least_upper_bound(Z,Y),X)))]]) ).
cnf(refute_0_403,plain,
multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) = multiply(least_upper_bound(identity,greatest_lower_bound(X_430,inverse(X_63))),X_63),
inference(subst,[],[refute_0_403:[bind(X,$fot(X_63)),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(X_430,inverse(X_63))))]]) ).
cnf(refute_0_405,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) != multiply(least_upper_bound(identity,greatest_lower_bound(X_430,inverse(X_63))),X_63)
| multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) != least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63)))
| multiply(least_upper_bound(identity,greatest_lower_bound(X_430,inverse(X_63))),X_63) = least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63),least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63)))) ),[0],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(X_430,inverse(X_63))),X_63))]]) ).
cnf(refute_0_406,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63) != least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63)))
| multiply(least_upper_bound(identity,greatest_lower_bound(X_430,inverse(X_63))),X_63) = least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63),multiply(least_upper_bound(identity,greatest_lower_bound(X_430,inverse(X_63))),X_63)) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X_430,inverse(X_63))),X_63) = least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_430,inverse(X_63)),identity),X_63),least_upper_bound(X_63,greatest_lower_bound(identity,multiply(X_430,X_63)))) )],[refute_0_356,refute_0_406]) ).
cnf(refute_0_408,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))))),
inference(subst,[],[refute_0_407:[bind(X_430,$fot(least_upper_bound(identity,X_59))),bind(X_63,$fot(inverse(least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_409,plain,
multiply(X_40,inverse(multiply(X_30,X_40))) = multiply(inverse(X_30),multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40))))),
inference(subst,[],[refute_0_8:[bind(X_31,$fot(multiply(X_40,inverse(multiply(X_30,X_40)))))]]) ).
cnf(refute_0_410,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(subst,[],[associativity:[bind(Z,$fot(inverse(multiply(X,Y))))]]) ).
cnf(refute_0_411,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_412,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_413,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( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),identity) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) )],[refute_0_410,refute_0_413]) ).
cnf(refute_0_415,plain,
identity = multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))),
inference(subst,[],[refute_0_414:[bind(X,$fot(X_30)),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_416,plain,
( identity != multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40))))
| multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))) = identity ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40))))))]]) ).
cnf(refute_0_417,plain,
multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40))))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
( multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))) != identity
| multiply(X_40,inverse(multiply(X_30,X_40))) != multiply(inverse(X_30),multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))))
| multiply(X_40,inverse(multiply(X_30,X_40))) = multiply(inverse(X_30),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_40,inverse(multiply(X_30,X_40))),multiply(inverse(X_30),multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_419,plain,
( multiply(X_40,inverse(multiply(X_30,X_40))) != multiply(inverse(X_30),multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))))
| multiply(X_40,inverse(multiply(X_30,X_40))) = multiply(inverse(X_30),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))),identity) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
multiply(X_40,inverse(multiply(X_30,X_40))) = multiply(inverse(X_30),identity),
inference(resolve,[$cnf( $equal(multiply(X_40,inverse(multiply(X_30,X_40))),multiply(inverse(X_30),multiply(X_30,multiply(X_40,inverse(multiply(X_30,X_40)))))) )],[refute_0_409,refute_0_419]) ).
cnf(refute_0_421,plain,
multiply(inverse(X_30),identity) = inverse(X_30),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(inverse(X_30)))]]) ).
cnf(refute_0_422,plain,
( multiply(X_40,inverse(multiply(X_30,X_40))) != multiply(inverse(X_30),identity)
| multiply(inverse(X_30),identity) != inverse(X_30)
| multiply(X_40,inverse(multiply(X_30,X_40))) = inverse(X_30) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_40,inverse(multiply(X_30,X_40))),inverse(X_30)) ),[0],$fot(multiply(inverse(X_30),identity))]]) ).
cnf(refute_0_423,plain,
( multiply(X_40,inverse(multiply(X_30,X_40))) != multiply(inverse(X_30),identity)
| multiply(X_40,inverse(multiply(X_30,X_40))) = inverse(X_30) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),identity),inverse(X_30)) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
multiply(X_40,inverse(multiply(X_30,X_40))) = inverse(X_30),
inference(resolve,[$cnf( $equal(multiply(X_40,inverse(multiply(X_30,X_40))),multiply(inverse(X_30),identity)) )],[refute_0_420,refute_0_423]) ).
cnf(refute_0_425,plain,
multiply(least_upper_bound(identity,X_59),inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59)))) = inverse(inverse(X_59)),
inference(subst,[],[refute_0_424:[bind(X_30,$fot(inverse(X_59))),bind(X_40,$fot(least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_426,plain,
( multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(identity,inverse(X_59))
| multiply(least_upper_bound(identity,X_59),inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59)))) != inverse(inverse(X_59))
| multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(inverse(X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_59),inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59)))),inverse(inverse(X_59))) ),[0,1,0],$fot(least_upper_bound(identity,inverse(X_59)))]]) ).
cnf(refute_0_427,plain,
( multiply(least_upper_bound(identity,X_59),inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59)))) != inverse(inverse(X_59))
| multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(inverse(X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(identity,inverse(X_59))) )],[refute_0_304,refute_0_426]) ).
cnf(refute_0_428,plain,
multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(inverse(X_59)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_59),inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59)))),inverse(inverse(X_59))) )],[refute_0_425,refute_0_427]) ).
cnf(refute_0_429,plain,
inverse(inverse(X_59)) = X_59,
inference(subst,[],[refute_0_83:[bind(X_35,$fot(X_59))]]) ).
cnf(refute_0_430,plain,
( multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) != inverse(inverse(X_59))
| inverse(inverse(X_59)) != X_59
| multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) = X_59 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))),X_59) ),[0],$fot(inverse(inverse(X_59)))]]) ).
cnf(refute_0_431,plain,
( multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) != inverse(inverse(X_59))
| multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) = X_59 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_59)),X_59) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) = X_59,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))),inverse(inverse(X_59))) )],[refute_0_428,refute_0_431]) ).
cnf(refute_0_433,plain,
( multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) != X_59
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))))) ),[1,1,1],$fot(X_59)]]) ).
cnf(refute_0_434,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))),X_59) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))))) )],[refute_0_408,refute_0_434]) ).
cnf(refute_0_436,plain,
multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(identity,inverse(X_59))),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_437,plain,
least_upper_bound(identity,greatest_lower_bound(X_59,identity)) = identity,
inference(subst,[],[refute_0_96:[bind(X_12,$fot(identity)),bind(X_13,$fot(X_59))]]) ).
cnf(refute_0_438,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) = least_upper_bound(identity,greatest_lower_bound(X_59,identity)),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(least_upper_bound(identity,greatest_lower_bound(X_59,identity))))]]) ).
cnf(refute_0_439,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) != least_upper_bound(identity,greatest_lower_bound(X_59,identity))
| least_upper_bound(identity,greatest_lower_bound(X_59,identity)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) = identity ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(X_59,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_440,plain,
( least_upper_bound(identity,greatest_lower_bound(X_59,identity)) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity),least_upper_bound(identity,greatest_lower_bound(X_59,identity))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) )],[refute_0_437,refute_0_440]) ).
cnf(refute_0_442,plain,
multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63) = multiply(least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)),X_63),
inference(subst,[],[refute_0_218:[bind(X_65,$fot(greatest_lower_bound(X_501,X_502)))]]) ).
cnf(refute_0_443,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X_20)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_444,plain,
least_upper_bound(X_20,X_19) = least_upper_bound(X_19,X_20),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_20)),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_445,plain,
( least_upper_bound(X_20,X_19) != least_upper_bound(X_19,X_20)
| least_upper_bound(X_19,X_20) = least_upper_bound(X_20,X_19) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_20,X_19))),bind(Y0,$fot(least_upper_bound(X_19,X_20)))]]) ).
cnf(refute_0_446,plain,
least_upper_bound(X_19,X_20) = least_upper_bound(X_20,X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,X_19),least_upper_bound(X_19,X_20)) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X_20)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(X_19,X_20) != least_upper_bound(X_20,X_19)
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X_20)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) ),[0,1],$fot(least_upper_bound(X_20,X_19))]]) ).
cnf(refute_0_448,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X_20)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,X_20),least_upper_bound(X_20,X_19)) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X_20)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) )],[refute_0_443,refute_0_448]) ).
cnf(refute_0_450,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X_20) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_451,plain,
( least_upper_bound(X_18,least_upper_bound(X_20,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(least_upper_bound(X_18,X_19),X_20) != least_upper_bound(X_18,least_upper_bound(X_19,X_20))
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(X_20,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X_20))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),X_20))]]) ).
cnf(refute_0_452,plain,
( least_upper_bound(X_18,least_upper_bound(X_20,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X_20),least_upper_bound(X_18,least_upper_bound(X_19,X_20))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_20,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) )],[refute_0_449,refute_0_452]) ).
cnf(refute_0_454,plain,
least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130))),
inference(subst,[],[refute_0_453:[bind(X_19,$fot(greatest_lower_bound(X_130,X_129))),bind(X_20,$fot(greatest_lower_bound(X_129,X_130)))]]) ).
cnf(refute_0_455,plain,
least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13))) = greatest_lower_bound(X_21,X_13),
inference(subst,[],[refute_0_96:[bind(X_12,$fot(greatest_lower_bound(X_21,X_13)))]]) ).
cnf(refute_0_456,plain,
greatest_lower_bound(greatest_lower_bound(X_7,X_13),least_upper_bound(X_7,greatest_lower_bound(X_7,X_13))) = greatest_lower_bound(X_7,X_13),
inference(subst,[],[refute_0_363:[bind(X_6,$fot(greatest_lower_bound(X_7,X_13)))]]) ).
cnf(refute_0_457,plain,
least_upper_bound(X_7,greatest_lower_bound(X_7,X_13)) = X_7,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_7)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_458,plain,
( greatest_lower_bound(greatest_lower_bound(X_7,X_13),least_upper_bound(X_7,greatest_lower_bound(X_7,X_13))) != greatest_lower_bound(X_7,X_13)
| least_upper_bound(X_7,greatest_lower_bound(X_7,X_13)) != X_7
| greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7) = greatest_lower_bound(X_7,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_7,X_13),least_upper_bound(X_7,greatest_lower_bound(X_7,X_13))),greatest_lower_bound(X_7,X_13)) ),[0,1],$fot(X_7)]]) ).
cnf(refute_0_459,plain,
( greatest_lower_bound(greatest_lower_bound(X_7,X_13),least_upper_bound(X_7,greatest_lower_bound(X_7,X_13))) != greatest_lower_bound(X_7,X_13)
| greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7) = greatest_lower_bound(X_7,X_13) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,greatest_lower_bound(X_7,X_13)),X_7) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7) = greatest_lower_bound(X_7,X_13),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_7,X_13),least_upper_bound(X_7,greatest_lower_bound(X_7,X_13))),greatest_lower_bound(X_7,X_13)) )],[refute_0_456,refute_0_459]) ).
cnf(refute_0_461,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_462,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_461]) ).
cnf(refute_0_463,plain,
greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7) = greatest_lower_bound(X_7,greatest_lower_bound(X_13,X_7)),
inference(subst,[],[refute_0_462:[bind(X,$fot(X_7)),bind(Y,$fot(X_13)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_464,plain,
( greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7) != greatest_lower_bound(X_7,X_13)
| greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7) != greatest_lower_bound(X_7,greatest_lower_bound(X_13,X_7))
| greatest_lower_bound(X_7,greatest_lower_bound(X_13,X_7)) = greatest_lower_bound(X_7,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7),greatest_lower_bound(X_7,X_13)) ),[0],$fot(greatest_lower_bound(X_7,greatest_lower_bound(X_13,X_7)))]]) ).
cnf(refute_0_465,plain,
( greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7) != greatest_lower_bound(X_7,X_13)
| greatest_lower_bound(X_7,greatest_lower_bound(X_13,X_7)) = greatest_lower_bound(X_7,X_13) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7),greatest_lower_bound(X_7,greatest_lower_bound(X_13,X_7))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
greatest_lower_bound(X_7,greatest_lower_bound(X_13,X_7)) = greatest_lower_bound(X_7,X_13),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_7,X_13),X_7),greatest_lower_bound(X_7,X_13)) )],[refute_0_460,refute_0_465]) ).
cnf(refute_0_467,plain,
greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13)) = greatest_lower_bound(X_13,X_21),
inference(subst,[],[refute_0_466:[bind(X_13,$fot(X_21)),bind(X_7,$fot(X_13))]]) ).
cnf(refute_0_468,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13)) != greatest_lower_bound(X_13,X_21)
| least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13))) != greatest_lower_bound(X_21,X_13)
| least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21)) = greatest_lower_bound(X_21,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13))),greatest_lower_bound(X_21,X_13)) ),[0,1],$fot(greatest_lower_bound(X_13,X_21))]]) ).
cnf(refute_0_469,plain,
( least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13))) != greatest_lower_bound(X_21,X_13)
| least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21)) = greatest_lower_bound(X_21,X_13) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13)),greatest_lower_bound(X_13,X_21)) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21)) = greatest_lower_bound(X_21,X_13),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_21,X_13))),greatest_lower_bound(X_21,X_13)) )],[refute_0_455,refute_0_469]) ).
cnf(refute_0_471,plain,
least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130)) = greatest_lower_bound(X_130,X_129),
inference(subst,[],[refute_0_470:[bind(X_13,$fot(X_129)),bind(X_21,$fot(X_130))]]) ).
cnf(refute_0_472,plain,
( least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130)))
| least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130)) != greatest_lower_bound(X_130,X_129)
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,greatest_lower_bound(X_130,X_129)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130)))) ),[1,1],$fot(greatest_lower_bound(X_130,X_129))]]) ).
cnf(refute_0_473,plain,
( least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130)))
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,greatest_lower_bound(X_130,X_129)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130)),greatest_lower_bound(X_130,X_129)) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,greatest_lower_bound(X_130,X_129)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_130,X_129),greatest_lower_bound(X_129,X_130)))) )],[refute_0_454,refute_0_473]) ).
cnf(refute_0_475,plain,
least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129)) = greatest_lower_bound(X_129,X_130),
inference(subst,[],[refute_0_470:[bind(X_13,$fot(X_130)),bind(X_21,$fot(X_129))]]) ).
cnf(refute_0_476,plain,
least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))))]]) ).
cnf(refute_0_477,plain,
( least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) != least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129)))
| least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129)) != greatest_lower_bound(X_129,X_130)
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,greatest_lower_bound(X_129,X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129)))) ),[1,1],$fot(greatest_lower_bound(X_129,X_130))]]) ).
cnf(refute_0_478,plain,
( least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129)) != greatest_lower_bound(X_129,X_130)
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,greatest_lower_bound(X_129,X_130)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129)))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) = least_upper_bound(X_18,greatest_lower_bound(X_129,X_130)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129)),greatest_lower_bound(X_129,X_130)) )],[refute_0_475,refute_0_478]) ).
cnf(refute_0_480,plain,
( least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) != least_upper_bound(X_18,greatest_lower_bound(X_129,X_130))
| least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) != least_upper_bound(X_18,greatest_lower_bound(X_130,X_129))
| least_upper_bound(X_18,greatest_lower_bound(X_129,X_130)) = least_upper_bound(X_18,greatest_lower_bound(X_130,X_129)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),least_upper_bound(X_18,greatest_lower_bound(X_130,X_129))) ),[0],$fot(least_upper_bound(X_18,greatest_lower_bound(X_129,X_130)))]]) ).
cnf(refute_0_481,plain,
( least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))) != least_upper_bound(X_18,greatest_lower_bound(X_130,X_129))
| least_upper_bound(X_18,greatest_lower_bound(X_129,X_130)) = least_upper_bound(X_18,greatest_lower_bound(X_130,X_129)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),least_upper_bound(X_18,greatest_lower_bound(X_129,X_130))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
least_upper_bound(X_18,greatest_lower_bound(X_129,X_130)) = least_upper_bound(X_18,greatest_lower_bound(X_130,X_129)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_129,X_130),greatest_lower_bound(X_130,X_129))),least_upper_bound(X_18,greatest_lower_bound(X_130,X_129))) )],[refute_0_474,refute_0_481]) ).
cnf(refute_0_483,plain,
least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)) = least_upper_bound(X_64,greatest_lower_bound(X_502,X_501)),
inference(subst,[],[refute_0_482:[bind(X_129,$fot(X_501)),bind(X_130,$fot(X_502)),bind(X_18,$fot(X_64))]]) ).
cnf(refute_0_484,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63) != multiply(least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)),X_63)
| least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)) != least_upper_bound(X_64,greatest_lower_bound(X_502,X_501))
| multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63) = multiply(least_upper_bound(X_64,greatest_lower_bound(X_502,X_501)),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63),multiply(least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)),X_63)) ),[1,0],$fot(least_upper_bound(X_64,greatest_lower_bound(X_502,X_501)))]]) ).
cnf(refute_0_485,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63) != multiply(least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)),X_63)
| multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63) = multiply(least_upper_bound(X_64,greatest_lower_bound(X_502,X_501)),X_63) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)),least_upper_bound(X_64,greatest_lower_bound(X_502,X_501))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63) = multiply(least_upper_bound(X_64,greatest_lower_bound(X_502,X_501)),X_63),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_501,X_502),X_64),X_63),multiply(least_upper_bound(X_64,greatest_lower_bound(X_501,X_502)),X_63)) )],[refute_0_442,refute_0_485]) ).
cnf(refute_0_487,plain,
multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity) = multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity),
inference(subst,[],[refute_0_486:[bind(X_501,$fot(identity)),bind(X_502,$fot(X_59)),bind(X_63,$fot(identity)),bind(X_64,$fot(identity))]]) ).
cnf(refute_0_488,plain,
( multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity) != multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity)
| multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) != identity
| multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity) = identity ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_489,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity) != identity
| multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity),multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity)) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(X_59,identity)),identity),identity) )],[refute_0_441,refute_0_489]) ).
cnf(refute_0_491,plain,
( multiply(least_upper_bound(X_64,identity),X_63) != least_upper_bound(X_63,multiply(X_64,X_63))
| least_upper_bound(X_63,multiply(X_64,X_63)) = multiply(least_upper_bound(X_64,identity),X_63) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(X_64,identity),X_63))),bind(Y0,$fot(least_upper_bound(X_63,multiply(X_64,X_63))))]]) ).
cnf(refute_0_492,plain,
least_upper_bound(X_63,multiply(X_64,X_63)) = multiply(least_upper_bound(X_64,identity),X_63),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,identity),X_63),least_upper_bound(X_63,multiply(X_64,X_63))) )],[refute_0_340,refute_0_491]) ).
cnf(refute_0_493,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)) = multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity),
inference(subst,[],[refute_0_492:[bind(X_63,$fot(identity)),bind(X_64,$fot(greatest_lower_bound(identity,X_59)))]]) ).
cnf(refute_0_494,plain,
( multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)) != multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity)
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)) = identity ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_495,plain,
( multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)),multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity)) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(identity,X_59),identity),identity),identity) )],[refute_0_490,refute_0_495]) ).
cnf(refute_0_497,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(least_upper_bound(Y,X_18))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_498,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_107:[bind(X_15,$fot(X_18))]]) ).
cnf(refute_0_499,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) ),[1,0],$fot(least_upper_bound(X_18,Y))]]) ).
cnf(refute_0_500,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) )],[refute_0_497,refute_0_500]) ).
cnf(refute_0_502,plain,
least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_503,plain,
least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y),
inference(subst,[],[refute_0_107:[bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_504,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) != least_upper_bound(X_19,Y)
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) ),[0,1],$fot(least_upper_bound(X_19,Y))]]) ).
cnf(refute_0_505,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(Y,X_19)),least_upper_bound(X_19,Y)) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_502,refute_0_505]) ).
cnf(refute_0_507,plain,
least_upper_bound(least_upper_bound(X_18,X_19),Y) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_508,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))]]) ).
cnf(refute_0_509,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) ),[1,1],$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))]]) ).
cnf(refute_0_510,plain,
( least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),Y),least_upper_bound(X_18,least_upper_bound(X_19,Y))) )],[refute_0_507,refute_0_510]) ).
cnf(refute_0_512,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_18,X_19)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X))))]]) ).
cnf(refute_0_513,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_202,refute_0_512]) ).
cnf(refute_0_514,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
inference(subst,[],[refute_0_513:[bind(X,$fot(X_19)),bind(X_18,$fot(least_upper_bound(X_18,X_19))),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_515,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))),bind(Z0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_516,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_511,refute_0_516]) ).
cnf(refute_0_518,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_519,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_506,refute_0_519]) ).
cnf(refute_0_521,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_522,plain,
least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_522:[bind(Y,$fot(X_20)),bind(X_18,$fot(Y)),bind(X_19,$fot(X_18))]]) ).
cnf(refute_0_524,plain,
least_upper_bound(least_upper_bound(Y,X_18),X_20) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_103:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_525,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))]]) ).
cnf(refute_0_526,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))
| least_upper_bound(least_upper_bound(Y,X_18),X_20) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))]]) ).
cnf(refute_0_527,plain,
( least_upper_bound(least_upper_bound(Y,X_18),X_20) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),X_20),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_524,refute_0_527]) ).
cnf(refute_0_529,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20))))]]) ).
cnf(refute_0_530,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_523,refute_0_530]) ).
cnf(refute_0_532,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))]]) ).
cnf(refute_0_533,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
least_upper_bound(least_upper_bound(X_18,Y),X_20) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(subst,[],[refute_0_103:[bind(X,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_535,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(least_upper_bound(X_18,Y),X_20) != least_upper_bound(X_18,least_upper_bound(Y,X_20))
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(X_18,least_upper_bound(Y,X_20))) ),[0],$fot(least_upper_bound(least_upper_bound(X_18,Y),X_20))]]) ).
cnf(refute_0_536,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,Y),X_20),least_upper_bound(X_18,least_upper_bound(Y,X_20))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_533,refute_0_536]) ).
cnf(refute_0_538,plain,
least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_501,refute_0_537]) ).
cnf(refute_0_539,plain,
least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))) = least_upper_bound(X_18,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))),
inference(subst,[],[refute_0_538:[bind(Y,$fot(multiply(X_51,X_52))),bind(X_20,$fot(multiply(X_51,X_53)))]]) ).
cnf(refute_0_540,plain,
( least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)) != multiply(X_51,least_upper_bound(X_52,X_53))
| least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))) != least_upper_bound(X_18,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)))
| least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))) = least_upper_bound(X_18,multiply(X_51,least_upper_bound(X_52,X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))),least_upper_bound(X_18,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)))) ),[1,1],$fot(multiply(X_51,least_upper_bound(X_52,X_53)))]]) ).
cnf(refute_0_541,plain,
( least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))) != least_upper_bound(X_18,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)))
| least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))) = least_upper_bound(X_18,multiply(X_51,least_upper_bound(X_52,X_53))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)),multiply(X_51,least_upper_bound(X_52,X_53))) )],[refute_0_206,refute_0_540]) ).
cnf(refute_0_542,plain,
least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))) = least_upper_bound(X_18,multiply(X_51,least_upper_bound(X_52,X_53))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_52),least_upper_bound(X_18,multiply(X_51,X_53))),least_upper_bound(X_18,least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)))) )],[refute_0_539,refute_0_541]) ).
cnf(refute_0_543,plain,
least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))),
inference(subst,[],[refute_0_542:[bind(X_18,$fot(identity)),bind(X_51,$fot(greatest_lower_bound(X_13,X_72))),bind(X_52,$fot(X_470)),bind(X_53,$fot(inverse(X_72)))]]) ).
cnf(refute_0_544,plain,
multiply(least_upper_bound(X_64,X_65),inverse(X_64)) = least_upper_bound(multiply(X_64,inverse(X_64)),multiply(X_65,inverse(X_64))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_64))),bind(Y,$fot(X_64)),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_545,plain,
multiply(X_64,inverse(X_64)) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_64))]]) ).
cnf(refute_0_546,plain,
( multiply(X_64,inverse(X_64)) != identity
| multiply(least_upper_bound(X_64,X_65),inverse(X_64)) != least_upper_bound(multiply(X_64,inverse(X_64)),multiply(X_65,inverse(X_64)))
| multiply(least_upper_bound(X_64,X_65),inverse(X_64)) = least_upper_bound(identity,multiply(X_65,inverse(X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_64)),least_upper_bound(multiply(X_64,inverse(X_64)),multiply(X_65,inverse(X_64)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_547,plain,
( multiply(least_upper_bound(X_64,X_65),inverse(X_64)) != least_upper_bound(multiply(X_64,inverse(X_64)),multiply(X_65,inverse(X_64)))
| multiply(least_upper_bound(X_64,X_65),inverse(X_64)) = least_upper_bound(identity,multiply(X_65,inverse(X_64))) ),
inference(resolve,[$cnf( $equal(multiply(X_64,inverse(X_64)),identity) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
multiply(least_upper_bound(X_64,X_65),inverse(X_64)) = least_upper_bound(identity,multiply(X_65,inverse(X_64))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_64)),least_upper_bound(multiply(X_64,inverse(X_64)),multiply(X_65,inverse(X_64)))) )],[refute_0_544,refute_0_547]) ).
cnf(refute_0_549,plain,
multiply(least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)),inverse(X_72)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))),
inference(subst,[],[refute_0_548:[bind(X_64,$fot(X_72)),bind(X_65,$fot(greatest_lower_bound(X_13,X_72)))]]) ).
cnf(refute_0_550,plain,
least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)) = X_72,
inference(subst,[],[refute_0_96:[bind(X_12,$fot(X_72))]]) ).
cnf(refute_0_551,plain,
( multiply(least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)),inverse(X_72)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))
| least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)) != X_72
| multiply(X_72,inverse(X_72)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)),inverse(X_72)),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) ),[0,0],$fot(X_72)]]) ).
cnf(refute_0_552,plain,
( multiply(least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)),inverse(X_72)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))
| multiply(X_72,inverse(X_72)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)),X_72) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
multiply(X_72,inverse(X_72)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_72,greatest_lower_bound(X_13,X_72)),inverse(X_72)),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) )],[refute_0_549,refute_0_552]) ).
cnf(refute_0_554,plain,
multiply(X_72,inverse(X_72)) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_72))]]) ).
cnf(refute_0_555,plain,
( multiply(X_72,inverse(X_72)) != identity
| multiply(X_72,inverse(X_72)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_72,inverse(X_72)),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_556,plain,
( multiply(X_72,inverse(X_72)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))
| identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))) ),
inference(resolve,[$cnf( $equal(multiply(X_72,inverse(X_72)),identity) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))),
inference(resolve,[$cnf( $equal(multiply(X_72,inverse(X_72)),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) )],[refute_0_553,refute_0_556]) ).
cnf(refute_0_558,plain,
( identity != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))) = identity ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))))]]) ).
cnf(refute_0_559,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))) != identity
| least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_561,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))
| least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72))),identity) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),inverse(X_72)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))) )],[refute_0_543,refute_0_561]) ).
cnf(refute_0_563,plain,
multiply(X_185,inverse(multiply(least_upper_bound(inverse(X_185),X_65),X_185))) = inverse(least_upper_bound(inverse(X_185),X_65)),
inference(subst,[],[refute_0_424:[bind(X_30,$fot(least_upper_bound(inverse(X_185),X_65))),bind(X_40,$fot(X_185))]]) ).
cnf(refute_0_564,plain,
multiply(least_upper_bound(inverse(X_185),X_65),X_185) = least_upper_bound(identity,multiply(X_65,X_185)),
inference(subst,[],[refute_0_133:[bind(X_63,$fot(X_185))]]) ).
cnf(refute_0_565,plain,
( multiply(X_185,inverse(multiply(least_upper_bound(inverse(X_185),X_65),X_185))) != inverse(least_upper_bound(inverse(X_185),X_65))
| multiply(least_upper_bound(inverse(X_185),X_65),X_185) != least_upper_bound(identity,multiply(X_65,X_185))
| multiply(X_185,inverse(least_upper_bound(identity,multiply(X_65,X_185)))) = inverse(least_upper_bound(inverse(X_185),X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_185,inverse(multiply(least_upper_bound(inverse(X_185),X_65),X_185))),inverse(least_upper_bound(inverse(X_185),X_65))) ),[0,1,0],$fot(least_upper_bound(identity,multiply(X_65,X_185)))]]) ).
cnf(refute_0_566,plain,
( multiply(X_185,inverse(multiply(least_upper_bound(inverse(X_185),X_65),X_185))) != inverse(least_upper_bound(inverse(X_185),X_65))
| multiply(X_185,inverse(least_upper_bound(identity,multiply(X_65,X_185)))) = inverse(least_upper_bound(inverse(X_185),X_65)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_185),X_65),X_185),least_upper_bound(identity,multiply(X_65,X_185))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
multiply(X_185,inverse(least_upper_bound(identity,multiply(X_65,X_185)))) = inverse(least_upper_bound(inverse(X_185),X_65)),
inference(resolve,[$cnf( $equal(multiply(X_185,inverse(multiply(least_upper_bound(inverse(X_185),X_65),X_185))),inverse(least_upper_bound(inverse(X_185),X_65))) )],[refute_0_563,refute_0_566]) ).
cnf(refute_0_568,plain,
multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395))))) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),
inference(subst,[],[refute_0_567:[bind(X_185,$fot(least_upper_bound(X_396,X_395))),bind(X_65,$fot(inverse(least_upper_bound(X_395,X_396))))]]) ).
cnf(refute_0_569,plain,
multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,least_upper_bound(Y,X_58))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)),
inference(subst,[],[refute_0_297:[bind(X_52,$fot(X_58)),bind(X_53,$fot(least_upper_bound(Y,X_58)))]]) ).
cnf(refute_0_570,plain,
least_upper_bound(X_58,least_upper_bound(Y,X_58)) = least_upper_bound(X_58,Y),
inference(subst,[],[refute_0_107:[bind(X_15,$fot(X_58))]]) ).
cnf(refute_0_571,plain,
( multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,least_upper_bound(Y,X_58))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58))
| least_upper_bound(X_58,least_upper_bound(Y,X_58)) != least_upper_bound(X_58,Y)
| multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,least_upper_bound(Y,X_58))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58))) ),[0,1],$fot(least_upper_bound(X_58,Y))]]) ).
cnf(refute_0_572,plain,
( multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,least_upper_bound(Y,X_58))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58))
| multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_58,least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,least_upper_bound(Y,X_58))),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58))) )],[refute_0_569,refute_0_572]) ).
cnf(refute_0_574,plain,
multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,least_upper_bound(X_58,X_16))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58)),
inference(subst,[],[refute_0_297:[bind(X_52,$fot(X_58)),bind(X_53,$fot(least_upper_bound(X_58,X_16)))]]) ).
cnf(refute_0_575,plain,
least_upper_bound(X_58,least_upper_bound(X_58,X_16)) = least_upper_bound(X_58,X_16),
inference(subst,[],[refute_0_114:[bind(X_17,$fot(X_58))]]) ).
cnf(refute_0_576,plain,
( multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,least_upper_bound(X_58,X_16))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))
| least_upper_bound(X_58,least_upper_bound(X_58,X_16)) != least_upper_bound(X_58,X_16)
| multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,least_upper_bound(X_58,X_16))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))) ),[0,1],$fot(least_upper_bound(X_58,X_16))]]) ).
cnf(refute_0_577,plain,
( multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,least_upper_bound(X_58,X_16))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))
| multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_58,least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,least_upper_bound(X_58,X_16))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))) )],[refute_0_574,refute_0_577]) ).
cnf(refute_0_579,plain,
multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_58,X_16)))]]) ).
cnf(refute_0_580,plain,
( multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) != identity
| multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))) ),[0],$fot(identity)]]) ).
cnf(refute_0_581,plain,
( multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)),identity) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,X_16)),least_upper_bound(X_58,X_16)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_58,X_16)),X_58))) )],[refute_0_578,refute_0_581]) ).
cnf(refute_0_583,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_81,X_80)),X_81)),
inference(subst,[],[refute_0_582:[bind(X_16,$fot(X_80)),bind(X_58,$fot(X_81))]]) ).
cnf(refute_0_584,plain,
least_upper_bound(X_80,X_81) = least_upper_bound(X_81,X_80),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_80)),bind(Y,$fot(X_81))]]) ).
cnf(refute_0_585,plain,
( least_upper_bound(X_80,X_81) != least_upper_bound(X_81,X_80)
| least_upper_bound(X_81,X_80) = least_upper_bound(X_80,X_81) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_80,X_81))),bind(Y0,$fot(least_upper_bound(X_81,X_80)))]]) ).
cnf(refute_0_586,plain,
least_upper_bound(X_81,X_80) = least_upper_bound(X_80,X_81),
inference(resolve,[$cnf( $equal(least_upper_bound(X_80,X_81),least_upper_bound(X_81,X_80)) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_81,X_80)),X_81))
| least_upper_bound(X_81,X_80) != least_upper_bound(X_80,X_81)
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_81,X_80)),X_81))) ),[1,1,0,0],$fot(least_upper_bound(X_80,X_81))]]) ).
cnf(refute_0_588,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_81,X_80)),X_81))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_81,X_80),least_upper_bound(X_80,X_81)) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_81,X_80)),X_81))) )],[refute_0_583,refute_0_588]) ).
cnf(refute_0_590,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81)) = identity ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81))))]]) ).
cnf(refute_0_591,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_80,X_81)),X_81))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)) = identity,
inference(subst,[],[refute_0_591:[bind(X_80,$fot(Y)),bind(X_81,$fot(X_58))]]) ).
cnf(refute_0_593,plain,
( multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)) != identity
| multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)),identity) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)))]]) ).
cnf(refute_0_594,plain,
( multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58))
| multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58)),identity) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X_58)),least_upper_bound(X_58,Y)),least_upper_bound(identity,multiply(inverse(least_upper_bound(Y,X_58)),X_58))) )],[refute_0_573,refute_0_594]) ).
cnf(refute_0_596,plain,
multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)) = identity,
inference(subst,[],[refute_0_595:[bind(Y,$fot(X_395)),bind(X_58,$fot(X_396))]]) ).
cnf(refute_0_597,plain,
( multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)) != identity
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395))))) != inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395))))),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) ),[0,1,0,1],$fot(identity)]]) ).
cnf(refute_0_598,plain,
( multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395))))) != inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)),identity) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395))))),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) )],[refute_0_568,refute_0_598]) ).
cnf(refute_0_600,plain,
multiply(least_upper_bound(X_396,X_395),identity) = least_upper_bound(X_396,X_395),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(least_upper_bound(X_396,X_395)))]]) ).
cnf(refute_0_601,plain,
least_upper_bound(identity,identity) = identity,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(identity))]]) ).
cnf(refute_0_602,plain,
inverse(least_upper_bound(identity,identity)) = inverse(least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_603,plain,
( inverse(least_upper_bound(identity,identity)) != inverse(least_upper_bound(identity,identity))
| least_upper_bound(identity,identity) != identity
| inverse(least_upper_bound(identity,identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),inverse(least_upper_bound(identity,identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_604,plain,
( least_upper_bound(identity,identity) != identity
| inverse(least_upper_bound(identity,identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),inverse(least_upper_bound(identity,identity))) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
inverse(least_upper_bound(identity,identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,identity)) != inverse(identity)
| inverse(least_upper_bound(identity,identity)) = identity ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(inverse(least_upper_bound(identity,identity)))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_607,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,identity)) = identity ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),inverse(identity)) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
inverse(least_upper_bound(identity,identity)) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_254,refute_0_607]) ).
cnf(refute_0_609,plain,
multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))))]]) ).
cnf(refute_0_610,plain,
( multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) != multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity)))
| inverse(least_upper_bound(identity,identity)) != identity
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = multiply(least_upper_bound(X_396,X_395),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))),multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_611,plain,
( inverse(least_upper_bound(identity,identity)) != identity
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = multiply(least_upper_bound(X_396,X_395),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))),multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity)))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = multiply(least_upper_bound(X_396,X_395),identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),identity) )],[refute_0_608,refute_0_611]) ).
cnf(refute_0_613,plain,
( multiply(least_upper_bound(X_396,X_395),identity) != least_upper_bound(X_396,X_395)
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) != multiply(least_upper_bound(X_396,X_395),identity)
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = least_upper_bound(X_396,X_395) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_396,X_395),identity))),bind(Z0,$fot(least_upper_bound(X_396,X_395)))]]) ).
cnf(refute_0_614,plain,
( multiply(least_upper_bound(X_396,X_395),identity) != least_upper_bound(X_396,X_395)
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = least_upper_bound(X_396,X_395) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))),multiply(least_upper_bound(X_396,X_395),identity)) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) = least_upper_bound(X_396,X_395),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),identity),least_upper_bound(X_396,X_395)) )],[refute_0_600,refute_0_614]) ).
cnf(refute_0_616,plain,
( multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) != inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))
| multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) != least_upper_bound(X_396,X_395)
| least_upper_bound(X_396,X_395) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) ),[0],$fot(least_upper_bound(X_396,X_395))]]) ).
cnf(refute_0_617,plain,
( multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))) != inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))
| least_upper_bound(X_396,X_395) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))),least_upper_bound(X_396,X_395)) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
least_upper_bound(X_396,X_395) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_396,X_395),inverse(least_upper_bound(identity,identity))),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) )],[refute_0_599,refute_0_617]) ).
cnf(refute_0_619,plain,
inverse(inverse(least_upper_bound(X_395,X_396))) = least_upper_bound(X_395,X_396),
inference(subst,[],[refute_0_83:[bind(X_35,$fot(least_upper_bound(X_395,X_396)))]]) ).
cnf(refute_0_620,plain,
inverse(X_142) = multiply(inverse(multiply(least_upper_bound(X_64,inverse(X_142)),X_142)),least_upper_bound(X_64,inverse(X_142))),
inference(subst,[],[refute_0_57:[bind(X_48,$fot(least_upper_bound(X_64,inverse(X_142)))),bind(X_49,$fot(X_142))]]) ).
cnf(refute_0_621,plain,
multiply(least_upper_bound(X_64,inverse(X_142)),X_142) = least_upper_bound(identity,multiply(X_64,X_142)),
inference(subst,[],[refute_0_146:[bind(X_63,$fot(X_142))]]) ).
cnf(refute_0_622,plain,
( multiply(least_upper_bound(X_64,inverse(X_142)),X_142) != least_upper_bound(identity,multiply(X_64,X_142))
| inverse(X_142) != multiply(inverse(multiply(least_upper_bound(X_64,inverse(X_142)),X_142)),least_upper_bound(X_64,inverse(X_142)))
| inverse(X_142) = multiply(inverse(least_upper_bound(identity,multiply(X_64,X_142))),least_upper_bound(X_64,inverse(X_142))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_142),multiply(inverse(multiply(least_upper_bound(X_64,inverse(X_142)),X_142)),least_upper_bound(X_64,inverse(X_142)))) ),[1,0,0],$fot(least_upper_bound(identity,multiply(X_64,X_142)))]]) ).
cnf(refute_0_623,plain,
( inverse(X_142) != multiply(inverse(multiply(least_upper_bound(X_64,inverse(X_142)),X_142)),least_upper_bound(X_64,inverse(X_142)))
| inverse(X_142) = multiply(inverse(least_upper_bound(identity,multiply(X_64,X_142))),least_upper_bound(X_64,inverse(X_142))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,inverse(X_142)),X_142),least_upper_bound(identity,multiply(X_64,X_142))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
inverse(X_142) = multiply(inverse(least_upper_bound(identity,multiply(X_64,X_142))),least_upper_bound(X_64,inverse(X_142))),
inference(resolve,[$cnf( $equal(inverse(X_142),multiply(inverse(multiply(least_upper_bound(X_64,inverse(X_142)),X_142)),least_upper_bound(X_64,inverse(X_142)))) )],[refute_0_620,refute_0_623]) ).
cnf(refute_0_625,plain,
inverse(least_upper_bound(X_396,X_395)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)))),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),
inference(subst,[],[refute_0_624:[bind(X_142,$fot(least_upper_bound(X_396,X_395))),bind(X_64,$fot(inverse(least_upper_bound(X_395,X_396))))]]) ).
cnf(refute_0_626,plain,
( multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)) != identity
| inverse(least_upper_bound(X_396,X_395)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)))),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))
| inverse(least_upper_bound(X_396,X_395)) = multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_396,X_395)),multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)))),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))) ),[1,0,0,1],$fot(identity)]]) ).
cnf(refute_0_627,plain,
( inverse(least_upper_bound(X_396,X_395)) != multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)))),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))
| inverse(least_upper_bound(X_396,X_395)) = multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)),identity) )],[refute_0_596,refute_0_626]) ).
cnf(refute_0_628,plain,
inverse(least_upper_bound(X_396,X_395)) = multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_396,X_395)),multiply(inverse(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_395,X_396)),least_upper_bound(X_396,X_395)))),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))) )],[refute_0_625,refute_0_627]) ).
cnf(refute_0_629,plain,
multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))))]]) ).
cnf(refute_0_630,plain,
multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))))]]) ).
cnf(refute_0_631,plain,
( multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) != multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))
| inverse(least_upper_bound(identity,identity)) != identity
| multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_632,plain,
( inverse(least_upper_bound(identity,identity)) != identity
| multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),identity) )],[refute_0_608,refute_0_632]) ).
cnf(refute_0_634,plain,
( multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) != least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))
| multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) != multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))
| multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))))),bind(Z0,$fot(least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))))]]) ).
cnf(refute_0_635,plain,
( multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) != least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))
| multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) = least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) )],[refute_0_629,refute_0_635]) ).
cnf(refute_0_637,plain,
( multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) != least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))
| inverse(least_upper_bound(X_396,X_395)) != multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))
| inverse(least_upper_bound(X_396,X_395)) = least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_396,X_395)),multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))) ),[1],$fot(least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))]]) ).
cnf(refute_0_638,plain,
( inverse(least_upper_bound(X_396,X_395)) != multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))
| inverse(least_upper_bound(X_396,X_395)) = least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
inverse(least_upper_bound(X_396,X_395)) = least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_396,X_395)),multiply(inverse(least_upper_bound(identity,identity)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))))) )],[refute_0_628,refute_0_638]) ).
cnf(refute_0_640,plain,
( inverse(least_upper_bound(X_396,X_395)) != least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))
| least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))) = inverse(least_upper_bound(X_396,X_395)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(X_396,X_395)))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))))]]) ).
cnf(refute_0_641,plain,
least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395))) = inverse(least_upper_bound(X_396,X_395)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_396,X_395)),least_upper_bound(inverse(least_upper_bound(X_395,X_396)),inverse(least_upper_bound(X_396,X_395)))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))) = inverse(least_upper_bound(X_395,X_396)),
inference(subst,[],[refute_0_641:[bind(X_395,$fot(X_396)),bind(X_396,$fot(X_395))]]) ).
cnf(refute_0_643,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) = inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))))]]) ).
cnf(refute_0_644,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) != inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))
| least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))) != inverse(least_upper_bound(X_395,X_396))
| inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) = inverse(inverse(least_upper_bound(X_395,X_396))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) ),[1,0],$fot(inverse(least_upper_bound(X_395,X_396)))]]) ).
cnf(refute_0_645,plain,
( least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))) != inverse(least_upper_bound(X_395,X_396))
| inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) = inverse(inverse(least_upper_bound(X_395,X_396))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) = inverse(inverse(least_upper_bound(X_395,X_396))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))),inverse(least_upper_bound(X_395,X_396))) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
( inverse(inverse(least_upper_bound(X_395,X_396))) != least_upper_bound(X_395,X_396)
| inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) != inverse(inverse(least_upper_bound(X_395,X_396)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) = least_upper_bound(X_395,X_396) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(X_395,X_396))))),bind(Z0,$fot(least_upper_bound(X_395,X_396)))]]) ).
cnf(refute_0_648,plain,
( inverse(inverse(least_upper_bound(X_395,X_396))) != least_upper_bound(X_395,X_396)
| inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) = least_upper_bound(X_395,X_396) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),inverse(inverse(least_upper_bound(X_395,X_396)))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) = least_upper_bound(X_395,X_396),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_395,X_396))),least_upper_bound(X_395,X_396)) )],[refute_0_619,refute_0_648]) ).
cnf(refute_0_650,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))) != least_upper_bound(X_395,X_396)
| least_upper_bound(X_396,X_395) != inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))
| least_upper_bound(X_396,X_395) = least_upper_bound(X_395,X_396) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_396,X_395),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) ),[1],$fot(least_upper_bound(X_395,X_396))]]) ).
cnf(refute_0_651,plain,
( least_upper_bound(X_396,X_395) != inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))
| least_upper_bound(X_396,X_395) = least_upper_bound(X_395,X_396) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396)))),least_upper_bound(X_395,X_396)) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
least_upper_bound(X_396,X_395) = least_upper_bound(X_395,X_396),
inference(resolve,[$cnf( $equal(least_upper_bound(X_396,X_395),inverse(least_upper_bound(inverse(least_upper_bound(X_396,X_395)),inverse(least_upper_bound(X_395,X_396))))) )],[refute_0_618,refute_0_651]) ).
cnf(refute_0_653,plain,
( least_upper_bound(X_396,X_395) != least_upper_bound(X_395,X_396)
| least_upper_bound(X_395,X_396) = least_upper_bound(X_396,X_395) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_396,X_395))),bind(Y0,$fot(least_upper_bound(X_395,X_396)))]]) ).
cnf(refute_0_654,plain,
least_upper_bound(X_395,X_396) = least_upper_bound(X_396,X_395),
inference(resolve,[$cnf( $equal(least_upper_bound(X_396,X_395),least_upper_bound(X_395,X_396)) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)),
inference(subst,[],[refute_0_654:[bind(X_395,$fot(multiply(greatest_lower_bound(X_13,X_72),X_470))),bind(X_396,$fot(identity))]]) ).
cnf(refute_0_656,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470))
| least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))) ),[0],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)))]]) ).
cnf(refute_0_657,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470))) )],[refute_0_655,refute_0_656]) ).
cnf(refute_0_658,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_13,X_72),X_470),identity),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))) )],[refute_0_562,refute_0_657]) ).
cnf(refute_0_659,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)) != least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))))]]) ).
cnf(refute_0_660,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),X_470)),least_upper_bound(identity,multiply(greatest_lower_bound(X_13,X_72),least_upper_bound(X_470,inverse(X_72))))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)),
inference(subst,[],[refute_0_660:[bind(X_13,$fot(identity)),bind(X_470,$fot(identity)),bind(X_72,$fot(X_59))]]) ).
cnf(refute_0_662,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity))
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = identity ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_663,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),identity)),identity) )],[refute_0_496,refute_0_663]) ).
cnf(refute_0_665,plain,
multiply(X_98,greatest_lower_bound(X_99,identity)) = greatest_lower_bound(multiply(X_98,X_99),multiply(X_98,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_98)),bind(Y,$fot(X_99)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_666,plain,
X_98 = multiply(X_98,identity),
inference(subst,[],[refute_0_47:[bind(X_33,$fot(X_98))]]) ).
cnf(refute_0_667,plain,
( X_98 != multiply(X_98,identity)
| multiply(X_98,identity) = X_98 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_98)),bind(Y0,$fot(multiply(X_98,identity)))]]) ).
cnf(refute_0_668,plain,
multiply(X_98,identity) = X_98,
inference(resolve,[$cnf( $equal(X_98,multiply(X_98,identity)) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
( multiply(X_98,greatest_lower_bound(X_99,identity)) != greatest_lower_bound(multiply(X_98,X_99),multiply(X_98,identity))
| multiply(X_98,identity) != X_98
| multiply(X_98,greatest_lower_bound(X_99,identity)) = greatest_lower_bound(multiply(X_98,X_99),X_98) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_98,greatest_lower_bound(X_99,identity)),greatest_lower_bound(multiply(X_98,X_99),multiply(X_98,identity))) ),[1,1],$fot(X_98)]]) ).
cnf(refute_0_670,plain,
( multiply(X_98,greatest_lower_bound(X_99,identity)) != greatest_lower_bound(multiply(X_98,X_99),multiply(X_98,identity))
| multiply(X_98,greatest_lower_bound(X_99,identity)) = greatest_lower_bound(multiply(X_98,X_99),X_98) ),
inference(resolve,[$cnf( $equal(multiply(X_98,identity),X_98) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
multiply(X_98,greatest_lower_bound(X_99,identity)) = greatest_lower_bound(multiply(X_98,X_99),X_98),
inference(resolve,[$cnf( $equal(multiply(X_98,greatest_lower_bound(X_99,identity)),greatest_lower_bound(multiply(X_98,X_99),multiply(X_98,identity))) )],[refute_0_665,refute_0_670]) ).
cnf(refute_0_672,plain,
greatest_lower_bound(multiply(X_98,X_99),X_98) = greatest_lower_bound(X_98,multiply(X_98,X_99)),
inference(subst,[],[refute_0_348:[bind(X,$fot(X_98)),bind(Y,$fot(multiply(X_98,X_99)))]]) ).
cnf(refute_0_673,plain,
( multiply(X_98,greatest_lower_bound(X_99,identity)) != greatest_lower_bound(multiply(X_98,X_99),X_98)
| greatest_lower_bound(multiply(X_98,X_99),X_98) != greatest_lower_bound(X_98,multiply(X_98,X_99))
| multiply(X_98,greatest_lower_bound(X_99,identity)) = greatest_lower_bound(X_98,multiply(X_98,X_99)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_98,greatest_lower_bound(X_99,identity)),greatest_lower_bound(X_98,multiply(X_98,X_99))) ),[0],$fot(greatest_lower_bound(multiply(X_98,X_99),X_98))]]) ).
cnf(refute_0_674,plain,
( multiply(X_98,greatest_lower_bound(X_99,identity)) != greatest_lower_bound(multiply(X_98,X_99),X_98)
| multiply(X_98,greatest_lower_bound(X_99,identity)) = greatest_lower_bound(X_98,multiply(X_98,X_99)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_98,X_99),X_98),greatest_lower_bound(X_98,multiply(X_98,X_99))) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
multiply(X_98,greatest_lower_bound(X_99,identity)) = greatest_lower_bound(X_98,multiply(X_98,X_99)),
inference(resolve,[$cnf( $equal(multiply(X_98,greatest_lower_bound(X_99,identity)),greatest_lower_bound(multiply(X_98,X_99),X_98)) )],[refute_0_671,refute_0_674]) ).
cnf(refute_0_676,plain,
multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) = greatest_lower_bound(least_upper_bound(identity,X_71),multiply(least_upper_bound(identity,X_71),inverse(X_71))),
inference(subst,[],[refute_0_675:[bind(X_98,$fot(least_upper_bound(identity,X_71))),bind(X_99,$fot(inverse(X_71)))]]) ).
cnf(refute_0_677,plain,
multiply(least_upper_bound(identity,X_71),inverse(X_71)) = least_upper_bound(identity,multiply(identity,inverse(X_71))),
inference(subst,[],[refute_0_69:[bind(X_64,$fot(identity)),bind(X_65,$fot(X_71))]]) ).
cnf(refute_0_678,plain,
multiply(identity,inverse(X_71)) = inverse(X_71),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_71)))]]) ).
cnf(refute_0_679,plain,
( multiply(identity,inverse(X_71)) != inverse(X_71)
| multiply(least_upper_bound(identity,X_71),inverse(X_71)) != least_upper_bound(identity,multiply(identity,inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),inverse(X_71)) = least_upper_bound(identity,inverse(X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),inverse(X_71)),least_upper_bound(identity,multiply(identity,inverse(X_71)))) ),[1,1],$fot(inverse(X_71))]]) ).
cnf(refute_0_680,plain,
( multiply(least_upper_bound(identity,X_71),inverse(X_71)) != least_upper_bound(identity,multiply(identity,inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),inverse(X_71)) = least_upper_bound(identity,inverse(X_71)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_71)),inverse(X_71)) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
multiply(least_upper_bound(identity,X_71),inverse(X_71)) = least_upper_bound(identity,inverse(X_71)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),inverse(X_71)),least_upper_bound(identity,multiply(identity,inverse(X_71)))) )],[refute_0_677,refute_0_680]) ).
cnf(refute_0_682,plain,
( multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) != greatest_lower_bound(least_upper_bound(identity,X_71),multiply(least_upper_bound(identity,X_71),inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),inverse(X_71)) != least_upper_bound(identity,inverse(X_71))
| multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)),greatest_lower_bound(least_upper_bound(identity,X_71),multiply(least_upper_bound(identity,X_71),inverse(X_71)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_71)))]]) ).
cnf(refute_0_683,plain,
( multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) != greatest_lower_bound(least_upper_bound(identity,X_71),multiply(least_upper_bound(identity,X_71),inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),inverse(X_71)),least_upper_bound(identity,inverse(X_71))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)),greatest_lower_bound(least_upper_bound(identity,X_71),multiply(least_upper_bound(identity,X_71),inverse(X_71)))) )],[refute_0_676,refute_0_683]) ).
cnf(refute_0_685,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_21,X_22)) = greatest_lower_bound(X_22,X_21),
inference(subst,[],[refute_0_466:[bind(X_13,$fot(X_21)),bind(X_7,$fot(X_22))]]) ).
cnf(refute_0_686,plain,
greatest_lower_bound(X_22,X_21) = greatest_lower_bound(X_21,X_22),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_687,plain,
( greatest_lower_bound(X_22,X_21) != greatest_lower_bound(X_21,X_22)
| greatest_lower_bound(X_21,X_22) = greatest_lower_bound(X_22,X_21) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_22,X_21))),bind(Y0,$fot(greatest_lower_bound(X_21,X_22)))]]) ).
cnf(refute_0_688,plain,
greatest_lower_bound(X_21,X_22) = greatest_lower_bound(X_22,X_21),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_21),greatest_lower_bound(X_21,X_22)) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
( greatest_lower_bound(X_21,X_22) != greatest_lower_bound(X_22,X_21)
| greatest_lower_bound(X_22,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(X_22,X_21)
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,X_21)) = greatest_lower_bound(X_22,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(X_22,X_21)) ),[0,1],$fot(greatest_lower_bound(X_22,X_21))]]) ).
cnf(refute_0_690,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_21,X_22)) != greatest_lower_bound(X_22,X_21)
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,X_21)) = greatest_lower_bound(X_22,X_21) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,X_22),greatest_lower_bound(X_22,X_21)) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_22,X_21)) = greatest_lower_bound(X_22,X_21),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_21,X_22)),greatest_lower_bound(X_22,X_21)) )],[refute_0_685,refute_0_690]) ).
cnf(refute_0_692,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = greatest_lower_bound(X_22,multiply(X_22,X_140)),
inference(subst,[],[refute_0_691:[bind(X_21,$fot(multiply(X_22,X_140)))]]) ).
cnf(refute_0_693,plain,
multiply(X_22,greatest_lower_bound(X_140,identity)) = greatest_lower_bound(X_22,multiply(X_22,X_140)),
inference(subst,[],[refute_0_675:[bind(X_98,$fot(X_22)),bind(X_99,$fot(X_140))]]) ).
cnf(refute_0_694,plain,
( multiply(X_22,greatest_lower_bound(X_140,identity)) != greatest_lower_bound(X_22,multiply(X_22,X_140))
| greatest_lower_bound(X_22,multiply(X_22,X_140)) = multiply(X_22,greatest_lower_bound(X_140,identity)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_22,greatest_lower_bound(X_140,identity)))),bind(Y0,$fot(greatest_lower_bound(X_22,multiply(X_22,X_140))))]]) ).
cnf(refute_0_695,plain,
greatest_lower_bound(X_22,multiply(X_22,X_140)) = multiply(X_22,greatest_lower_bound(X_140,identity)),
inference(resolve,[$cnf( $equal(multiply(X_22,greatest_lower_bound(X_140,identity)),greatest_lower_bound(X_22,multiply(X_22,X_140))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
( greatest_lower_bound(X_22,multiply(X_22,X_140)) != multiply(X_22,greatest_lower_bound(X_140,identity))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) != greatest_lower_bound(X_22,multiply(X_22,X_140))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(X_140,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))),greatest_lower_bound(X_22,multiply(X_22,X_140))) ),[1],$fot(multiply(X_22,greatest_lower_bound(X_140,identity)))]]) ).
cnf(refute_0_697,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) != greatest_lower_bound(X_22,multiply(X_22,X_140))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(X_140,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,multiply(X_22,X_140)),multiply(X_22,greatest_lower_bound(X_140,identity))) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(X_140,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))),greatest_lower_bound(X_22,multiply(X_22,X_140))) )],[refute_0_692,refute_0_697]) ).
cnf(refute_0_699,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)) = greatest_lower_bound(identity,X_140),
inference(subst,[],[refute_0_466:[bind(X_13,$fot(X_140)),bind(X_7,$fot(identity))]]) ).
cnf(refute_0_700,plain,
multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))),
introduced(tautology,[refl,[$fot(multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))))]]) ).
cnf(refute_0_701,plain,
( multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) != multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)) != greatest_lower_bound(identity,X_140)
| multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(identity,X_140)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))),multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_140))]]) ).
cnf(refute_0_702,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)) != greatest_lower_bound(identity,X_140)
| multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(identity,X_140)) ),
inference(resolve,[$cnf( $equal(multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))),multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(identity,X_140)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)),greatest_lower_bound(identity,X_140)) )],[refute_0_699,refute_0_702]) ).
cnf(refute_0_704,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_470:[bind(X_13,$fot(multiply(X,Y))),bind(X_21,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_705,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_706,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_705]) ).
cnf(refute_0_707,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$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_708,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( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_706,refute_0_707]) ).
cnf(refute_0_709,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_704,refute_0_708]) ).
cnf(refute_0_710,plain,
least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) = greatest_lower_bound(Y,Z),
inference(subst,[],[refute_0_470:[bind(X_13,$fot(Z)),bind(X_21,$fot(Y))]]) ).
cnf(refute_0_711,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_712,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_713,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( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_710,refute_0_713]) ).
cnf(refute_0_715,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_716,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_715]) ).
cnf(refute_0_717,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
inference(subst,[],[refute_0_716:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_718,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_167:[bind(X0,$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_719,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( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_717,refute_0_718]) ).
cnf(refute_0_720,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_714,refute_0_719]) ).
cnf(refute_0_721,plain,
greatest_lower_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(subst,[],[refute_0_706:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_722,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_723,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_724,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( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_167:[bind(X0,$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_727,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( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_720,refute_0_727]) ).
cnf(refute_0_729,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_65:[bind(X,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y,$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_730,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_167:[bind(X0,$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_731,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( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_728,refute_0_731]) ).
cnf(refute_0_733,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$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_734,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( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
introduced(tautology,[equality,[$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_736,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( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_721,refute_0_735]) ).
cnf(refute_0_737,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_734,refute_0_736]) ).
cnf(refute_0_738,plain,
multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_709,refute_0_737]) ).
cnf(refute_0_739,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_740,plain,
multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_738,refute_0_739]) ).
cnf(refute_0_741,plain,
multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity)) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))),
inference(subst,[],[refute_0_740:[bind(X,$fot(X_22)),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(X_140,identity)))]]) ).
cnf(refute_0_742,plain,
( multiply(X_98,greatest_lower_bound(X_99,identity)) != greatest_lower_bound(X_98,multiply(X_98,X_99))
| greatest_lower_bound(X_98,multiply(X_98,X_99)) = multiply(X_98,greatest_lower_bound(X_99,identity)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_98,greatest_lower_bound(X_99,identity)))),bind(Y0,$fot(greatest_lower_bound(X_98,multiply(X_98,X_99))))]]) ).
cnf(refute_0_743,plain,
greatest_lower_bound(X_98,multiply(X_98,X_99)) = multiply(X_98,greatest_lower_bound(X_99,identity)),
inference(resolve,[$cnf( $equal(multiply(X_98,greatest_lower_bound(X_99,identity)),greatest_lower_bound(X_98,multiply(X_98,X_99))) )],[refute_0_675,refute_0_742]) ).
cnf(refute_0_744,plain,
greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity)),
inference(subst,[],[refute_0_743:[bind(X_98,$fot(X_22)),bind(X_99,$fot(greatest_lower_bound(X_140,identity)))]]) ).
cnf(refute_0_745,plain,
( multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity)) != multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))
| greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))) != multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity))
| greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))))),bind(Y0,$fot(multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity)))),bind(Z0,$fot(multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))))]]) ).
cnf(refute_0_746,plain,
( multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity)) != multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))
| greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))),multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))),
inference(resolve,[$cnf( $equal(multiply(X_22,greatest_lower_bound(greatest_lower_bound(X_140,identity),identity)),multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))) )],[refute_0_741,refute_0_746]) ).
cnf(refute_0_748,plain,
greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)),X_43),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_41)),bind(Y,$fot(greatest_lower_bound(X_13,X_41))),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_749,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)) = greatest_lower_bound(X_41,X_13),
inference(subst,[],[refute_0_466:[bind(X_7,$fot(X_41))]]) ).
cnf(refute_0_750,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)) != greatest_lower_bound(X_41,X_13)
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)),X_43)
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)),X_43)) ),[1,0],$fot(greatest_lower_bound(X_41,X_13))]]) ).
cnf(refute_0_751,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)),X_43)
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)),greatest_lower_bound(X_41,X_13)) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_41)),X_43)) )],[refute_0_748,refute_0_751]) ).
cnf(refute_0_753,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42))) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(greatest_lower_bound(X_13,X_42)))]]) ).
cnf(refute_0_754,plain,
greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42)) = greatest_lower_bound(X_42,X_13),
inference(subst,[],[refute_0_466:[bind(X_7,$fot(X_42))]]) ).
cnf(refute_0_755,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42))) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42))
| greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42)) != greatest_lower_bound(X_42,X_13)
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42))),greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42))) ),[0,1],$fot(greatest_lower_bound(X_42,X_13))]]) ).
cnf(refute_0_756,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42))) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42)),greatest_lower_bound(X_42,X_13)) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,greatest_lower_bound(X_13,X_42))),greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42))) )],[refute_0_753,refute_0_756]) ).
cnf(refute_0_758,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)),
inference(subst,[],[refute_0_462:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_759,plain,
greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)) = greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)))]]) ).
cnf(refute_0_760,plain,
( greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)) != greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13))
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13))) ),[1,1],$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))]]) ).
cnf(refute_0_761,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))
| greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) )],[refute_0_758,refute_0_761]) ).
cnf(refute_0_763,plain,
greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_41,X_42)))]]) ).
cnf(refute_0_764,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X))]]) ).
cnf(refute_0_765,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X)
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),X) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X)))]]) ).
cnf(refute_0_766,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_42),X) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),X)) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X)
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),X) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,X))
| greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X))]]) ).
cnf(refute_0_768,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X)
| greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X))) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),X)) )],[refute_0_763,refute_0_768]) ).
cnf(refute_0_770,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,X))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)) = greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X))))]]) ).
cnf(refute_0_771,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,X)) = greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_41,X_42)),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X))) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) = greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)),
inference(subst,[],[refute_0_771:[bind(X,$fot(X_42)),bind(X_41,$fot(greatest_lower_bound(X_41,X_42))),bind(X_42,$fot(X_13))]]) ).
cnf(refute_0_773,plain,
( greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)) != greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) != greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13))
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)))),bind(Y0,$fot(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)))),bind(Z0,$fot(greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))))]]) ).
cnf(refute_0_774,plain,
( greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)) != greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)),greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13))) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_13)),greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))) )],[refute_0_762,refute_0_774]) ).
cnf(refute_0_776,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42))
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)) != greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)),greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)))]]) ).
cnf(refute_0_777,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42)),greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))) )],[refute_0_775,refute_0_776]) ).
cnf(refute_0_778,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) = greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_13,X_42))) )],[refute_0_757,refute_0_777]) ).
cnf(refute_0_779,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) != greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))
| greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))),bind(Y0,$fot(greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))))]]) ).
cnf(refute_0_780,plain,
greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13))) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)),greatest_lower_bound(X_42,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_13)))) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) = greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)),
inference(subst,[],[refute_0_780:[bind(X_13,$fot(X_43)),bind(X_41,$fot(X_13)),bind(X_42,$fot(X_41))]]) ).
cnf(refute_0_782,plain,
greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43) = greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)),
inference(subst,[],[refute_0_462:[bind(X,$fot(X_13)),bind(Y,$fot(X_41)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_783,plain,
greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)))]]) ).
cnf(refute_0_784,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43))
| greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43) != greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43))) ),[1,1],$fot(greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)))]]) ).
cnf(refute_0_785,plain,
( greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43) != greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43))) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43),greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) )],[refute_0_782,refute_0_785]) ).
cnf(refute_0_787,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) != greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)))
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))))),bind(Z0,$fot(greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))))]]) ).
cnf(refute_0_788,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) != greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)))) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) = greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))),greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) )],[refute_0_781,refute_0_788]) ).
cnf(refute_0_790,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) = greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)) ),[0],$fot(greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)))]]) ).
cnf(refute_0_791,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) = greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43))) )],[refute_0_789,refute_0_790]) ).
cnf(refute_0_792,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43)),
inference(subst,[],[refute_0_462:[bind(X,$fot(X_41)),bind(Y,$fot(X_13)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_793,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)
| greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43) != greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43))
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)),greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43))]]) ).
cnf(refute_0_794,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43),greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)),greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)) )],[refute_0_791,refute_0_794]) ).
cnf(refute_0_796,plain,
greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(greatest_lower_bound(X_13,X_41),X_43)),greatest_lower_bound(greatest_lower_bound(X_41,X_13),X_43)) )],[refute_0_752,refute_0_795]) ).
cnf(refute_0_797,plain,
greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))) = greatest_lower_bound(X_41,greatest_lower_bound(X_13,multiply(X_13,X_140))),
inference(subst,[],[refute_0_796:[bind(X_43,$fot(multiply(X_13,X_140)))]]) ).
cnf(refute_0_798,plain,
multiply(X_13,greatest_lower_bound(X_140,identity)) = greatest_lower_bound(X_13,multiply(X_13,X_140)),
inference(subst,[],[refute_0_675:[bind(X_98,$fot(X_13)),bind(X_99,$fot(X_140))]]) ).
cnf(refute_0_799,plain,
( multiply(X_13,greatest_lower_bound(X_140,identity)) != greatest_lower_bound(X_13,multiply(X_13,X_140))
| greatest_lower_bound(X_13,multiply(X_13,X_140)) = multiply(X_13,greatest_lower_bound(X_140,identity)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_13,greatest_lower_bound(X_140,identity)))),bind(Y0,$fot(greatest_lower_bound(X_13,multiply(X_13,X_140))))]]) ).
cnf(refute_0_800,plain,
greatest_lower_bound(X_13,multiply(X_13,X_140)) = multiply(X_13,greatest_lower_bound(X_140,identity)),
inference(resolve,[$cnf( $equal(multiply(X_13,greatest_lower_bound(X_140,identity)),greatest_lower_bound(X_13,multiply(X_13,X_140))) )],[refute_0_798,refute_0_799]) ).
cnf(refute_0_801,plain,
( greatest_lower_bound(X_13,multiply(X_13,X_140)) != multiply(X_13,greatest_lower_bound(X_140,identity))
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))) != greatest_lower_bound(X_41,greatest_lower_bound(X_13,multiply(X_13,X_140)))
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))) = greatest_lower_bound(X_41,multiply(X_13,greatest_lower_bound(X_140,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))),greatest_lower_bound(X_41,greatest_lower_bound(X_13,multiply(X_13,X_140)))) ),[1,1],$fot(multiply(X_13,greatest_lower_bound(X_140,identity)))]]) ).
cnf(refute_0_802,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))) != greatest_lower_bound(X_41,greatest_lower_bound(X_13,multiply(X_13,X_140)))
| greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))) = greatest_lower_bound(X_41,multiply(X_13,greatest_lower_bound(X_140,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,multiply(X_13,X_140)),multiply(X_13,greatest_lower_bound(X_140,identity))) )],[refute_0_800,refute_0_801]) ).
cnf(refute_0_803,plain,
greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))) = greatest_lower_bound(X_41,multiply(X_13,greatest_lower_bound(X_140,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_41,multiply(X_13,X_140))),greatest_lower_bound(X_41,greatest_lower_bound(X_13,multiply(X_13,X_140)))) )],[refute_0_797,refute_0_802]) ).
cnf(refute_0_804,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))),
inference(subst,[],[refute_0_803:[bind(X_13,$fot(X_22)),bind(X_41,$fot(X_22))]]) ).
cnf(refute_0_805,plain,
( greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))) != multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) != greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity)))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))))),bind(Y0,$fot(greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))))),bind(Z0,$fot(multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))))]]) ).
cnf(refute_0_806,plain,
( greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))) != multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))),greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity)))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,multiply(X_22,greatest_lower_bound(X_140,identity))),multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))) )],[refute_0_747,refute_0_806]) ).
cnf(refute_0_808,plain,
( multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) != multiply(X_22,greatest_lower_bound(identity,X_140))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) != multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(identity,X_140)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))))),bind(Y0,$fot(multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))))),bind(Z0,$fot(multiply(X_22,greatest_lower_bound(identity,X_140))))]]) ).
cnf(refute_0_809,plain,
( multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))) != multiply(X_22,greatest_lower_bound(identity,X_140))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(identity,X_140)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))),multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity)))) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) = multiply(X_22,greatest_lower_bound(identity,X_140)),
inference(resolve,[$cnf( $equal(multiply(X_22,greatest_lower_bound(identity,greatest_lower_bound(X_140,identity))),multiply(X_22,greatest_lower_bound(identity,X_140))) )],[refute_0_703,refute_0_809]) ).
cnf(refute_0_811,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) != multiply(X_22,greatest_lower_bound(X_140,identity))
| greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) != multiply(X_22,greatest_lower_bound(identity,X_140))
| multiply(X_22,greatest_lower_bound(identity,X_140)) = multiply(X_22,greatest_lower_bound(X_140,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))),multiply(X_22,greatest_lower_bound(X_140,identity))) ),[0],$fot(multiply(X_22,greatest_lower_bound(identity,X_140)))]]) ).
cnf(refute_0_812,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))) != multiply(X_22,greatest_lower_bound(X_140,identity))
| multiply(X_22,greatest_lower_bound(identity,X_140)) = multiply(X_22,greatest_lower_bound(X_140,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))),multiply(X_22,greatest_lower_bound(identity,X_140))) )],[refute_0_810,refute_0_811]) ).
cnf(refute_0_813,plain,
multiply(X_22,greatest_lower_bound(identity,X_140)) = multiply(X_22,greatest_lower_bound(X_140,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_22,multiply(X_22,X_140))),multiply(X_22,greatest_lower_bound(X_140,identity))) )],[refute_0_698,refute_0_812]) ).
cnf(refute_0_814,plain,
( multiply(X_22,greatest_lower_bound(identity,X_140)) != multiply(X_22,greatest_lower_bound(X_140,identity))
| multiply(X_22,greatest_lower_bound(X_140,identity)) = multiply(X_22,greatest_lower_bound(identity,X_140)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_22,greatest_lower_bound(identity,X_140)))),bind(Y0,$fot(multiply(X_22,greatest_lower_bound(X_140,identity))))]]) ).
cnf(refute_0_815,plain,
multiply(X_22,greatest_lower_bound(X_140,identity)) = multiply(X_22,greatest_lower_bound(identity,X_140)),
inference(resolve,[$cnf( $equal(multiply(X_22,greatest_lower_bound(identity,X_140)),multiply(X_22,greatest_lower_bound(X_140,identity))) )],[refute_0_813,refute_0_814]) ).
cnf(refute_0_816,plain,
multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) = multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))),
inference(subst,[],[refute_0_815:[bind(X_140,$fot(inverse(X_71))),bind(X_22,$fot(least_upper_bound(identity,X_71)))]]) ).
cnf(refute_0_817,plain,
( multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) != multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) != greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)),greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))) ),[0],$fot(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))))]]) ).
cnf(refute_0_818,plain,
( multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)) != greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)),multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71)))) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(inverse(X_71),identity)),greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))) )],[refute_0_684,refute_0_818]) ).
cnf(refute_0_820,plain,
multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))))) = inverse(inverse(least_upper_bound(inverse(X_31),X_69))),
inference(subst,[],[refute_0_424:[bind(X_30,$fot(inverse(least_upper_bound(inverse(X_31),X_69)))),bind(X_40,$fot(least_upper_bound(identity,multiply(X_69,X_31))))]]) ).
cnf(refute_0_821,plain,
X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_69)),multiply(least_upper_bound(inverse(X_31),X_69),X_31)),
inference(subst,[],[refute_0_8:[bind(X_30,$fot(least_upper_bound(inverse(X_31),X_69)))]]) ).
cnf(refute_0_822,plain,
multiply(least_upper_bound(inverse(X_31),X_69),X_31) = least_upper_bound(identity,multiply(X_69,X_31)),
inference(subst,[],[refute_0_133:[bind(X_63,$fot(X_31)),bind(X_65,$fot(X_69))]]) ).
cnf(refute_0_823,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),X_69)),multiply(least_upper_bound(inverse(X_31),X_69),X_31))
| multiply(least_upper_bound(inverse(X_31),X_69),X_31) != least_upper_bound(identity,multiply(X_69,X_31))
| X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),X_69)),multiply(least_upper_bound(inverse(X_31),X_69),X_31))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_69,X_31)))]]) ).
cnf(refute_0_824,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),X_69)),multiply(least_upper_bound(inverse(X_31),X_69),X_31))
| X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_31),X_69),X_31),least_upper_bound(identity,multiply(X_69,X_31))) )],[refute_0_822,refute_0_823]) ).
cnf(refute_0_825,plain,
X_31 = multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),X_69)),multiply(least_upper_bound(inverse(X_31),X_69),X_31))) )],[refute_0_821,refute_0_824]) ).
cnf(refute_0_826,plain,
( X_31 != multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31)))
| multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))) = X_31 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31)))))]]) ).
cnf(refute_0_827,plain,
multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31)))) )],[refute_0_825,refute_0_826]) ).
cnf(refute_0_828,plain,
( multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))) != X_31
| multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))))) != inverse(inverse(least_upper_bound(inverse(X_31),X_69)))
| multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) = inverse(inverse(least_upper_bound(inverse(X_31),X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))))),inverse(inverse(least_upper_bound(inverse(X_31),X_69)))) ),[0,1,0],$fot(X_31)]]) ).
cnf(refute_0_829,plain,
( multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))))) != inverse(inverse(least_upper_bound(inverse(X_31),X_69)))
| multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) = inverse(inverse(least_upper_bound(inverse(X_31),X_69))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))),X_31) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) = inverse(inverse(least_upper_bound(inverse(X_31),X_69))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(multiply(inverse(least_upper_bound(inverse(X_31),X_69)),least_upper_bound(identity,multiply(X_69,X_31))))),inverse(inverse(least_upper_bound(inverse(X_31),X_69)))) )],[refute_0_820,refute_0_829]) ).
cnf(refute_0_831,plain,
inverse(inverse(least_upper_bound(inverse(X_31),X_69))) = least_upper_bound(inverse(X_31),X_69),
inference(subst,[],[refute_0_83:[bind(X_35,$fot(least_upper_bound(inverse(X_31),X_69)))]]) ).
cnf(refute_0_832,plain,
( multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) != inverse(inverse(least_upper_bound(inverse(X_31),X_69)))
| inverse(inverse(least_upper_bound(inverse(X_31),X_69))) != least_upper_bound(inverse(X_31),X_69)
| multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) = least_upper_bound(inverse(X_31),X_69) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)),least_upper_bound(inverse(X_31),X_69)) ),[0],$fot(inverse(inverse(least_upper_bound(inverse(X_31),X_69))))]]) ).
cnf(refute_0_833,plain,
( multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) != inverse(inverse(least_upper_bound(inverse(X_31),X_69)))
| multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) = least_upper_bound(inverse(X_31),X_69) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X_31),X_69))),least_upper_bound(inverse(X_31),X_69)) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)) = least_upper_bound(inverse(X_31),X_69),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_69,X_31)),inverse(X_31)),inverse(inverse(least_upper_bound(inverse(X_31),X_69)))) )],[refute_0_830,refute_0_833]) ).
cnf(refute_0_835,plain,
multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105))))),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)),
inference(subst,[],[refute_0_834:[bind(X_31,$fot(inverse(greatest_lower_bound(identity,inverse(X_105))))),bind(X_69,$fot(greatest_lower_bound(identity,X_105)))]]) ).
cnf(refute_0_836,plain,
multiply(greatest_lower_bound(identity,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(identity,X_105)))) = inverse(inverse(X_105)),
inference(subst,[],[refute_0_424:[bind(X_30,$fot(inverse(X_105))),bind(X_40,$fot(greatest_lower_bound(identity,X_105)))]]) ).
cnf(refute_0_837,plain,
multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) = greatest_lower_bound(multiply(inverse(X_99),X_99),multiply(inverse(X_99),X_100)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_99))),bind(Y,$fot(X_99)),bind(Z,$fot(X_100))]]) ).
cnf(refute_0_838,plain,
multiply(inverse(X_99),X_99) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_99))]]) ).
cnf(refute_0_839,plain,
( multiply(inverse(X_99),X_99) != identity
| multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) != greatest_lower_bound(multiply(inverse(X_99),X_99),multiply(inverse(X_99),X_100))
| multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) = greatest_lower_bound(identity,multiply(inverse(X_99),X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)),greatest_lower_bound(multiply(inverse(X_99),X_99),multiply(inverse(X_99),X_100))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_840,plain,
( multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) != greatest_lower_bound(multiply(inverse(X_99),X_99),multiply(inverse(X_99),X_100))
| multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) = greatest_lower_bound(identity,multiply(inverse(X_99),X_100)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),X_99),identity) )],[refute_0_838,refute_0_839]) ).
cnf(refute_0_841,plain,
multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)) = greatest_lower_bound(identity,multiply(inverse(X_99),X_100)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),greatest_lower_bound(X_99,X_100)),greatest_lower_bound(multiply(inverse(X_99),X_99),multiply(inverse(X_99),X_100))) )],[refute_0_837,refute_0_840]) ).
cnf(refute_0_842,plain,
multiply(inverse(X_104),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(identity,multiply(inverse(X_104),identity)),
inference(subst,[],[refute_0_841:[bind(X_100,$fot(identity)),bind(X_99,$fot(X_104))]]) ).
cnf(refute_0_843,plain,
inverse(X_104) = multiply(inverse(X_104),identity),
inference(subst,[],[refute_0_47:[bind(X_33,$fot(inverse(X_104)))]]) ).
cnf(refute_0_844,plain,
( inverse(X_104) != multiply(inverse(X_104),identity)
| multiply(inverse(X_104),identity) = inverse(X_104) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(X_104))),bind(Y0,$fot(multiply(inverse(X_104),identity)))]]) ).
cnf(refute_0_845,plain,
multiply(inverse(X_104),identity) = inverse(X_104),
inference(resolve,[$cnf( $equal(inverse(X_104),multiply(inverse(X_104),identity)) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
( multiply(inverse(X_104),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(identity,multiply(inverse(X_104),identity))
| multiply(inverse(X_104),identity) != inverse(X_104)
| multiply(inverse(X_104),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(identity,inverse(X_104)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,multiply(inverse(X_104),identity))) ),[1,1],$fot(inverse(X_104))]]) ).
cnf(refute_0_847,plain,
( multiply(inverse(X_104),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(identity,multiply(inverse(X_104),identity))
| multiply(inverse(X_104),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(identity,inverse(X_104)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_104),identity),inverse(X_104)) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
multiply(inverse(X_104),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(identity,inverse(X_104)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,multiply(inverse(X_104),identity))) )],[refute_0_842,refute_0_847]) ).
cnf(refute_0_849,plain,
multiply(inverse(X_105),greatest_lower_bound(X_105,identity)) = greatest_lower_bound(identity,inverse(X_105)),
inference(subst,[],[refute_0_848:[bind(X_104,$fot(X_105))]]) ).
cnf(refute_0_850,plain,
greatest_lower_bound(identity,X_105) = greatest_lower_bound(X_105,identity),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_105))]]) ).
cnf(refute_0_851,plain,
( greatest_lower_bound(identity,X_105) != greatest_lower_bound(X_105,identity)
| greatest_lower_bound(X_105,identity) = greatest_lower_bound(identity,X_105) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(identity,X_105))),bind(Y0,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_852,plain,
greatest_lower_bound(X_105,identity) = greatest_lower_bound(identity,X_105),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_105),greatest_lower_bound(X_105,identity)) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
( multiply(inverse(X_105),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(identity,inverse(X_105))
| greatest_lower_bound(X_105,identity) != greatest_lower_bound(identity,X_105)
| multiply(inverse(X_105),greatest_lower_bound(identity,X_105)) = greatest_lower_bound(identity,inverse(X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,identity)),greatest_lower_bound(identity,inverse(X_105))) ),[0,1],$fot(greatest_lower_bound(identity,X_105))]]) ).
cnf(refute_0_854,plain,
( multiply(inverse(X_105),greatest_lower_bound(X_105,identity)) != greatest_lower_bound(identity,inverse(X_105))
| multiply(inverse(X_105),greatest_lower_bound(identity,X_105)) = greatest_lower_bound(identity,inverse(X_105)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,identity),greatest_lower_bound(identity,X_105)) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
multiply(inverse(X_105),greatest_lower_bound(identity,X_105)) = greatest_lower_bound(identity,inverse(X_105)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,identity)),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_849,refute_0_854]) ).
cnf(refute_0_856,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(identity,X_105)))) != inverse(inverse(X_105))
| multiply(inverse(X_105),greatest_lower_bound(identity,X_105)) != greatest_lower_bound(identity,inverse(X_105))
| multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(inverse(X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(identity,X_105)))),inverse(inverse(X_105))) ),[0,1,0],$fot(greatest_lower_bound(identity,inverse(X_105)))]]) ).
cnf(refute_0_857,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(identity,X_105)))) != inverse(inverse(X_105))
| multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(inverse(X_105)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(identity,X_105)),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(inverse(X_105)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(identity,X_105)))),inverse(inverse(X_105))) )],[refute_0_836,refute_0_857]) ).
cnf(refute_0_859,plain,
inverse(inverse(X_105)) = X_105,
inference(subst,[],[refute_0_83:[bind(X_35,$fot(X_105))]]) ).
cnf(refute_0_860,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) != inverse(inverse(X_105))
| inverse(inverse(X_105)) != X_105
| multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = X_105 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))),X_105) ),[0],$fot(inverse(inverse(X_105)))]]) ).
cnf(refute_0_861,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) != inverse(inverse(X_105))
| multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = X_105 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_105)),X_105) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = X_105,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))),inverse(inverse(X_105))) )],[refute_0_858,refute_0_861]) ).
cnf(refute_0_863,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) != X_105
| multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105))))),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))
| multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105))))),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))) ),[0,0,1],$fot(X_105)]]) ).
cnf(refute_0_864,plain,
( multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105))))),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))
| multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))),X_105) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_105),inverse(greatest_lower_bound(identity,inverse(X_105))))),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))) )],[refute_0_835,refute_0_864]) ).
cnf(refute_0_866,plain,
inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))) = greatest_lower_bound(identity,inverse(X_105)),
inference(subst,[],[refute_0_83:[bind(X_35,$fot(greatest_lower_bound(identity,inverse(X_105))))]]) ).
cnf(refute_0_867,plain,
multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))))]]) ).
cnf(refute_0_868,plain,
( multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))
| inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))) != greatest_lower_bound(identity,inverse(X_105))
| multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_105)))]]) ).
cnf(refute_0_869,plain,
( inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))) != greatest_lower_bound(identity,inverse(X_105))
| multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_866,refute_0_869]) ).
cnf(refute_0_871,plain,
( multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105)))
| multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))
| multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) = least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))) ),[0],$fot(multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))))]]) ).
cnf(refute_0_872,plain,
( multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))
| multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) = least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105)))) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
multiply(X_51,least_upper_bound(X_52,identity)) = least_upper_bound(multiply(X_51,X_52),multiply(X_51,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_874,plain,
X_51 = multiply(X_51,identity),
inference(subst,[],[refute_0_47:[bind(X_33,$fot(X_51))]]) ).
cnf(refute_0_875,plain,
( X_51 != multiply(X_51,identity)
| multiply(X_51,identity) = X_51 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_51)),bind(Y0,$fot(multiply(X_51,identity)))]]) ).
cnf(refute_0_876,plain,
multiply(X_51,identity) = X_51,
inference(resolve,[$cnf( $equal(X_51,multiply(X_51,identity)) )],[refute_0_874,refute_0_875]) ).
cnf(refute_0_877,plain,
( multiply(X_51,identity) != X_51
| multiply(X_51,least_upper_bound(X_52,identity)) != least_upper_bound(multiply(X_51,X_52),multiply(X_51,identity))
| multiply(X_51,least_upper_bound(X_52,identity)) = least_upper_bound(multiply(X_51,X_52),X_51) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,identity)),least_upper_bound(multiply(X_51,X_52),multiply(X_51,identity))) ),[1,1],$fot(X_51)]]) ).
cnf(refute_0_878,plain,
( multiply(X_51,least_upper_bound(X_52,identity)) != least_upper_bound(multiply(X_51,X_52),multiply(X_51,identity))
| multiply(X_51,least_upper_bound(X_52,identity)) = least_upper_bound(multiply(X_51,X_52),X_51) ),
inference(resolve,[$cnf( $equal(multiply(X_51,identity),X_51) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
multiply(X_51,least_upper_bound(X_52,identity)) = least_upper_bound(multiply(X_51,X_52),X_51),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,identity)),least_upper_bound(multiply(X_51,X_52),multiply(X_51,identity))) )],[refute_0_873,refute_0_878]) ).
cnf(refute_0_880,plain,
least_upper_bound(multiply(X_51,X_52),X_51) = least_upper_bound(X_51,multiply(X_51,X_52)),
inference(subst,[],[refute_0_65:[bind(X,$fot(X_51)),bind(Y,$fot(multiply(X_51,X_52)))]]) ).
cnf(refute_0_881,plain,
( multiply(X_51,least_upper_bound(X_52,identity)) != least_upper_bound(multiply(X_51,X_52),X_51)
| least_upper_bound(multiply(X_51,X_52),X_51) != least_upper_bound(X_51,multiply(X_51,X_52))
| multiply(X_51,least_upper_bound(X_52,identity)) = least_upper_bound(X_51,multiply(X_51,X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_51,least_upper_bound(X_52,identity)),least_upper_bound(X_51,multiply(X_51,X_52))) ),[0],$fot(least_upper_bound(multiply(X_51,X_52),X_51))]]) ).
cnf(refute_0_882,plain,
( multiply(X_51,least_upper_bound(X_52,identity)) != least_upper_bound(multiply(X_51,X_52),X_51)
| multiply(X_51,least_upper_bound(X_52,identity)) = least_upper_bound(X_51,multiply(X_51,X_52)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_52),X_51),least_upper_bound(X_51,multiply(X_51,X_52))) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
multiply(X_51,least_upper_bound(X_52,identity)) = least_upper_bound(X_51,multiply(X_51,X_52)),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,identity)),least_upper_bound(multiply(X_51,X_52),X_51)) )],[refute_0_879,refute_0_882]) ).
cnf(refute_0_884,plain,
multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) = least_upper_bound(greatest_lower_bound(identity,X_111),multiply(greatest_lower_bound(identity,X_111),inverse(X_111))),
inference(subst,[],[refute_0_883:[bind(X_51,$fot(greatest_lower_bound(identity,X_111))),bind(X_52,$fot(inverse(X_111)))]]) ).
cnf(refute_0_885,plain,
multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) = greatest_lower_bound(multiply(X_107,inverse(X_108)),multiply(X_108,inverse(X_108))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_108))),bind(Y,$fot(X_107)),bind(Z,$fot(X_108))]]) ).
cnf(refute_0_886,plain,
multiply(X_108,inverse(X_108)) = identity,
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_108))]]) ).
cnf(refute_0_887,plain,
( multiply(X_108,inverse(X_108)) != identity
| multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) != greatest_lower_bound(multiply(X_107,inverse(X_108)),multiply(X_108,inverse(X_108)))
| multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) = greatest_lower_bound(multiply(X_107,inverse(X_108)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)),greatest_lower_bound(multiply(X_107,inverse(X_108)),multiply(X_108,inverse(X_108)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_888,plain,
( multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) != greatest_lower_bound(multiply(X_107,inverse(X_108)),multiply(X_108,inverse(X_108)))
| multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) = greatest_lower_bound(multiply(X_107,inverse(X_108)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_108,inverse(X_108)),identity) )],[refute_0_886,refute_0_887]) ).
cnf(refute_0_889,plain,
multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) = greatest_lower_bound(multiply(X_107,inverse(X_108)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)),greatest_lower_bound(multiply(X_107,inverse(X_108)),multiply(X_108,inverse(X_108)))) )],[refute_0_885,refute_0_888]) ).
cnf(refute_0_890,plain,
greatest_lower_bound(multiply(X_107,inverse(X_108)),identity) = greatest_lower_bound(identity,multiply(X_107,inverse(X_108))),
inference(subst,[],[refute_0_348:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_107,inverse(X_108))))]]) ).
cnf(refute_0_891,plain,
( multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) != greatest_lower_bound(multiply(X_107,inverse(X_108)),identity)
| greatest_lower_bound(multiply(X_107,inverse(X_108)),identity) != greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))
| multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) = greatest_lower_bound(identity,multiply(X_107,inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) ),[0],$fot(greatest_lower_bound(multiply(X_107,inverse(X_108)),identity))]]) ).
cnf(refute_0_892,plain,
( multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) != greatest_lower_bound(multiply(X_107,inverse(X_108)),identity)
| multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) = greatest_lower_bound(identity,multiply(X_107,inverse(X_108))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,inverse(X_108)),identity),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) = greatest_lower_bound(identity,multiply(X_107,inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)),greatest_lower_bound(multiply(X_107,inverse(X_108)),identity)) )],[refute_0_889,refute_0_892]) ).
cnf(refute_0_894,plain,
multiply(greatest_lower_bound(identity,X_110),inverse(X_110)) = greatest_lower_bound(identity,multiply(identity,inverse(X_110))),
inference(subst,[],[refute_0_893:[bind(X_107,$fot(identity)),bind(X_108,$fot(X_110))]]) ).
cnf(refute_0_895,plain,
multiply(identity,inverse(X_110)) = inverse(X_110),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_110)))]]) ).
cnf(refute_0_896,plain,
( multiply(greatest_lower_bound(identity,X_110),inverse(X_110)) != greatest_lower_bound(identity,multiply(identity,inverse(X_110)))
| multiply(identity,inverse(X_110)) != inverse(X_110)
| multiply(greatest_lower_bound(identity,X_110),inverse(X_110)) = greatest_lower_bound(identity,inverse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_110),inverse(X_110)),greatest_lower_bound(identity,multiply(identity,inverse(X_110)))) ),[1,1],$fot(inverse(X_110))]]) ).
cnf(refute_0_897,plain,
( multiply(greatest_lower_bound(identity,X_110),inverse(X_110)) != greatest_lower_bound(identity,multiply(identity,inverse(X_110)))
| multiply(greatest_lower_bound(identity,X_110),inverse(X_110)) = greatest_lower_bound(identity,inverse(X_110)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_110)),inverse(X_110)) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
multiply(greatest_lower_bound(identity,X_110),inverse(X_110)) = greatest_lower_bound(identity,inverse(X_110)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_110),inverse(X_110)),greatest_lower_bound(identity,multiply(identity,inverse(X_110)))) )],[refute_0_894,refute_0_897]) ).
cnf(refute_0_899,plain,
multiply(greatest_lower_bound(identity,X_111),inverse(X_111)) = greatest_lower_bound(identity,inverse(X_111)),
inference(subst,[],[refute_0_898:[bind(X_110,$fot(X_111))]]) ).
cnf(refute_0_900,plain,
( multiply(greatest_lower_bound(identity,X_111),inverse(X_111)) != greatest_lower_bound(identity,inverse(X_111))
| multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) != least_upper_bound(greatest_lower_bound(identity,X_111),multiply(greatest_lower_bound(identity,X_111),inverse(X_111)))
| multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) = least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)),least_upper_bound(greatest_lower_bound(identity,X_111),multiply(greatest_lower_bound(identity,X_111),inverse(X_111)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_111)))]]) ).
cnf(refute_0_901,plain,
( multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) != least_upper_bound(greatest_lower_bound(identity,X_111),multiply(greatest_lower_bound(identity,X_111),inverse(X_111)))
| multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) = least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_111),inverse(X_111)),greatest_lower_bound(identity,inverse(X_111))) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) = least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)),least_upper_bound(greatest_lower_bound(identity,X_111),multiply(greatest_lower_bound(identity,X_111),inverse(X_111)))) )],[refute_0_884,refute_0_901]) ).
cnf(refute_0_903,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_85))) = least_upper_bound(X_17,multiply(X_17,X_85)),
inference(subst,[],[refute_0_114:[bind(X_16,$fot(multiply(X_17,X_85)))]]) ).
cnf(refute_0_904,plain,
multiply(X_17,least_upper_bound(X_85,identity)) = least_upper_bound(X_17,multiply(X_17,X_85)),
inference(subst,[],[refute_0_883:[bind(X_51,$fot(X_17)),bind(X_52,$fot(X_85))]]) ).
cnf(refute_0_905,plain,
( multiply(X_17,least_upper_bound(X_85,identity)) != least_upper_bound(X_17,multiply(X_17,X_85))
| least_upper_bound(X_17,multiply(X_17,X_85)) = multiply(X_17,least_upper_bound(X_85,identity)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_17,least_upper_bound(X_85,identity)))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_17,X_85))))]]) ).
cnf(refute_0_906,plain,
least_upper_bound(X_17,multiply(X_17,X_85)) = multiply(X_17,least_upper_bound(X_85,identity)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(X_85,identity)),least_upper_bound(X_17,multiply(X_17,X_85))) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
( least_upper_bound(X_17,multiply(X_17,X_85)) != multiply(X_17,least_upper_bound(X_85,identity))
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_85))) != least_upper_bound(X_17,multiply(X_17,X_85))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = least_upper_bound(X_17,multiply(X_17,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_85))),least_upper_bound(X_17,multiply(X_17,X_85))) ),[0,1],$fot(multiply(X_17,least_upper_bound(X_85,identity)))]]) ).
cnf(refute_0_908,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_85))) != least_upper_bound(X_17,multiply(X_17,X_85))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = least_upper_bound(X_17,multiply(X_17,X_85)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,X_85)),multiply(X_17,least_upper_bound(X_85,identity))) )],[refute_0_906,refute_0_907]) ).
cnf(refute_0_909,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = least_upper_bound(X_17,multiply(X_17,X_85)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_85))),least_upper_bound(X_17,multiply(X_17,X_85))) )],[refute_0_903,refute_0_908]) ).
cnf(refute_0_910,plain,
least_upper_bound(identity,least_upper_bound(X_85,identity)) = least_upper_bound(identity,X_85),
inference(subst,[],[refute_0_107:[bind(Y,$fot(X_85)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_911,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))),
introduced(tautology,[refl,[$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))))]]) ).
cnf(refute_0_912,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))
| least_upper_bound(identity,least_upper_bound(X_85,identity)) != least_upper_bound(identity,X_85)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_85))]]) ).
cnf(refute_0_913,plain,
( least_upper_bound(identity,least_upper_bound(X_85,identity)) != least_upper_bound(identity,X_85)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,X_85)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,X_85)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_85,identity)),least_upper_bound(identity,X_85)) )],[refute_0_910,refute_0_913]) ).
cnf(refute_0_915,plain,
least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) = least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_51,X_53))),bind(Y,$fot(multiply(X_51,X_52)))]]) ).
cnf(refute_0_916,plain,
( least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)) != multiply(X_51,least_upper_bound(X_52,X_53))
| least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) != least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))
| least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) = multiply(X_51,least_upper_bound(X_52,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)),least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))) ),[1],$fot(multiply(X_51,least_upper_bound(X_52,X_53)))]]) ).
cnf(refute_0_917,plain,
( least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) != least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))
| least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) = multiply(X_51,least_upper_bound(X_52,X_53)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53)),multiply(X_51,least_upper_bound(X_52,X_53))) )],[refute_0_206,refute_0_916]) ).
cnf(refute_0_918,plain,
least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) = multiply(X_51,least_upper_bound(X_52,X_53)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)),least_upper_bound(multiply(X_51,X_52),multiply(X_51,X_53))) )],[refute_0_915,refute_0_917]) ).
cnf(refute_0_919,plain,
least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) = multiply(X_51,least_upper_bound(X_53,X_52)),
inference(subst,[],[refute_0_716:[bind(X,$fot(X_51)),bind(Y,$fot(X_53)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_920,plain,
( least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) != multiply(X_51,least_upper_bound(X_52,X_53))
| least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) != multiply(X_51,least_upper_bound(X_53,X_52))
| multiply(X_51,least_upper_bound(X_53,X_52)) = multiply(X_51,least_upper_bound(X_52,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)),multiply(X_51,least_upper_bound(X_52,X_53))) ),[0],$fot(multiply(X_51,least_upper_bound(X_53,X_52)))]]) ).
cnf(refute_0_921,plain,
( least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)) != multiply(X_51,least_upper_bound(X_52,X_53))
| multiply(X_51,least_upper_bound(X_53,X_52)) = multiply(X_51,least_upper_bound(X_52,X_53)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)),multiply(X_51,least_upper_bound(X_53,X_52))) )],[refute_0_919,refute_0_920]) ).
cnf(refute_0_922,plain,
multiply(X_51,least_upper_bound(X_53,X_52)) = multiply(X_51,least_upper_bound(X_52,X_53)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_53),multiply(X_51,X_52)),multiply(X_51,least_upper_bound(X_52,X_53))) )],[refute_0_918,refute_0_921]) ).
cnf(refute_0_923,plain,
( multiply(X_51,least_upper_bound(X_53,X_52)) != multiply(X_51,least_upper_bound(X_52,X_53))
| multiply(X_51,least_upper_bound(X_52,X_53)) = multiply(X_51,least_upper_bound(X_53,X_52)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_51,least_upper_bound(X_53,X_52)))),bind(Y0,$fot(multiply(X_51,least_upper_bound(X_52,X_53))))]]) ).
cnf(refute_0_924,plain,
multiply(X_51,least_upper_bound(X_52,X_53)) = multiply(X_51,least_upper_bound(X_53,X_52)),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(X_53,X_52)),multiply(X_51,least_upper_bound(X_52,X_53))) )],[refute_0_922,refute_0_923]) ).
cnf(refute_0_925,plain,
multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity)) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))),
inference(subst,[],[refute_0_924:[bind(X_51,$fot(X_17)),bind(X_52,$fot(least_upper_bound(X_85,identity))),bind(X_53,$fot(identity))]]) ).
cnf(refute_0_926,plain,
( multiply(X_51,least_upper_bound(X_52,identity)) != least_upper_bound(X_51,multiply(X_51,X_52))
| least_upper_bound(X_51,multiply(X_51,X_52)) = multiply(X_51,least_upper_bound(X_52,identity)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_51,least_upper_bound(X_52,identity)))),bind(Y0,$fot(least_upper_bound(X_51,multiply(X_51,X_52))))]]) ).
cnf(refute_0_927,plain,
least_upper_bound(X_51,multiply(X_51,X_52)) = multiply(X_51,least_upper_bound(X_52,identity)),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,identity)),least_upper_bound(X_51,multiply(X_51,X_52))) )],[refute_0_883,refute_0_926]) ).
cnf(refute_0_928,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity)),
inference(subst,[],[refute_0_927:[bind(X_51,$fot(X_17)),bind(X_52,$fot(least_upper_bound(X_85,identity)))]]) ).
cnf(refute_0_929,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) != multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))))),bind(Y0,$fot(multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity)))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))))]]) ).
cnf(refute_0_930,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))),multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity))) )],[refute_0_928,refute_0_929]) ).
cnf(refute_0_931,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(least_upper_bound(X_85,identity),identity)),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))) )],[refute_0_925,refute_0_930]) ).
cnf(refute_0_932,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) != multiply(X_17,least_upper_bound(identity,X_85))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,X_85)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))))),bind(Y0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,X_85))))]]) ).
cnf(refute_0_933,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))) != multiply(X_17,least_upper_bound(identity,X_85))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,X_85)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity)))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) = multiply(X_17,least_upper_bound(identity,X_85)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_85,identity))),multiply(X_17,least_upper_bound(identity,X_85))) )],[refute_0_914,refute_0_933]) ).
cnf(refute_0_935,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) != multiply(X_17,least_upper_bound(identity,X_85))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) != least_upper_bound(X_17,multiply(X_17,X_85))
| multiply(X_17,least_upper_bound(identity,X_85)) = least_upper_bound(X_17,multiply(X_17,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))),least_upper_bound(X_17,multiply(X_17,X_85))) ),[0],$fot(multiply(X_17,least_upper_bound(identity,X_85)))]]) ).
cnf(refute_0_936,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) != least_upper_bound(X_17,multiply(X_17,X_85))
| multiply(X_17,least_upper_bound(identity,X_85)) = least_upper_bound(X_17,multiply(X_17,X_85)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))),multiply(X_17,least_upper_bound(identity,X_85))) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
( multiply(X_17,least_upper_bound(identity,X_85)) != least_upper_bound(X_17,multiply(X_17,X_85))
| least_upper_bound(X_17,multiply(X_17,X_85)) != multiply(X_17,least_upper_bound(X_85,identity))
| multiply(X_17,least_upper_bound(identity,X_85)) = multiply(X_17,least_upper_bound(X_85,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_17,least_upper_bound(identity,X_85)),multiply(X_17,least_upper_bound(X_85,identity))) ),[0],$fot(least_upper_bound(X_17,multiply(X_17,X_85)))]]) ).
cnf(refute_0_938,plain,
( multiply(X_17,least_upper_bound(identity,X_85)) != least_upper_bound(X_17,multiply(X_17,X_85))
| multiply(X_17,least_upper_bound(identity,X_85)) = multiply(X_17,least_upper_bound(X_85,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,X_85)),multiply(X_17,least_upper_bound(X_85,identity))) )],[refute_0_906,refute_0_937]) ).
cnf(refute_0_939,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))) != least_upper_bound(X_17,multiply(X_17,X_85))
| multiply(X_17,least_upper_bound(identity,X_85)) = multiply(X_17,least_upper_bound(X_85,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,X_85)),least_upper_bound(X_17,multiply(X_17,X_85))) )],[refute_0_936,refute_0_938]) ).
cnf(refute_0_940,plain,
multiply(X_17,least_upper_bound(identity,X_85)) = multiply(X_17,least_upper_bound(X_85,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_85,identity))),least_upper_bound(X_17,multiply(X_17,X_85))) )],[refute_0_909,refute_0_939]) ).
cnf(refute_0_941,plain,
( multiply(X_17,least_upper_bound(identity,X_85)) != multiply(X_17,least_upper_bound(X_85,identity))
| multiply(X_17,least_upper_bound(X_85,identity)) = multiply(X_17,least_upper_bound(identity,X_85)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_17,least_upper_bound(identity,X_85)))),bind(Y0,$fot(multiply(X_17,least_upper_bound(X_85,identity))))]]) ).
cnf(refute_0_942,plain,
multiply(X_17,least_upper_bound(X_85,identity)) = multiply(X_17,least_upper_bound(identity,X_85)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,X_85)),multiply(X_17,least_upper_bound(X_85,identity))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) = multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))),
inference(subst,[],[refute_0_942:[bind(X_17,$fot(greatest_lower_bound(identity,X_111))),bind(X_85,$fot(inverse(X_111)))]]) ).
cnf(refute_0_944,plain,
( multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) != multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111)))
| multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) != least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111)))
| multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))) = least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)),least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))))]]) ).
cnf(refute_0_945,plain,
( multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)) != least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111)))
| multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))) = least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)),multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111)))) )],[refute_0_943,refute_0_944]) ).
cnf(refute_0_946,plain,
multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))) = least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(inverse(X_111),identity)),least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111)))) )],[refute_0_902,refute_0_945]) ).
cnf(refute_0_947,plain,
( multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))) != least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111)))
| least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))) = multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111)))))]]) ).
cnf(refute_0_948,plain,
least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111))) = multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_111),least_upper_bound(identity,inverse(X_111))),least_upper_bound(greatest_lower_bound(identity,X_111),greatest_lower_bound(identity,inverse(X_111)))) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))),
inference(subst,[],[refute_0_948:[bind(X_111,$fot(X_105))]]) ).
cnf(refute_0_950,plain,
least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))))]]) ).
cnf(refute_0_951,plain,
( inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))) != greatest_lower_bound(identity,inverse(X_105))
| least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))
| least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_105)))]]) ).
cnf(refute_0_952,plain,
( inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))) != greatest_lower_bound(identity,inverse(X_105))
| least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_866,refute_0_952]) ).
cnf(refute_0_954,plain,
( least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) != multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))
| least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105)))
| least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))))]]) ).
cnf(refute_0_955,plain,
( least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) != multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))
| least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105)))) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))),multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))) )],[refute_0_949,refute_0_955]) ).
cnf(refute_0_957,plain,
least_upper_bound(X_55,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,least_upper_bound(X_55,inverse(Y))))),
inference(subst,[],[refute_0_14:[bind(X_33,$fot(least_upper_bound(X_55,inverse(Y))))]]) ).
cnf(refute_0_958,plain,
multiply(X_51,least_upper_bound(X_52,inverse(X_51))) = least_upper_bound(multiply(X_51,X_52),multiply(X_51,inverse(X_51))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(inverse(X_51)))]]) ).
cnf(refute_0_959,plain,
( multiply(X_51,inverse(X_51)) != identity
| multiply(X_51,least_upper_bound(X_52,inverse(X_51))) != least_upper_bound(multiply(X_51,X_52),multiply(X_51,inverse(X_51)))
| multiply(X_51,least_upper_bound(X_52,inverse(X_51))) = least_upper_bound(multiply(X_51,X_52),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,inverse(X_51))),least_upper_bound(multiply(X_51,X_52),multiply(X_51,inverse(X_51)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_960,plain,
( multiply(X_51,least_upper_bound(X_52,inverse(X_51))) != least_upper_bound(multiply(X_51,X_52),multiply(X_51,inverse(X_51)))
| multiply(X_51,least_upper_bound(X_52,inverse(X_51))) = least_upper_bound(multiply(X_51,X_52),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_51,inverse(X_51)),identity) )],[refute_0_271,refute_0_959]) ).
cnf(refute_0_961,plain,
multiply(X_51,least_upper_bound(X_52,inverse(X_51))) = least_upper_bound(multiply(X_51,X_52),identity),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,inverse(X_51))),least_upper_bound(multiply(X_51,X_52),multiply(X_51,inverse(X_51)))) )],[refute_0_958,refute_0_960]) ).
cnf(refute_0_962,plain,
least_upper_bound(multiply(X_51,X_52),identity) = least_upper_bound(identity,multiply(X_51,X_52)),
inference(subst,[],[refute_0_65:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_51,X_52)))]]) ).
cnf(refute_0_963,plain,
( multiply(X_51,least_upper_bound(X_52,inverse(X_51))) != least_upper_bound(multiply(X_51,X_52),identity)
| least_upper_bound(multiply(X_51,X_52),identity) != least_upper_bound(identity,multiply(X_51,X_52))
| multiply(X_51,least_upper_bound(X_52,inverse(X_51))) = least_upper_bound(identity,multiply(X_51,X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_51,least_upper_bound(X_52,inverse(X_51))),least_upper_bound(identity,multiply(X_51,X_52))) ),[0],$fot(least_upper_bound(multiply(X_51,X_52),identity))]]) ).
cnf(refute_0_964,plain,
( multiply(X_51,least_upper_bound(X_52,inverse(X_51))) != least_upper_bound(multiply(X_51,X_52),identity)
| multiply(X_51,least_upper_bound(X_52,inverse(X_51))) = least_upper_bound(identity,multiply(X_51,X_52)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_52),identity),least_upper_bound(identity,multiply(X_51,X_52))) )],[refute_0_962,refute_0_963]) ).
cnf(refute_0_965,plain,
multiply(X_51,least_upper_bound(X_52,inverse(X_51))) = least_upper_bound(identity,multiply(X_51,X_52)),
inference(resolve,[$cnf( $equal(multiply(X_51,least_upper_bound(X_52,inverse(X_51))),least_upper_bound(multiply(X_51,X_52),identity)) )],[refute_0_961,refute_0_964]) ).
cnf(refute_0_966,plain,
multiply(Y,least_upper_bound(X_55,inverse(Y))) = least_upper_bound(identity,multiply(Y,X_55)),
inference(subst,[],[refute_0_965:[bind(X_51,$fot(Y)),bind(X_52,$fot(X_55))]]) ).
cnf(refute_0_967,plain,
( multiply(Y,least_upper_bound(X_55,inverse(Y))) != least_upper_bound(identity,multiply(Y,X_55))
| least_upper_bound(X_55,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,least_upper_bound(X_55,inverse(Y)))))
| least_upper_bound(X_55,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_55,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,least_upper_bound(X_55,inverse(Y)))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(Y,X_55)))]]) ).
cnf(refute_0_968,plain,
( least_upper_bound(X_55,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,least_upper_bound(X_55,inverse(Y)))))
| least_upper_bound(X_55,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) ),
inference(resolve,[$cnf( $equal(multiply(Y,least_upper_bound(X_55,inverse(Y))),least_upper_bound(identity,multiply(Y,X_55))) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
least_upper_bound(X_55,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_55,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,least_upper_bound(X_55,inverse(Y)))))) )],[refute_0_957,refute_0_968]) ).
cnf(refute_0_970,plain,
multiply(inverse(Y),identity) = inverse(Y),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(inverse(Y)))]]) ).
cnf(refute_0_971,plain,
least_upper_bound(multiply(inverse(Y),identity),X_55) = least_upper_bound(multiply(inverse(Y),identity),X_55),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(Y),identity),X_55))]]) ).
cnf(refute_0_972,plain,
( multiply(inverse(Y),identity) != inverse(Y)
| least_upper_bound(multiply(inverse(Y),identity),X_55) != least_upper_bound(multiply(inverse(Y),identity),X_55)
| least_upper_bound(multiply(inverse(Y),identity),X_55) = least_upper_bound(inverse(Y),X_55) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(Y),identity),X_55),least_upper_bound(multiply(inverse(Y),identity),X_55)) ),[1,0],$fot(inverse(Y))]]) ).
cnf(refute_0_973,plain,
( multiply(inverse(Y),identity) != inverse(Y)
| least_upper_bound(multiply(inverse(Y),identity),X_55) = least_upper_bound(inverse(Y),X_55) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(Y),identity),X_55),least_upper_bound(multiply(inverse(Y),identity),X_55)) )],[refute_0_971,refute_0_972]) ).
cnf(refute_0_974,plain,
least_upper_bound(multiply(inverse(Y),identity),X_55) = least_upper_bound(inverse(Y),X_55),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),identity),inverse(Y)) )],[refute_0_970,refute_0_973]) ).
cnf(refute_0_975,plain,
multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_52),multiply(inverse(X_30),multiply(X_30,X_31))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_30))),bind(Y,$fot(X_52)),bind(Z,$fot(multiply(X_30,X_31)))]]) ).
cnf(refute_0_976,plain,
( multiply(inverse(X_30),multiply(X_30,X_31)) != X_31
| multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))) != least_upper_bound(multiply(inverse(X_30),X_52),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_52),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))),least_upper_bound(multiply(inverse(X_30),X_52),multiply(inverse(X_30),multiply(X_30,X_31)))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_977,plain,
( multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))) != least_upper_bound(multiply(inverse(X_30),X_52),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_52),X_31) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),multiply(X_30,X_31)),X_31) )],[refute_0_235,refute_0_976]) ).
cnf(refute_0_978,plain,
multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))) = least_upper_bound(multiply(inverse(X_30),X_52),X_31),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),least_upper_bound(X_52,multiply(X_30,X_31))),least_upper_bound(multiply(inverse(X_30),X_52),multiply(inverse(X_30),multiply(X_30,X_31)))) )],[refute_0_975,refute_0_977]) ).
cnf(refute_0_979,plain,
multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55))) = least_upper_bound(multiply(inverse(Y),identity),X_55),
inference(subst,[],[refute_0_978:[bind(X_30,$fot(Y)),bind(X_31,$fot(X_55)),bind(X_52,$fot(identity))]]) ).
cnf(refute_0_980,plain,
multiply(inverse(Y),X_76) = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_76)))),
inference(subst,[],[refute_0_14:[bind(X_33,$fot(multiply(inverse(Y),X_76)))]]) ).
cnf(refute_0_981,plain,
X_76 = multiply(Y,multiply(inverse(Y),X_76)),
inference(subst,[],[refute_0_315:[bind(X_31,$fot(X_76)),bind(X_35,$fot(Y))]]) ).
cnf(refute_0_982,plain,
( X_76 != multiply(Y,multiply(inverse(Y),X_76))
| multiply(Y,multiply(inverse(Y),X_76)) = X_76 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_76)),bind(Y0,$fot(multiply(Y,multiply(inverse(Y),X_76))))]]) ).
cnf(refute_0_983,plain,
multiply(Y,multiply(inverse(Y),X_76)) = X_76,
inference(resolve,[$cnf( $equal(X_76,multiply(Y,multiply(inverse(Y),X_76))) )],[refute_0_981,refute_0_982]) ).
cnf(refute_0_984,plain,
( multiply(Y,multiply(inverse(Y),X_76)) != X_76
| multiply(inverse(Y),X_76) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_76))))
| multiply(inverse(Y),X_76) = multiply(inverse(multiply(X,Y)),multiply(X,X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(Y),X_76),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_76))))) ),[1,1,1],$fot(X_76)]]) ).
cnf(refute_0_985,plain,
( multiply(inverse(Y),X_76) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_76))))
| multiply(inverse(Y),X_76) = multiply(inverse(multiply(X,Y)),multiply(X,X_76)) ),
inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(Y),X_76)),X_76) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
multiply(inverse(Y),X_76) = multiply(inverse(multiply(X,Y)),multiply(X,X_76)),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),X_76),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_76))))) )],[refute_0_980,refute_0_985]) ).
cnf(refute_0_987,plain,
( multiply(inverse(Y),X_76) != multiply(inverse(multiply(X,Y)),multiply(X,X_76))
| multiply(inverse(multiply(X,Y)),multiply(X,X_76)) = multiply(inverse(Y),X_76) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(inverse(Y),X_76))),bind(Y0,$fot(multiply(inverse(multiply(X,Y)),multiply(X,X_76))))]]) ).
cnf(refute_0_988,plain,
multiply(inverse(multiply(X,Y)),multiply(X,X_76)) = multiply(inverse(Y),X_76),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),X_76),multiply(inverse(multiply(X,Y)),multiply(X,X_76))) )],[refute_0_986,refute_0_987]) ).
cnf(refute_0_989,plain,
multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) = multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55))),
inference(subst,[],[refute_0_988:[bind(X_76,$fot(least_upper_bound(identity,multiply(Y,X_55))))]]) ).
cnf(refute_0_990,plain,
( multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55))) != least_upper_bound(multiply(inverse(Y),identity),X_55)
| multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) != multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55)))
| multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) = least_upper_bound(multiply(inverse(Y),identity),X_55) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))))),bind(Y0,$fot(multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55))))),bind(Z0,$fot(least_upper_bound(multiply(inverse(Y),identity),X_55)))]]) ).
cnf(refute_0_991,plain,
( multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55))) != least_upper_bound(multiply(inverse(Y),identity),X_55)
| multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) = least_upper_bound(multiply(inverse(Y),identity),X_55) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))),multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55)))) )],[refute_0_989,refute_0_990]) ).
cnf(refute_0_992,plain,
multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) = least_upper_bound(multiply(inverse(Y),identity),X_55),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),least_upper_bound(identity,multiply(Y,X_55))),least_upper_bound(multiply(inverse(Y),identity),X_55)) )],[refute_0_979,refute_0_991]) ).
cnf(refute_0_993,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) != least_upper_bound(multiply(inverse(Y),identity),X_55)
| least_upper_bound(multiply(inverse(Y),identity),X_55) != least_upper_bound(inverse(Y),X_55)
| multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) = least_upper_bound(inverse(Y),X_55) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(Y),identity),X_55))),bind(Z0,$fot(least_upper_bound(inverse(Y),X_55)))]]) ).
cnf(refute_0_994,plain,
( least_upper_bound(multiply(inverse(Y),identity),X_55) != least_upper_bound(inverse(Y),X_55)
| multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) = least_upper_bound(inverse(Y),X_55) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))),least_upper_bound(multiply(inverse(Y),identity),X_55)) )],[refute_0_992,refute_0_993]) ).
cnf(refute_0_995,plain,
multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) = least_upper_bound(inverse(Y),X_55),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(Y),identity),X_55),least_upper_bound(inverse(Y),X_55)) )],[refute_0_974,refute_0_994]) ).
cnf(refute_0_996,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))) != least_upper_bound(inverse(Y),X_55)
| least_upper_bound(X_55,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55))))
| least_upper_bound(X_55,inverse(Y)) = least_upper_bound(inverse(Y),X_55) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_55,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55))))) ),[1],$fot(least_upper_bound(inverse(Y),X_55))]]) ).
cnf(refute_0_997,plain,
( least_upper_bound(X_55,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55))))
| least_upper_bound(X_55,inverse(Y)) = least_upper_bound(inverse(Y),X_55) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55)))),least_upper_bound(inverse(Y),X_55)) )],[refute_0_995,refute_0_996]) ).
cnf(refute_0_998,plain,
least_upper_bound(X_55,inverse(Y)) = least_upper_bound(inverse(Y),X_55),
inference(resolve,[$cnf( $equal(least_upper_bound(X_55,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,least_upper_bound(identity,multiply(Y,X_55))))) )],[refute_0_969,refute_0_997]) ).
cnf(refute_0_999,plain,
( least_upper_bound(X_55,inverse(Y)) != least_upper_bound(inverse(Y),X_55)
| least_upper_bound(inverse(Y),X_55) = least_upper_bound(X_55,inverse(Y)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_55,inverse(Y)))),bind(Y0,$fot(least_upper_bound(inverse(Y),X_55)))]]) ).
cnf(refute_0_1000,plain,
least_upper_bound(inverse(Y),X_55) = least_upper_bound(X_55,inverse(Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_55,inverse(Y)),least_upper_bound(inverse(Y),X_55)) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) = least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),
inference(subst,[],[refute_0_1000:[bind(Y,$fot(inverse(greatest_lower_bound(identity,inverse(X_105))))),bind(X_55,$fot(greatest_lower_bound(identity,X_105)))]]) ).
cnf(refute_0_1002,plain,
( least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))
| least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) != least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))
| least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))))]]) ).
cnf(refute_0_1003,plain,
( least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))
| least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)),least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))))) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))) )],[refute_0_956,refute_0_1003]) ).
cnf(refute_0_1005,plain,
( multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) != least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))
| least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)) != multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))
| multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))),multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))) ),[0],$fot(least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)))]]) ).
cnf(refute_0_1006,plain,
( multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) != least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))
| multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105)),multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105)))) )],[refute_0_1004,refute_0_1005]) ).
cnf(refute_0_1007,plain,
( multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))) != least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))
| multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))),least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))) )],[refute_0_872,refute_0_1006]) ).
cnf(refute_0_1008,plain,
multiply(least_upper_bound(identity,X_105),greatest_lower_bound(identity,inverse(X_105))) = multiply(greatest_lower_bound(identity,X_105),least_upper_bound(identity,inverse(X_105))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_105),inverse(inverse(greatest_lower_bound(identity,inverse(X_105))))),least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_105)))),greatest_lower_bound(identity,X_105))) )],[refute_0_865,refute_0_1007]) ).
cnf(refute_0_1009,plain,
multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))) = multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))),
inference(subst,[],[refute_0_1008:[bind(X_105,$fot(X_71))]]) ).
cnf(refute_0_1010,plain,
( multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))) != multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))
| multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))) != greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))
| multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))),greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))))]]) ).
cnf(refute_0_1011,plain,
( multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))) != greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))
| multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))),multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) = greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_71),greatest_lower_bound(identity,inverse(X_71))),greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))) )],[refute_0_819,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) != greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))
| greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) = multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))))]]) ).
cnf(refute_0_1014,plain,
greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))) = multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_71),least_upper_bound(identity,inverse(X_71))),greatest_lower_bound(least_upper_bound(identity,X_71),least_upper_bound(identity,inverse(X_71)))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) = multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))),
inference(subst,[],[refute_0_1014:[bind(X_71,$fot(X_59))]]) ).
cnf(refute_0_1016,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_1017,plain,
( greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) != multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))))) ),[1,1],$fot(multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_1018,plain,
( greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) != multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1016,refute_0_1017]) ).
cnf(refute_0_1019,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))),multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1015,refute_0_1018]) ).
cnf(refute_0_1020,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) != identity
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = identity ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1021,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) != identity
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1019,refute_0_1020]) ).
cnf(refute_0_1022,plain,
least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),identity) )],[refute_0_664,refute_0_1021]) ).
cnf(refute_0_1023,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_1024,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) != multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))
| least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) = multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1025,plain,
( least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) != identity
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) = multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1023,refute_0_1024]) ).
cnf(refute_0_1026,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) = multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),identity) )],[refute_0_1022,refute_0_1025]) ).
cnf(refute_0_1027,plain,
( multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))) != inverse(least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) != multiply(identity,inverse(least_upper_bound(identity,inverse(X_59))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(identity,inverse(X_59))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))))),bind(Y0,$fot(multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_1028,plain,
( multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))) != inverse(least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))),multiply(identity,inverse(least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1026,refute_0_1027]) ).
cnf(refute_0_1029,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(identity,inverse(X_59))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) )],[refute_0_436,refute_0_1028]) ).
cnf(refute_0_1030,plain,
multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) = least_upper_bound(inverse(X_108),multiply(greatest_lower_bound(X_107,X_108),inverse(X_108))),
inference(subst,[],[refute_0_340:[bind(X_63,$fot(inverse(X_108))),bind(X_64,$fot(greatest_lower_bound(X_107,X_108)))]]) ).
cnf(refute_0_1031,plain,
( multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)) != greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))
| multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) != least_upper_bound(inverse(X_108),multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)))
| multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) = least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)),least_upper_bound(inverse(X_108),multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))]]) ).
cnf(refute_0_1032,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) != least_upper_bound(inverse(X_108),multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)))
| multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) = least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) )],[refute_0_893,refute_0_1031]) ).
cnf(refute_0_1033,plain,
multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) = least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)),least_upper_bound(inverse(X_108),multiply(greatest_lower_bound(X_107,X_108),inverse(X_108)))) )],[refute_0_1030,refute_0_1032]) ).
cnf(refute_0_1034,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_126,X_17))) = least_upper_bound(X_17,multiply(X_126,X_17)),
inference(subst,[],[refute_0_114:[bind(X_16,$fot(multiply(X_126,X_17)))]]) ).
cnf(refute_0_1035,plain,
multiply(least_upper_bound(X_126,identity),X_17) = least_upper_bound(X_17,multiply(X_126,X_17)),
inference(subst,[],[refute_0_340:[bind(X_63,$fot(X_17)),bind(X_64,$fot(X_126))]]) ).
cnf(refute_0_1036,plain,
( multiply(least_upper_bound(X_126,identity),X_17) != least_upper_bound(X_17,multiply(X_126,X_17))
| least_upper_bound(X_17,multiply(X_126,X_17)) = multiply(least_upper_bound(X_126,identity),X_17) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(X_126,identity),X_17))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_126,X_17))))]]) ).
cnf(refute_0_1037,plain,
least_upper_bound(X_17,multiply(X_126,X_17)) = multiply(least_upper_bound(X_126,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_126,identity),X_17),least_upper_bound(X_17,multiply(X_126,X_17))) )],[refute_0_1035,refute_0_1036]) ).
cnf(refute_0_1038,plain,
( least_upper_bound(X_17,multiply(X_126,X_17)) != multiply(least_upper_bound(X_126,identity),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_126,X_17))) != least_upper_bound(X_17,multiply(X_126,X_17))
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = least_upper_bound(X_17,multiply(X_126,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_126,X_17))),least_upper_bound(X_17,multiply(X_126,X_17))) ),[0,1],$fot(multiply(least_upper_bound(X_126,identity),X_17))]]) ).
cnf(refute_0_1039,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_126,X_17))) != least_upper_bound(X_17,multiply(X_126,X_17))
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = least_upper_bound(X_17,multiply(X_126,X_17)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_126,X_17)),multiply(least_upper_bound(X_126,identity),X_17)) )],[refute_0_1037,refute_0_1038]) ).
cnf(refute_0_1040,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = least_upper_bound(X_17,multiply(X_126,X_17)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_126,X_17))),least_upper_bound(X_17,multiply(X_126,X_17))) )],[refute_0_1034,refute_0_1039]) ).
cnf(refute_0_1041,plain,
least_upper_bound(identity,least_upper_bound(X_126,identity)) = least_upper_bound(identity,X_126),
inference(subst,[],[refute_0_107:[bind(Y,$fot(X_126)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1042,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17))]]) ).
cnf(refute_0_1043,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)
| least_upper_bound(identity,least_upper_bound(X_126,identity)) != least_upper_bound(identity,X_126)
| multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) = multiply(least_upper_bound(identity,X_126),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)) ),[1,0],$fot(least_upper_bound(identity,X_126))]]) ).
cnf(refute_0_1044,plain,
( least_upper_bound(identity,least_upper_bound(X_126,identity)) != least_upper_bound(identity,X_126)
| multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) = multiply(least_upper_bound(identity,X_126),X_17) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)) )],[refute_0_1042,refute_0_1043]) ).
cnf(refute_0_1045,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) = multiply(least_upper_bound(identity,X_126),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_126,identity)),least_upper_bound(identity,X_126)) )],[refute_0_1041,refute_0_1044]) ).
cnf(refute_0_1046,plain,
multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17),
inference(subst,[],[refute_0_220:[bind(X_63,$fot(X_17)),bind(X_64,$fot(least_upper_bound(X_126,identity))),bind(X_65,$fot(identity))]]) ).
cnf(refute_0_1047,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17),
inference(subst,[],[refute_0_492:[bind(X_63,$fot(X_17)),bind(X_64,$fot(least_upper_bound(X_126,identity)))]]) ).
cnf(refute_0_1048,plain,
( multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) != multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)))]]) ).
cnf(refute_0_1049,plain,
( multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)),multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17)) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)) )],[refute_0_1046,refute_0_1049]) ).
cnf(refute_0_1051,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) != multiply(least_upper_bound(identity,X_126),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = multiply(least_upper_bound(identity,X_126),X_17) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_126),X_17)))]]) ).
cnf(refute_0_1052,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17) != multiply(least_upper_bound(identity,X_126),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = multiply(least_upper_bound(identity,X_126),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17)) )],[refute_0_1050,refute_0_1051]) ).
cnf(refute_0_1053,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) = multiply(least_upper_bound(identity,X_126),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_17),multiply(least_upper_bound(identity,X_126),X_17)) )],[refute_0_1045,refute_0_1052]) ).
cnf(refute_0_1054,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) != multiply(least_upper_bound(identity,X_126),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) != least_upper_bound(X_17,multiply(X_126,X_17))
| multiply(least_upper_bound(identity,X_126),X_17) = least_upper_bound(X_17,multiply(X_126,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)),least_upper_bound(X_17,multiply(X_126,X_17))) ),[0],$fot(multiply(least_upper_bound(identity,X_126),X_17))]]) ).
cnf(refute_0_1055,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) != least_upper_bound(X_17,multiply(X_126,X_17))
| multiply(least_upper_bound(identity,X_126),X_17) = least_upper_bound(X_17,multiply(X_126,X_17)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)),multiply(least_upper_bound(identity,X_126),X_17)) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
( multiply(least_upper_bound(identity,X_126),X_17) != least_upper_bound(X_17,multiply(X_126,X_17))
| least_upper_bound(X_17,multiply(X_126,X_17)) != multiply(least_upper_bound(X_126,identity),X_17)
| multiply(least_upper_bound(identity,X_126),X_17) = multiply(least_upper_bound(X_126,identity),X_17) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_126),X_17),multiply(least_upper_bound(X_126,identity),X_17)) ),[0],$fot(least_upper_bound(X_17,multiply(X_126,X_17)))]]) ).
cnf(refute_0_1057,plain,
( multiply(least_upper_bound(identity,X_126),X_17) != least_upper_bound(X_17,multiply(X_126,X_17))
| multiply(least_upper_bound(identity,X_126),X_17) = multiply(least_upper_bound(X_126,identity),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_126,X_17)),multiply(least_upper_bound(X_126,identity),X_17)) )],[refute_0_1037,refute_0_1056]) ).
cnf(refute_0_1058,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)) != least_upper_bound(X_17,multiply(X_126,X_17))
| multiply(least_upper_bound(identity,X_126),X_17) = multiply(least_upper_bound(X_126,identity),X_17) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_126),X_17),least_upper_bound(X_17,multiply(X_126,X_17))) )],[refute_0_1055,refute_0_1057]) ).
cnf(refute_0_1059,plain,
multiply(least_upper_bound(identity,X_126),X_17) = multiply(least_upper_bound(X_126,identity),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_126,identity),X_17)),least_upper_bound(X_17,multiply(X_126,X_17))) )],[refute_0_1040,refute_0_1058]) ).
cnf(refute_0_1060,plain,
( multiply(least_upper_bound(identity,X_126),X_17) != multiply(least_upper_bound(X_126,identity),X_17)
| multiply(least_upper_bound(X_126,identity),X_17) = multiply(least_upper_bound(identity,X_126),X_17) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(identity,X_126),X_17))),bind(Y0,$fot(multiply(least_upper_bound(X_126,identity),X_17)))]]) ).
cnf(refute_0_1061,plain,
multiply(least_upper_bound(X_126,identity),X_17) = multiply(least_upper_bound(identity,X_126),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_126),X_17),multiply(least_upper_bound(X_126,identity),X_17)) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) = multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)),
inference(subst,[],[refute_0_1061:[bind(X_126,$fot(greatest_lower_bound(X_107,X_108))),bind(X_17,$fot(inverse(X_108)))]]) ).
cnf(refute_0_1063,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) != multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108))
| multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) != least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))
| multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)) = least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)),least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))) ),[0],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)))]]) ).
cnf(refute_0_1064,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)) != least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))
| multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)) = least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)),multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108))) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)) = least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_107,X_108),identity),inverse(X_108)),least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))) )],[refute_0_1033,refute_0_1064]) ).
cnf(refute_0_1066,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)) != least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))
| least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) = multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)))),bind(Y0,$fot(least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))))]]) ).
cnf(refute_0_1067,plain,
least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108)))) = multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(X_107,X_108)),inverse(X_108)),least_upper_bound(inverse(X_108),greatest_lower_bound(identity,multiply(X_107,inverse(X_108))))) )],[refute_0_1065,refute_0_1066]) ).
cnf(refute_0_1068,plain,
least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))),
inference(subst,[],[refute_0_1067:[bind(X_107,$fot(least_upper_bound(identity,X_59))),bind(X_108,$fot(least_upper_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_1069,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))))
| least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))))) != multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))))))),bind(Z0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))))]]) ).
cnf(refute_0_1070,plain,
( least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))))) != multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))))) )],[refute_0_408,refute_0_1069]) ).
cnf(refute_0_1071,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1068,refute_0_1070]) ).
cnf(refute_0_1072,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) != inverse(least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(identity,inverse(X_59))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_1073,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) != inverse(least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))),multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1071,refute_0_1072]) ).
cnf(refute_0_1074,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(identity,inverse(X_59))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1029,refute_0_1073]) ).
cnf(refute_0_1075,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != inverse(least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))
| inverse(least_upper_bound(identity,inverse(X_59))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))) ),[0],$fot(inverse(least_upper_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_1076,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))
| inverse(least_upper_bound(identity,inverse(X_59))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1074,refute_0_1075]) ).
cnf(refute_0_1077,plain,
least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)) = greatest_lower_bound(X_41,X_42),
inference(subst,[],[lub_absorbtion:[bind(X,$fot(greatest_lower_bound(X_41,X_42)))]]) ).
cnf(refute_0_1078,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1079,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)))]]) ).
cnf(refute_0_1080,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)) )],[refute_0_1078,refute_0_1079]) ).
cnf(refute_0_1081,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y))
| least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)) != greatest_lower_bound(X_41,X_42)
| least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y))) = greatest_lower_bound(X_41,X_42) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)),greatest_lower_bound(X_41,X_42)) ),[0,1],$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y)))]]) ).
cnf(refute_0_1082,plain,
( least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)) != greatest_lower_bound(X_41,X_42)
| least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y))) = greatest_lower_bound(X_41,X_42) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y),greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y))) )],[refute_0_1080,refute_0_1081]) ).
cnf(refute_0_1083,plain,
least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(X_41,greatest_lower_bound(X_42,Y))) = greatest_lower_bound(X_41,X_42),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_41,X_42),greatest_lower_bound(greatest_lower_bound(X_41,X_42),Y)),greatest_lower_bound(X_41,X_42)) )],[refute_0_1077,refute_0_1082]) ).
cnf(refute_0_1084,plain,
least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))))) = greatest_lower_bound(X_301,X_302),
inference(subst,[],[refute_0_1083:[bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_302))))),bind(X_41,$fot(X_301)),bind(X_42,$fot(X_302))]]) ).
cnf(refute_0_1085,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity))),
inference(subst,[],[refute_0_675:[bind(X_98,$fot(inverse(least_upper_bound(identity,inverse(X_145))))),bind(X_99,$fot(least_upper_bound(X_145,identity)))]]) ).
cnf(refute_0_1086,plain,
inverse(inverse(X_72)) = multiply(inverse(multiply(least_upper_bound(X_72,identity),inverse(X_72))),least_upper_bound(X_72,identity)),
inference(subst,[],[refute_0_57:[bind(X_48,$fot(least_upper_bound(X_72,identity))),bind(X_49,$fot(inverse(X_72)))]]) ).
cnf(refute_0_1087,plain,
multiply(least_upper_bound(X_72,identity),inverse(X_72)) = least_upper_bound(identity,multiply(identity,inverse(X_72))),
inference(subst,[],[refute_0_548:[bind(X_64,$fot(X_72)),bind(X_65,$fot(identity))]]) ).
cnf(refute_0_1088,plain,
multiply(identity,inverse(X_72)) = inverse(X_72),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_72)))]]) ).
cnf(refute_0_1089,plain,
( multiply(identity,inverse(X_72)) != inverse(X_72)
| multiply(least_upper_bound(X_72,identity),inverse(X_72)) != least_upper_bound(identity,multiply(identity,inverse(X_72)))
| multiply(least_upper_bound(X_72,identity),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_72,identity),inverse(X_72)),least_upper_bound(identity,multiply(identity,inverse(X_72)))) ),[1,1],$fot(inverse(X_72))]]) ).
cnf(refute_0_1090,plain,
( multiply(least_upper_bound(X_72,identity),inverse(X_72)) != least_upper_bound(identity,multiply(identity,inverse(X_72)))
| multiply(least_upper_bound(X_72,identity),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_72)),inverse(X_72)) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
multiply(least_upper_bound(X_72,identity),inverse(X_72)) = least_upper_bound(identity,inverse(X_72)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_72,identity),inverse(X_72)),least_upper_bound(identity,multiply(identity,inverse(X_72)))) )],[refute_0_1087,refute_0_1090]) ).
cnf(refute_0_1092,plain,
( multiply(least_upper_bound(X_72,identity),inverse(X_72)) != least_upper_bound(identity,inverse(X_72))
| inverse(inverse(X_72)) != multiply(inverse(multiply(least_upper_bound(X_72,identity),inverse(X_72))),least_upper_bound(X_72,identity))
| inverse(inverse(X_72)) = multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_72)),multiply(inverse(multiply(least_upper_bound(X_72,identity),inverse(X_72))),least_upper_bound(X_72,identity))) ),[1,0,0],$fot(least_upper_bound(identity,inverse(X_72)))]]) ).
cnf(refute_0_1093,plain,
( inverse(inverse(X_72)) != multiply(inverse(multiply(least_upper_bound(X_72,identity),inverse(X_72))),least_upper_bound(X_72,identity))
| inverse(inverse(X_72)) = multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_72,identity),inverse(X_72)),least_upper_bound(identity,inverse(X_72))) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
inverse(inverse(X_72)) = multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_72)),multiply(inverse(multiply(least_upper_bound(X_72,identity),inverse(X_72))),least_upper_bound(X_72,identity))) )],[refute_0_1086,refute_0_1093]) ).
cnf(refute_0_1095,plain,
inverse(inverse(X_72)) = X_72,
inference(subst,[],[refute_0_83:[bind(X_35,$fot(X_72))]]) ).
cnf(refute_0_1096,plain,
( inverse(inverse(X_72)) != X_72
| inverse(inverse(X_72)) != multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity))
| X_72 = multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_72)),multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity))) ),[0],$fot(X_72)]]) ).
cnf(refute_0_1097,plain,
( inverse(inverse(X_72)) != multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity))
| X_72 = multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_72)),X_72) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
X_72 = multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_72)),multiply(inverse(least_upper_bound(identity,inverse(X_72))),least_upper_bound(X_72,identity))) )],[refute_0_1094,refute_0_1097]) ).
cnf(refute_0_1099,plain,
X_145 = multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)),
inference(subst,[],[refute_0_1098:[bind(X_72,$fot(X_145))]]) ).
cnf(refute_0_1100,plain,
( X_145 != multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)) = X_145 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_145)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity))))]]) ).
cnf(refute_0_1101,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)) = X_145,
inference(resolve,[$cnf( $equal(X_145,multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity))) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)) != X_145
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)))) ),[1,1],$fot(X_145)]]) ).
cnf(refute_0_1103,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)),X_145) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),least_upper_bound(X_145,identity)))) )],[refute_0_1085,refute_0_1103]) ).
cnf(refute_0_1105,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity) = inverse(least_upper_bound(identity,inverse(X_145))),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(inverse(least_upper_bound(identity,inverse(X_145)))))]]) ).
cnf(refute_0_1106,plain,
greatest_lower_bound(identity,least_upper_bound(X_145,identity)) = identity,
inference(subst,[],[refute_0_363:[bind(X_6,$fot(identity)),bind(X_7,$fot(X_145))]]) ).
cnf(refute_0_1107,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))))]]) ).
cnf(refute_0_1108,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) != multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity)))
| greatest_lower_bound(identity,least_upper_bound(X_145,identity)) != identity
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1109,plain,
( greatest_lower_bound(identity,least_upper_bound(X_145,identity)) != identity
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity)))) )],[refute_0_1107,refute_0_1108]) ).
cnf(refute_0_1110,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) = multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_145,identity)),identity) )],[refute_0_1106,refute_0_1109]) ).
cnf(refute_0_1111,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) != multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity)
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity) != inverse(least_upper_bound(identity,inverse(X_145)))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) = inverse(least_upper_bound(identity,inverse(X_145))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_145)))))]]) ).
cnf(refute_0_1112,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity) != inverse(least_upper_bound(identity,inverse(X_145)))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) = inverse(least_upper_bound(identity,inverse(X_145))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))),multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity)) )],[refute_0_1110,refute_0_1111]) ).
cnf(refute_0_1113,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) = inverse(least_upper_bound(identity,inverse(X_145))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),identity),inverse(least_upper_bound(identity,inverse(X_145)))) )],[refute_0_1105,refute_0_1112]) ).
cnf(refute_0_1114,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))),
inference(subst,[],[refute_0_815:[bind(X_140,$fot(least_upper_bound(X_145,identity))),bind(X_22,$fot(inverse(least_upper_bound(identity,inverse(X_145)))))]]) ).
cnf(refute_0_1115,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) != inverse(least_upper_bound(identity,inverse(X_145)))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity)))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = inverse(least_upper_bound(identity,inverse(X_145))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_145)))))]]) ).
cnf(refute_0_1116,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))) != inverse(least_upper_bound(identity,inverse(X_145)))
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = inverse(least_upper_bound(identity,inverse(X_145))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)),multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity)))) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) = inverse(least_upper_bound(identity,inverse(X_145))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(identity,least_upper_bound(X_145,identity))),inverse(least_upper_bound(identity,inverse(X_145)))) )],[refute_0_1113,refute_0_1116]) ).
cnf(refute_0_1118,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)
| multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) != inverse(least_upper_bound(identity,inverse(X_145)))
| inverse(least_upper_bound(identity,inverse(X_145))) = greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)) ),[0],$fot(inverse(least_upper_bound(identity,inverse(X_145))))]]) ).
cnf(refute_0_1119,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)
| inverse(least_upper_bound(identity,inverse(X_145))) = greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)),inverse(least_upper_bound(identity,inverse(X_145)))) )],[refute_0_1117,refute_0_1118]) ).
cnf(refute_0_1120,plain,
greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145) = greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145)))),
inference(subst,[],[refute_0_348:[bind(X,$fot(X_145)),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_145)))))]]) ).
cnf(refute_0_1121,plain,
( greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145) != greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145))))
| inverse(least_upper_bound(identity,inverse(X_145))) != greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)
| inverse(least_upper_bound(identity,inverse(X_145))) = greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)) ),[1],$fot(greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145)))))]]) ).
cnf(refute_0_1122,plain,
( inverse(least_upper_bound(identity,inverse(X_145))) != greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)
| inverse(least_upper_bound(identity,inverse(X_145))) = greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145),greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145))))) )],[refute_0_1120,refute_0_1121]) ).
cnf(refute_0_1123,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)) != greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)
| inverse(least_upper_bound(identity,inverse(X_145))) = greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)) )],[refute_0_1119,refute_0_1122]) ).
cnf(refute_0_1124,plain,
inverse(least_upper_bound(identity,inverse(X_145))) = greatest_lower_bound(X_145,inverse(least_upper_bound(identity,inverse(X_145)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_145))),greatest_lower_bound(least_upper_bound(X_145,identity),identity)),greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_145))),X_145)) )],[refute_0_1104,refute_0_1123]) ).
cnf(refute_0_1125,plain,
inverse(least_upper_bound(identity,inverse(X_302))) = greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))),
inference(subst,[],[refute_0_1124:[bind(X_145,$fot(X_302))]]) ).
cnf(refute_0_1126,plain,
( inverse(least_upper_bound(identity,inverse(X_302))) != greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302))))
| greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))) = inverse(least_upper_bound(identity,inverse(X_302))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_302))))),bind(Y0,$fot(greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302))))))]]) ).
cnf(refute_0_1127,plain,
greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))) = inverse(least_upper_bound(identity,inverse(X_302))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_302))),greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302))))) )],[refute_0_1125,refute_0_1126]) ).
cnf(refute_0_1128,plain,
( greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))) != inverse(least_upper_bound(identity,inverse(X_302)))
| least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))))) != greatest_lower_bound(X_301,X_302)
| least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,inverse(least_upper_bound(identity,inverse(X_302))))) = greatest_lower_bound(X_301,X_302) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))))),greatest_lower_bound(X_301,X_302)) ),[0,1,1],$fot(inverse(least_upper_bound(identity,inverse(X_302))))]]) ).
cnf(refute_0_1129,plain,
( least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))))) != greatest_lower_bound(X_301,X_302)
| least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,inverse(least_upper_bound(identity,inverse(X_302))))) = greatest_lower_bound(X_301,X_302) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))),inverse(least_upper_bound(identity,inverse(X_302)))) )],[refute_0_1127,refute_0_1128]) ).
cnf(refute_0_1130,plain,
least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,inverse(least_upper_bound(identity,inverse(X_302))))) = greatest_lower_bound(X_301,X_302),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_301,X_302),greatest_lower_bound(X_301,greatest_lower_bound(X_302,inverse(least_upper_bound(identity,inverse(X_302)))))),greatest_lower_bound(X_301,X_302)) )],[refute_0_1084,refute_0_1129]) ).
cnf(refute_0_1131,plain,
least_upper_bound(greatest_lower_bound(identity,X_302),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))) = greatest_lower_bound(identity,X_302),
inference(subst,[],[refute_0_1130:[bind(X_301,$fot(identity))]]) ).
cnf(refute_0_1132,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(identity,Y)),inverse(least_upper_bound(identity,Y))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(subst,[],[refute_0_898:[bind(X_110,$fot(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_1133,plain,
greatest_lower_bound(identity,least_upper_bound(identity,Y)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1134,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(identity,Y)),inverse(least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| greatest_lower_bound(identity,least_upper_bound(identity,Y)) != identity
| multiply(identity,inverse(least_upper_bound(identity,Y))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(identity,Y)),inverse(least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_1135,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(identity,Y)),inverse(least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| multiply(identity,inverse(least_upper_bound(identity,Y))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,Y)),identity) )],[refute_0_1133,refute_0_1134]) ).
cnf(refute_0_1136,plain,
multiply(identity,inverse(least_upper_bound(identity,Y))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(identity,Y)),inverse(least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1132,refute_0_1135]) ).
cnf(refute_0_1137,plain,
multiply(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(least_upper_bound(identity,Y))))]]) ).
cnf(refute_0_1138,plain,
( multiply(identity,inverse(least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| multiply(identity,inverse(least_upper_bound(identity,Y))) != inverse(least_upper_bound(identity,Y))
| inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0],$fot(inverse(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_1139,plain,
( multiply(identity,inverse(least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,Y))),inverse(least_upper_bound(identity,Y))) )],[refute_0_1137,refute_0_1138]) ).
cnf(refute_0_1140,plain,
inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1136,refute_0_1139]) ).
cnf(refute_0_1141,plain,
inverse(least_upper_bound(identity,inverse(X_302))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302)))),
inference(subst,[],[refute_0_1140:[bind(Y,$fot(inverse(X_302)))]]) ).
cnf(refute_0_1142,plain,
( inverse(least_upper_bound(identity,inverse(X_302))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302)))) = inverse(least_upper_bound(identity,inverse(X_302))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_302))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))))]]) ).
cnf(refute_0_1143,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302)))) = inverse(least_upper_bound(identity,inverse(X_302))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_302))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))) )],[refute_0_1141,refute_0_1142]) ).
cnf(refute_0_1144,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302)))) != inverse(least_upper_bound(identity,inverse(X_302)))
| least_upper_bound(greatest_lower_bound(identity,X_302),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))) != greatest_lower_bound(identity,X_302)
| least_upper_bound(greatest_lower_bound(identity,X_302),inverse(least_upper_bound(identity,inverse(X_302)))) = greatest_lower_bound(identity,X_302) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_302),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))),greatest_lower_bound(identity,X_302)) ),[0,1],$fot(inverse(least_upper_bound(identity,inverse(X_302))))]]) ).
cnf(refute_0_1145,plain,
( least_upper_bound(greatest_lower_bound(identity,X_302),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))) != greatest_lower_bound(identity,X_302)
| least_upper_bound(greatest_lower_bound(identity,X_302),inverse(least_upper_bound(identity,inverse(X_302)))) = greatest_lower_bound(identity,X_302) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302)))),inverse(least_upper_bound(identity,inverse(X_302)))) )],[refute_0_1143,refute_0_1144]) ).
cnf(refute_0_1146,plain,
least_upper_bound(greatest_lower_bound(identity,X_302),inverse(least_upper_bound(identity,inverse(X_302)))) = greatest_lower_bound(identity,X_302),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_302),greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(X_302))))),greatest_lower_bound(identity,X_302)) )],[refute_0_1131,refute_0_1145]) ).
cnf(refute_0_1147,plain,
least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) = greatest_lower_bound(identity,X_59),
inference(subst,[],[refute_0_1146:[bind(X_302,$fot(X_59))]]) ).
cnf(refute_0_1148,plain,
least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))),
inference(subst,[],[refute_0_482:[bind(X_129,$fot(inverse(least_upper_bound(identity,Y)))),bind(X_130,$fot(identity)),bind(X_18,$fot(X_503))]]) ).
cnf(refute_0_1149,plain,
( inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(identity,Y)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))))]]) ).
cnf(refute_0_1150,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1140,refute_0_1149]) ).
cnf(refute_0_1151,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) != inverse(least_upper_bound(identity,Y))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) != least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)),least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))))) ),[1,1],$fot(inverse(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_1152,plain,
( least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) != least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),inverse(least_upper_bound(identity,Y))) )],[refute_0_1150,refute_0_1151]) ).
cnf(refute_0_1153,plain,
least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)),least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))))) )],[refute_0_1148,refute_0_1152]) ).
cnf(refute_0_1154,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(X_7,identity)),inverse(least_upper_bound(X_7,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))),
inference(subst,[],[refute_0_898:[bind(X_110,$fot(least_upper_bound(X_7,identity)))]]) ).
cnf(refute_0_1155,plain,
greatest_lower_bound(identity,least_upper_bound(X_7,identity)) = identity,
inference(subst,[],[refute_0_363:[bind(X_6,$fot(identity))]]) ).
cnf(refute_0_1156,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(X_7,identity)),inverse(least_upper_bound(X_7,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))
| greatest_lower_bound(identity,least_upper_bound(X_7,identity)) != identity
| multiply(identity,inverse(least_upper_bound(X_7,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(X_7,identity)),inverse(least_upper_bound(X_7,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_1157,plain,
( multiply(greatest_lower_bound(identity,least_upper_bound(X_7,identity)),inverse(least_upper_bound(X_7,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))
| multiply(identity,inverse(least_upper_bound(X_7,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_7,identity)),identity) )],[refute_0_1155,refute_0_1156]) ).
cnf(refute_0_1158,plain,
multiply(identity,inverse(least_upper_bound(X_7,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,least_upper_bound(X_7,identity)),inverse(least_upper_bound(X_7,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))) )],[refute_0_1154,refute_0_1157]) ).
cnf(refute_0_1159,plain,
multiply(identity,inverse(least_upper_bound(X_7,identity))) = inverse(least_upper_bound(X_7,identity)),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(least_upper_bound(X_7,identity))))]]) ).
cnf(refute_0_1160,plain,
( multiply(identity,inverse(least_upper_bound(X_7,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))
| multiply(identity,inverse(least_upper_bound(X_7,identity))) != inverse(least_upper_bound(X_7,identity))
| inverse(least_upper_bound(X_7,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(X_7,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))) ),[0],$fot(inverse(least_upper_bound(X_7,identity)))]]) ).
cnf(refute_0_1161,plain,
( multiply(identity,inverse(least_upper_bound(X_7,identity))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))
| inverse(least_upper_bound(X_7,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(X_7,identity))),inverse(least_upper_bound(X_7,identity))) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
inverse(least_upper_bound(X_7,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(least_upper_bound(X_7,identity))),greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))) )],[refute_0_1158,refute_0_1161]) ).
cnf(refute_0_1163,plain,
( inverse(least_upper_bound(X_7,identity)) != greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))) = inverse(least_upper_bound(X_7,identity)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(X_7,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))))]]) ).
cnf(refute_0_1164,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity))) = inverse(least_upper_bound(X_7,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_7,identity)),greatest_lower_bound(identity,inverse(least_upper_bound(X_7,identity)))) )],[refute_0_1162,refute_0_1163]) ).
cnf(refute_0_1165,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))) = inverse(least_upper_bound(Y,identity)),
inference(subst,[],[refute_0_1164:[bind(X_7,$fot(Y))]]) ).
cnf(refute_0_1166,plain,
least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))) = least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))))]]) ).
cnf(refute_0_1167,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))) != inverse(least_upper_bound(Y,identity))
| least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))) != least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))))
| least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))) = least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))),least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))))) ),[1,1],$fot(inverse(least_upper_bound(Y,identity)))]]) ).
cnf(refute_0_1168,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))) != inverse(least_upper_bound(Y,identity))
| least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))) = least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))),least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))))) )],[refute_0_1166,refute_0_1167]) ).
cnf(refute_0_1169,plain,
least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))) = least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))),inverse(least_upper_bound(Y,identity))) )],[refute_0_1165,refute_0_1168]) ).
cnf(refute_0_1170,plain,
least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))) = least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501)),
inference(subst,[],[refute_0_482:[bind(X_129,$fot(X_501)),bind(X_130,$fot(inverse(least_upper_bound(identity,X_59)))),bind(X_18,$fot(X_503))]]) ).
cnf(refute_0_1171,plain,
multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),multiply(inverse(X_104),greatest_lower_bound(X_104,identity))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(greatest_lower_bound(X_104,identity))),bind(Y,$fot(X_107)),bind(Z,$fot(inverse(X_104)))]]) ).
cnf(refute_0_1172,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),multiply(inverse(X_104),greatest_lower_bound(X_104,identity)))
| multiply(inverse(X_104),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(identity,inverse(X_104))
| multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)),greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),multiply(inverse(X_104),greatest_lower_bound(X_104,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_104)))]]) ).
cnf(refute_0_1173,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),multiply(inverse(X_104),greatest_lower_bound(X_104,identity)))
| multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) )],[refute_0_848,refute_0_1172]) ).
cnf(refute_0_1174,plain,
multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)),greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),multiply(inverse(X_104),greatest_lower_bound(X_104,identity)))) )],[refute_0_1171,refute_0_1173]) ).
cnf(refute_0_1175,plain,
greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)))) = greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),
inference(subst,[],[refute_0_363:[bind(X_6,$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))))]]) ).
cnf(refute_0_1176,plain,
least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)) = X_12,
inference(subst,[],[refute_0_96:[bind(X_13,$fot(greatest_lower_bound(X_41,X_42)))]]) ).
cnf(refute_0_1177,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_1178,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)))]]) ).
cnf(refute_0_1179,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)) )],[refute_0_1177,refute_0_1178]) ).
cnf(refute_0_1180,plain,
( greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12))
| least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)),X_12) ),[0,1],$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12)))]]) ).
cnf(refute_0_1181,plain,
( least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12))) = X_12 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12))) )],[refute_0_1179,refute_0_1180]) ).
cnf(refute_0_1182,plain,
least_upper_bound(X_12,greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_12))) = X_12,
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_12)),X_12) )],[refute_0_1176,refute_0_1181]) ).
cnf(refute_0_1183,plain,
least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))) = X_7,
inference(subst,[],[refute_0_1182:[bind(X_12,$fot(X_7)),bind(X_41,$fot(X_94)),bind(X_42,$fot(X_95))]]) ).
cnf(refute_0_1184,plain,
( greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)))) != greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))
| least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))) != X_7
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)))),greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))) ),[0,1],$fot(X_7)]]) ).
cnf(refute_0_1185,plain,
( greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)))) != greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))),X_7) )],[refute_0_1183,refute_0_1184]) ).
cnf(refute_0_1186,plain,
greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),least_upper_bound(X_7,greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)))),greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))) )],[refute_0_1175,refute_0_1185]) ).
cnf(refute_0_1187,plain,
greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)) = greatest_lower_bound(X_7,X_95),
inference(subst,[],[refute_0_466:[bind(X_13,$fot(X_95))]]) ).
cnf(refute_0_1188,plain,
greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))))]]) ).
cnf(refute_0_1189,plain,
( greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)) != greatest_lower_bound(X_7,X_95)
| greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) != greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))
| greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))),greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))) ),[1,1],$fot(greatest_lower_bound(X_7,X_95))]]) ).
cnf(refute_0_1190,plain,
( greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)) != greatest_lower_bound(X_7,X_95)
| greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))),greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))) )],[refute_0_1188,refute_0_1189]) ).
cnf(refute_0_1191,plain,
greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)),greatest_lower_bound(X_7,X_95)) )],[refute_0_1187,refute_0_1190]) ).
cnf(refute_0_1192,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_1193,plain,
greatest_lower_bound(X_43,X_42) = greatest_lower_bound(X_42,X_43),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_43)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_1194,plain,
( greatest_lower_bound(X_43,X_42) != greatest_lower_bound(X_42,X_43)
| greatest_lower_bound(X_42,X_43) = greatest_lower_bound(X_43,X_42) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_43,X_42))),bind(Y0,$fot(greatest_lower_bound(X_42,X_43)))]]) ).
cnf(refute_0_1195,plain,
greatest_lower_bound(X_42,X_43) = greatest_lower_bound(X_43,X_42),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_43,X_42),greatest_lower_bound(X_42,X_43)) )],[refute_0_1193,refute_0_1194]) ).
cnf(refute_0_1196,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43)
| greatest_lower_bound(X_42,X_43) != greatest_lower_bound(X_43,X_42)
| greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43)) ),[0,1],$fot(greatest_lower_bound(X_43,X_42))]]) ).
cnf(refute_0_1197,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43)
| greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,X_43),greatest_lower_bound(X_43,X_42)) )],[refute_0_1195,refute_0_1196]) ).
cnf(refute_0_1198,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) = greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43)) )],[refute_0_1192,refute_0_1197]) ).
cnf(refute_0_1199,plain,
greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)),
inference(subst,[],[refute_0_462:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_1200,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43)
| greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43))]]) ).
cnf(refute_0_1201,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) != greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43)
| greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43))) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) = greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)),greatest_lower_bound(greatest_lower_bound(X_41,X_42),X_43)) )],[refute_0_1198,refute_0_1201]) ).
cnf(refute_0_1203,plain,
( greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) != greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43))))]]) ).
cnf(refute_0_1204,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43)) = greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(X_43,X_42)),greatest_lower_bound(X_41,greatest_lower_bound(X_42,X_43))) )],[refute_0_1202,refute_0_1203]) ).
cnf(refute_0_1205,plain,
greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7)) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))),
inference(subst,[],[refute_0_1204:[bind(X_41,$fot(X_94)),bind(X_42,$fot(greatest_lower_bound(X_95,X_7))),bind(X_43,$fot(X_7))]]) ).
cnf(refute_0_1206,plain,
greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7)),
inference(subst,[],[refute_0_462:[bind(X,$fot(X_94)),bind(Y,$fot(greatest_lower_bound(X_95,X_7))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_1207,plain,
( greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7)) != greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) != greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7))),bind(Y0,$fot(greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7)))),bind(Z0,$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))))]]) ).
cnf(refute_0_1208,plain,
( greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7)) != greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7),greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7))) )],[refute_0_1206,refute_0_1207]) ).
cnf(refute_0_1209,plain,
greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_94,greatest_lower_bound(greatest_lower_bound(X_95,X_7),X_7)),greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))) )],[refute_0_1205,refute_0_1208]) ).
cnf(refute_0_1210,plain,
( greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) != greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) != greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7))),bind(Y0,$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))))),bind(Z0,$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95))))]]) ).
cnf(refute_0_1211,plain,
( greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))) != greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7),greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7)))) )],[refute_0_1209,refute_0_1210]) ).
cnf(refute_0_1212,plain,
greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_94,greatest_lower_bound(X_7,greatest_lower_bound(X_95,X_7))),greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95))) )],[refute_0_1191,refute_0_1211]) ).
cnf(refute_0_1213,plain,
( greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) != greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95))
| greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) != greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))
| greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) = greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7),greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))) ),[0],$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)))]]) ).
cnf(refute_0_1214,plain,
( greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7) != greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))
| greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) = greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7),greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95))) )],[refute_0_1212,refute_0_1213]) ).
cnf(refute_0_1215,plain,
greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) = greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)),X_7),greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))) )],[refute_0_1186,refute_0_1214]) ).
cnf(refute_0_1216,plain,
( greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) != greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))
| greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)))),bind(Y0,$fot(greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))))]]) ).
cnf(refute_0_1217,plain,
greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7)) = greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_94,greatest_lower_bound(X_7,X_95)),greatest_lower_bound(X_94,greatest_lower_bound(X_95,X_7))) )],[refute_0_1215,refute_0_1216]) ).
cnf(refute_0_1218,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))),
inference(subst,[],[refute_0_1217:[bind(X_7,$fot(inverse(X_104))),bind(X_94,$fot(identity)),bind(X_95,$fot(multiply(X_107,greatest_lower_bound(X_104,identity))))]]) ).
cnf(refute_0_1219,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) != greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43))
| greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43)) = greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)))),bind(Y0,$fot(greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43))))]]) ).
cnf(refute_0_1220,plain,
greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43)) = greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_41,X_43)),greatest_lower_bound(X_41,greatest_lower_bound(X_13,X_43))) )],[refute_0_796,refute_0_1219]) ).
cnf(refute_0_1221,plain,
greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104))),
inference(subst,[],[refute_0_1220:[bind(X_13,$fot(identity)),bind(X_41,$fot(multiply(X_107,greatest_lower_bound(X_104,identity)))),bind(X_43,$fot(inverse(X_104)))]]) ).
cnf(refute_0_1222,plain,
( greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))
| greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))))]]) ).
cnf(refute_0_1223,plain,
( greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))
| greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))),greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104)))) )],[refute_0_1221,refute_0_1222]) ).
cnf(refute_0_1224,plain,
greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),inverse(X_104))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))) )],[refute_0_1218,refute_0_1223]) ).
cnf(refute_0_1225,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104)))
| greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))
| multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))) ),[0],$fot(greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))))]]) ).
cnf(refute_0_1226,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104)))
| multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))) )],[refute_0_1224,refute_0_1225]) ).
cnf(refute_0_1227,plain,
multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)),greatest_lower_bound(multiply(X_107,greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,inverse(X_104)))) )],[refute_0_1174,refute_0_1226]) ).
cnf(refute_0_1228,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))),
inference(subst,[],[refute_0_1227:[bind(X_104,$fot(least_upper_bound(identity,X_59))),bind(X_107,$fot(X_222))]]) ).
cnf(refute_0_1229,plain,
inverse(least_upper_bound(identity,X_59)) = multiply(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),inverse(X_59)),
inference(subst,[],[refute_0_57:[bind(X_48,$fot(inverse(X_59))),bind(X_49,$fot(least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_1230,plain,
( multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(identity,inverse(X_59))
| inverse(least_upper_bound(identity,X_59)) != multiply(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),inverse(X_59))
| inverse(least_upper_bound(identity,X_59)) = multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_59)),multiply(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),inverse(X_59))) ),[1,0,0],$fot(least_upper_bound(identity,inverse(X_59)))]]) ).
cnf(refute_0_1231,plain,
( inverse(least_upper_bound(identity,X_59)) != multiply(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),inverse(X_59))
| inverse(least_upper_bound(identity,X_59)) = multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(identity,inverse(X_59))) )],[refute_0_304,refute_0_1230]) ).
cnf(refute_0_1232,plain,
inverse(least_upper_bound(identity,X_59)) = multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_59)),multiply(inverse(multiply(inverse(X_59),least_upper_bound(identity,X_59))),inverse(X_59))) )],[refute_0_1229,refute_0_1231]) ).
cnf(refute_0_1233,plain,
multiply(least_upper_bound(X_59,identity),identity) = least_upper_bound(X_59,identity),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(least_upper_bound(X_59,identity)))]]) ).
cnf(refute_0_1234,plain,
least_upper_bound(identity,multiply(X_59,identity)) = multiply(least_upper_bound(X_59,identity),identity),
inference(subst,[],[refute_0_492:[bind(X_63,$fot(identity)),bind(X_64,$fot(X_59))]]) ).
cnf(refute_0_1235,plain,
( multiply(least_upper_bound(X_59,identity),identity) != least_upper_bound(X_59,identity)
| least_upper_bound(identity,multiply(X_59,identity)) != multiply(least_upper_bound(X_59,identity),identity)
| least_upper_bound(identity,multiply(X_59,identity)) = least_upper_bound(X_59,identity) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(identity,multiply(X_59,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_59,identity),identity))),bind(Z0,$fot(least_upper_bound(X_59,identity)))]]) ).
cnf(refute_0_1236,plain,
( multiply(least_upper_bound(X_59,identity),identity) != least_upper_bound(X_59,identity)
| least_upper_bound(identity,multiply(X_59,identity)) = least_upper_bound(X_59,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_59,identity)),multiply(least_upper_bound(X_59,identity),identity)) )],[refute_0_1234,refute_0_1235]) ).
cnf(refute_0_1237,plain,
least_upper_bound(identity,multiply(X_59,identity)) = least_upper_bound(X_59,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_59,identity),identity),least_upper_bound(X_59,identity)) )],[refute_0_1233,refute_0_1236]) ).
cnf(refute_0_1238,plain,
multiply(X_59,least_upper_bound(identity,inverse(X_59))) = least_upper_bound(identity,multiply(X_59,identity)),
inference(subst,[],[refute_0_965:[bind(X_51,$fot(X_59)),bind(X_52,$fot(identity))]]) ).
cnf(refute_0_1239,plain,
( multiply(X_59,least_upper_bound(identity,inverse(X_59))) != least_upper_bound(identity,multiply(X_59,identity))
| least_upper_bound(identity,multiply(X_59,identity)) != least_upper_bound(X_59,identity)
| multiply(X_59,least_upper_bound(identity,inverse(X_59))) = least_upper_bound(X_59,identity) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(X_59,least_upper_bound(identity,inverse(X_59))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_59,identity)))),bind(Z0,$fot(least_upper_bound(X_59,identity)))]]) ).
cnf(refute_0_1240,plain,
( least_upper_bound(identity,multiply(X_59,identity)) != least_upper_bound(X_59,identity)
| multiply(X_59,least_upper_bound(identity,inverse(X_59))) = least_upper_bound(X_59,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_59,least_upper_bound(identity,inverse(X_59))),least_upper_bound(identity,multiply(X_59,identity))) )],[refute_0_1238,refute_0_1239]) ).
cnf(refute_0_1241,plain,
multiply(X_59,least_upper_bound(identity,inverse(X_59))) = least_upper_bound(X_59,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_59,identity)),least_upper_bound(X_59,identity)) )],[refute_0_1237,refute_0_1240]) ).
cnf(refute_0_1242,plain,
inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))) = inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_1243,plain,
( multiply(X_59,least_upper_bound(identity,inverse(X_59))) != least_upper_bound(X_59,identity)
| inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))) != inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59))))
| inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(X_59,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))),inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59))))) ),[1,0],$fot(least_upper_bound(X_59,identity))]]) ).
cnf(refute_0_1244,plain,
( multiply(X_59,least_upper_bound(identity,inverse(X_59))) != least_upper_bound(X_59,identity)
| inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(X_59,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))),inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1242,refute_0_1243]) ).
cnf(refute_0_1245,plain,
inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))) = inverse(least_upper_bound(X_59,identity)),
inference(resolve,[$cnf( $equal(multiply(X_59,least_upper_bound(identity,inverse(X_59))),least_upper_bound(X_59,identity)) )],[refute_0_1241,refute_0_1244]) ).
cnf(refute_0_1246,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) = inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))),
inference(subst,[],[refute_0_324:[bind(X_30,$fot(X_59)),bind(X_31,$fot(least_upper_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_1247,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) != inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59))))
| inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))) != inverse(least_upper_bound(X_59,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) = inverse(least_upper_bound(X_59,identity)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)))),bind(Y0,$fot(inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))))),bind(Z0,$fot(inverse(least_upper_bound(X_59,identity))))]]) ).
cnf(refute_0_1248,plain,
( inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))) != inverse(least_upper_bound(X_59,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) = inverse(least_upper_bound(X_59,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)),inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1246,refute_0_1247]) ).
cnf(refute_0_1249,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) = inverse(least_upper_bound(X_59,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_59,least_upper_bound(identity,inverse(X_59)))),inverse(least_upper_bound(X_59,identity))) )],[refute_0_1245,refute_0_1248]) ).
cnf(refute_0_1250,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)) != inverse(least_upper_bound(X_59,identity))
| inverse(least_upper_bound(identity,X_59)) != multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59))
| inverse(least_upper_bound(identity,X_59)) = inverse(least_upper_bound(X_59,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_59)),multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59))) ),[1],$fot(inverse(least_upper_bound(X_59,identity)))]]) ).
cnf(refute_0_1251,plain,
( inverse(least_upper_bound(identity,X_59)) != multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59))
| inverse(least_upper_bound(identity,X_59)) = inverse(least_upper_bound(X_59,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59)),inverse(least_upper_bound(X_59,identity))) )],[refute_0_1249,refute_0_1250]) ).
cnf(refute_0_1252,plain,
inverse(least_upper_bound(identity,X_59)) = inverse(least_upper_bound(X_59,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_59)),multiply(inverse(least_upper_bound(identity,inverse(X_59))),inverse(X_59))) )],[refute_0_1232,refute_0_1251]) ).
cnf(refute_0_1253,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))
| inverse(least_upper_bound(identity,X_59)) != inverse(least_upper_bound(X_59,identity))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))) ),[0,0,1],$fot(inverse(least_upper_bound(X_59,identity)))]]) ).
cnf(refute_0_1254,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_59)),inverse(least_upper_bound(X_59,identity))) )],[refute_0_1252,refute_0_1253]) ).
cnf(refute_0_1255,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))) )],[refute_0_1228,refute_0_1254]) ).
cnf(refute_0_1256,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity) = greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))))]]) ).
cnf(refute_0_1257,plain,
greatest_lower_bound(identity,least_upper_bound(identity,X_59)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_59))]]) ).
cnf(refute_0_1258,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))))]]) ).
cnf(refute_0_1259,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))
| greatest_lower_bound(identity,least_upper_bound(identity,X_59)) != identity
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1260,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_59)) != identity
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))) )],[refute_0_1258,refute_0_1259]) ).
cnf(refute_0_1261,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_59)),identity) )],[refute_0_1257,refute_0_1260]) ).
cnf(refute_0_1262,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity)
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity) != greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity))),bind(Z0,$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))))]]) ).
cnf(refute_0_1263,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity) != greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity)) )],[refute_0_1261,refute_0_1262]) ).
cnf(refute_0_1264,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),identity),greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))) )],[refute_0_1256,refute_0_1263]) ).
cnf(refute_0_1265,plain,
multiply(X_216,least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21))) = multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))),
inference(subst,[],[refute_0_922:[bind(X_51,$fot(X_216)),bind(X_52,$fot(greatest_lower_bound(X_13,X_21))),bind(X_53,$fot(greatest_lower_bound(X_21,X_13)))]]) ).
cnf(refute_0_1266,plain,
( multiply(X_216,least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21))) != multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))
| least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21)) != greatest_lower_bound(X_21,X_13)
| multiply(X_216,greatest_lower_bound(X_21,X_13)) = multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_216,least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21))),multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))) ),[0,1],$fot(greatest_lower_bound(X_21,X_13))]]) ).
cnf(refute_0_1267,plain,
( multiply(X_216,least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21))) != multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))
| multiply(X_216,greatest_lower_bound(X_21,X_13)) = multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21)),greatest_lower_bound(X_21,X_13)) )],[refute_0_470,refute_0_1266]) ).
cnf(refute_0_1268,plain,
multiply(X_216,greatest_lower_bound(X_21,X_13)) = multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))),
inference(resolve,[$cnf( $equal(multiply(X_216,least_upper_bound(greatest_lower_bound(X_21,X_13),greatest_lower_bound(X_13,X_21))),multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))) )],[refute_0_1265,refute_0_1267]) ).
cnf(refute_0_1269,plain,
least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)) = greatest_lower_bound(X_13,X_21),
inference(subst,[],[refute_0_470:[bind(X_13,$fot(X_21)),bind(X_21,$fot(X_13))]]) ).
cnf(refute_0_1270,plain,
multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) = multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))),
introduced(tautology,[refl,[$fot(multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))))]]) ).
cnf(refute_0_1271,plain,
( multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) != multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))
| least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)) != greatest_lower_bound(X_13,X_21)
| multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) = multiply(X_216,greatest_lower_bound(X_13,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))),multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))) ),[1,1],$fot(greatest_lower_bound(X_13,X_21))]]) ).
cnf(refute_0_1272,plain,
( least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)) != greatest_lower_bound(X_13,X_21)
| multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) = multiply(X_216,greatest_lower_bound(X_13,X_21)) ),
inference(resolve,[$cnf( $equal(multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))),multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))) )],[refute_0_1270,refute_0_1271]) ).
cnf(refute_0_1273,plain,
multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) = multiply(X_216,greatest_lower_bound(X_13,X_21)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)),greatest_lower_bound(X_13,X_21)) )],[refute_0_1269,refute_0_1272]) ).
cnf(refute_0_1274,plain,
( multiply(X_216,greatest_lower_bound(X_21,X_13)) != multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))
| multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))) != multiply(X_216,greatest_lower_bound(X_13,X_21))
| multiply(X_216,greatest_lower_bound(X_21,X_13)) = multiply(X_216,greatest_lower_bound(X_13,X_21)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_216,greatest_lower_bound(X_21,X_13)),multiply(X_216,greatest_lower_bound(X_13,X_21))) ),[0],$fot(multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))))]]) ).
cnf(refute_0_1275,plain,
( multiply(X_216,greatest_lower_bound(X_21,X_13)) != multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))
| multiply(X_216,greatest_lower_bound(X_21,X_13)) = multiply(X_216,greatest_lower_bound(X_13,X_21)) ),
inference(resolve,[$cnf( $equal(multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13))),multiply(X_216,greatest_lower_bound(X_13,X_21))) )],[refute_0_1273,refute_0_1274]) ).
cnf(refute_0_1276,plain,
multiply(X_216,greatest_lower_bound(X_21,X_13)) = multiply(X_216,greatest_lower_bound(X_13,X_21)),
inference(resolve,[$cnf( $equal(multiply(X_216,greatest_lower_bound(X_21,X_13)),multiply(X_216,least_upper_bound(greatest_lower_bound(X_13,X_21),greatest_lower_bound(X_21,X_13)))) )],[refute_0_1268,refute_0_1275]) ).
cnf(refute_0_1277,plain,
( multiply(X_216,greatest_lower_bound(X_21,X_13)) != multiply(X_216,greatest_lower_bound(X_13,X_21))
| multiply(X_216,greatest_lower_bound(X_13,X_21)) = multiply(X_216,greatest_lower_bound(X_21,X_13)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_216,greatest_lower_bound(X_21,X_13)))),bind(Y0,$fot(multiply(X_216,greatest_lower_bound(X_13,X_21))))]]) ).
cnf(refute_0_1278,plain,
multiply(X_216,greatest_lower_bound(X_13,X_21)) = multiply(X_216,greatest_lower_bound(X_21,X_13)),
inference(resolve,[$cnf( $equal(multiply(X_216,greatest_lower_bound(X_21,X_13)),multiply(X_216,greatest_lower_bound(X_13,X_21))) )],[refute_0_1276,refute_0_1277]) ).
cnf(refute_0_1279,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),
inference(subst,[],[refute_0_1278:[bind(X_13,$fot(least_upper_bound(identity,X_59))),bind(X_21,$fot(identity)),bind(X_216,$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))))]]) ).
cnf(refute_0_1280,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))))),bind(Z0,$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))))]]) ).
cnf(refute_0_1281,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))) )],[refute_0_1279,refute_0_1280]) ).
cnf(refute_0_1282,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))) )],[refute_0_1264,refute_0_1281]) ).
cnf(refute_0_1283,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))
| greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))) ),[0],$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))))]]) ).
cnf(refute_0_1284,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))
| greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity)))) )],[refute_0_1282,refute_0_1283]) ).
cnf(refute_0_1285,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),
inference(subst,[],[refute_0_49:[bind(X_33,$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))))]]) ).
cnf(refute_0_1286,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))))]]) ).
cnf(refute_0_1287,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))
| greatest_lower_bound(identity,least_upper_bound(identity,X_59)) != identity
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1288,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_59)) != identity
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))) )],[refute_0_1286,refute_0_1287]) ).
cnf(refute_0_1289,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_59)),identity) )],[refute_0_1257,refute_0_1288]) ).
cnf(refute_0_1290,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity)
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity) != greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity))),bind(Z0,$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))))]]) ).
cnf(refute_0_1291,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity) != greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))
| multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity)) )],[refute_0_1289,refute_0_1290]) ).
cnf(refute_0_1292,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),identity),greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))) )],[refute_0_1285,refute_0_1291]) ).
cnf(refute_0_1293,plain,
multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))),
inference(subst,[],[refute_0_1227:[bind(X_104,$fot(X_221)),bind(X_107,$fot(X_222))]]) ).
cnf(refute_0_1294,plain,
greatest_lower_bound(identity,X_221) = greatest_lower_bound(X_221,identity),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_221))]]) ).
cnf(refute_0_1295,plain,
( greatest_lower_bound(identity,X_221) != greatest_lower_bound(X_221,identity)
| greatest_lower_bound(X_221,identity) = greatest_lower_bound(identity,X_221) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(identity,X_221))),bind(Y0,$fot(greatest_lower_bound(X_221,identity)))]]) ).
cnf(refute_0_1296,plain,
greatest_lower_bound(X_221,identity) = greatest_lower_bound(identity,X_221),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_221),greatest_lower_bound(X_221,identity)) )],[refute_0_1294,refute_0_1295]) ).
cnf(refute_0_1297,plain,
( multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity))))
| greatest_lower_bound(X_221,identity) != greatest_lower_bound(identity,X_221)
| multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity))))) ),[0,1],$fot(greatest_lower_bound(identity,X_221))]]) ).
cnf(refute_0_1298,plain,
( multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity))))
| multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_221,identity),greatest_lower_bound(identity,X_221)) )],[refute_0_1296,refute_0_1297]) ).
cnf(refute_0_1299,plain,
multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity))))) )],[refute_0_1293,refute_0_1298]) ).
cnf(refute_0_1300,plain,
( multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))) = multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))))]]) ).
cnf(refute_0_1301,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity)))) = multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_107,inverse(X_104)),greatest_lower_bound(X_104,identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_104),multiply(X_107,greatest_lower_bound(X_104,identity))))) )],[refute_0_1227,refute_0_1300]) ).
cnf(refute_0_1302,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))) = multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)),
inference(subst,[],[refute_0_1301:[bind(X_104,$fot(X_221)),bind(X_107,$fot(X_222))]]) ).
cnf(refute_0_1303,plain,
( multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))) != multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity))
| multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) = multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)),multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))))]]) ).
cnf(refute_0_1304,plain,
( multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity))))
| multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) = multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity)))),multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity))) )],[refute_0_1302,refute_0_1303]) ).
cnf(refute_0_1305,plain,
multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) = multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_221),multiply(X_222,greatest_lower_bound(X_221,identity))))) )],[refute_0_1299,refute_0_1304]) ).
cnf(refute_0_1306,plain,
( multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) != multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity))
| multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)) = multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity))))]]) ).
cnf(refute_0_1307,plain,
multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity)) = multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(identity,X_221)),multiply(greatest_lower_bound(X_222,inverse(X_221)),greatest_lower_bound(X_221,identity))) )],[refute_0_1305,refute_0_1306]) ).
cnf(refute_0_1308,plain,
multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),
inference(subst,[],[refute_0_1307:[bind(X_221,$fot(least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_1309,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),
inference(subst,[],[refute_0_1301:[bind(X_104,$fot(least_upper_bound(identity,X_59))),bind(X_107,$fot(X_222))]]) ).
cnf(refute_0_1310,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))))]]) ).
cnf(refute_0_1311,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity))) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) = multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))) )],[refute_0_1308,refute_0_1311]) ).
cnf(refute_0_1313,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) != multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))))),bind(Z0,$fot(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))))]]) ).
cnf(refute_0_1314,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))) != greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))),multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59)))) )],[refute_0_1312,refute_0_1313]) ).
cnf(refute_0_1315,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(identity,least_upper_bound(identity,X_59))),greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))) )],[refute_0_1292,refute_0_1314]) ).
cnf(refute_0_1316,plain,
( greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))) != greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))
| greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))))]]) ).
cnf(refute_0_1317,plain,
( greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))
| greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity)))),greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59)))) )],[refute_0_1315,refute_0_1316]) ).
cnf(refute_0_1318,plain,
( multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))
| greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))) )],[refute_0_1284,refute_0_1317]) ).
cnf(refute_0_1319,plain,
greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))) = greatest_lower_bound(X_222,inverse(least_upper_bound(identity,X_59))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_222,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(least_upper_bound(identity,X_59),identity)),greatest_lower_bound(identity,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),multiply(X_222,greatest_lower_bound(least_upper_bound(identity,X_59),identity))))) )],[refute_0_1255,refute_0_1318]) ).
cnf(refute_0_1320,plain,
greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity))) = greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59))),
inference(subst,[],[refute_0_1319:[bind(X_222,$fot(X_501))]]) ).
cnf(refute_0_1321,plain,
( greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity))) != greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))
| greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59))) = greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity))))),bind(Y0,$fot(greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))))]]) ).
cnf(refute_0_1322,plain,
greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59))) = greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity))),greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))) )],[refute_0_1320,refute_0_1321]) ).
cnf(refute_0_1323,plain,
( greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59))) != greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))
| least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))) != least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501))
| least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))) = least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))),least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501))) ),[0,1],$fot(greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity))))]]) ).
cnf(refute_0_1324,plain,
( least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))) != least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501))
| least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))) = least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59))),greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))) )],[refute_0_1322,refute_0_1323]) ).
cnf(refute_0_1325,plain,
least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))) = least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(identity,X_59)))),least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501))) )],[refute_0_1170,refute_0_1324]) ).
cnf(refute_0_1326,plain,
( least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))) != least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501)) = least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))))),bind(Y0,$fot(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501))))]]) ).
cnf(refute_0_1327,plain,
least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501)) = least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(X_501,inverse(least_upper_bound(X_59,identity)))),least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,X_59)),X_501))) )],[refute_0_1325,refute_0_1326]) ).
cnf(refute_0_1328,plain,
least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))),
inference(subst,[],[refute_0_1327:[bind(X_501,$fot(identity)),bind(X_59,$fot(Y))]]) ).
cnf(refute_0_1329,plain,
( least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))) != least_upper_bound(X_503,inverse(least_upper_bound(Y,identity)))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) != least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)))),bind(Y0,$fot(least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))))),bind(Z0,$fot(least_upper_bound(X_503,inverse(least_upper_bound(Y,identity)))))]]) ).
cnf(refute_0_1330,plain,
( least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))) != least_upper_bound(X_503,inverse(least_upper_bound(Y,identity)))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)),least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity))))) )],[refute_0_1328,refute_0_1329]) ).
cnf(refute_0_1331,plain,
least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) = least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(identity,inverse(least_upper_bound(Y,identity)))),least_upper_bound(X_503,inverse(least_upper_bound(Y,identity)))) )],[refute_0_1169,refute_0_1330]) ).
cnf(refute_0_1332,plain,
( least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) != least_upper_bound(X_503,inverse(least_upper_bound(Y,identity)))
| least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) != least_upper_bound(X_503,inverse(least_upper_bound(identity,Y)))
| least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))) = least_upper_bound(X_503,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)),least_upper_bound(X_503,inverse(least_upper_bound(identity,Y)))) ),[0],$fot(least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))))]]) ).
cnf(refute_0_1333,plain,
( least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)) != least_upper_bound(X_503,inverse(least_upper_bound(identity,Y)))
| least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))) = least_upper_bound(X_503,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)),least_upper_bound(X_503,inverse(least_upper_bound(Y,identity)))) )],[refute_0_1331,refute_0_1332]) ).
cnf(refute_0_1334,plain,
least_upper_bound(X_503,inverse(least_upper_bound(Y,identity))) = least_upper_bound(X_503,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_503,greatest_lower_bound(inverse(least_upper_bound(identity,Y)),identity)),least_upper_bound(X_503,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1153,refute_0_1333]) ).
cnf(refute_0_1335,plain,
least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))) = least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))),
inference(subst,[],[refute_0_1334:[bind(Y,$fot(inverse(X_59))),bind(X_503,$fot(greatest_lower_bound(identity,X_59)))]]) ).
cnf(refute_0_1336,plain,
( least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) != greatest_lower_bound(identity,X_59)
| least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))) != least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))
| least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))) = greatest_lower_bound(identity,X_59) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))))),bind(Z0,$fot(greatest_lower_bound(identity,X_59)))]]) ).
cnf(refute_0_1337,plain,
( least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))) != greatest_lower_bound(identity,X_59)
| least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))) = greatest_lower_bound(identity,X_59) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))),least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59))))) )],[refute_0_1335,refute_0_1336]) ).
cnf(refute_0_1338,plain,
least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))) = greatest_lower_bound(identity,X_59),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(identity,inverse(X_59)))),greatest_lower_bound(identity,X_59)) )],[refute_0_1147,refute_0_1337]) ).
cnf(refute_0_1339,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y) = least_upper_bound(Y,inverse(least_upper_bound(identity,X_504))),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(inverse(least_upper_bound(identity,X_504))))]]) ).
cnf(refute_0_1340,plain,
least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))) = least_upper_bound(Y,inverse(least_upper_bound(identity,X_504))),
inference(subst,[],[refute_0_1334:[bind(Y,$fot(X_504)),bind(X_503,$fot(Y))]]) ).
cnf(refute_0_1341,plain,
( least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))) != least_upper_bound(Y,inverse(least_upper_bound(identity,X_504)))
| least_upper_bound(Y,inverse(least_upper_bound(identity,X_504))) = least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))))),bind(Y0,$fot(least_upper_bound(Y,inverse(least_upper_bound(identity,X_504)))))]]) ).
cnf(refute_0_1342,plain,
least_upper_bound(Y,inverse(least_upper_bound(identity,X_504))) = least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))),least_upper_bound(Y,inverse(least_upper_bound(identity,X_504)))) )],[refute_0_1340,refute_0_1341]) ).
cnf(refute_0_1343,plain,
( least_upper_bound(Y,inverse(least_upper_bound(identity,X_504))) != least_upper_bound(Y,inverse(least_upper_bound(X_504,identity)))
| least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y) != least_upper_bound(Y,inverse(least_upper_bound(identity,X_504)))
| least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y) = least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y),least_upper_bound(Y,inverse(least_upper_bound(identity,X_504)))) ),[1],$fot(least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))))]]) ).
cnf(refute_0_1344,plain,
( least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y) != least_upper_bound(Y,inverse(least_upper_bound(identity,X_504)))
| least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y) = least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,inverse(least_upper_bound(identity,X_504))),least_upper_bound(Y,inverse(least_upper_bound(X_504,identity)))) )],[refute_0_1342,refute_0_1343]) ).
cnf(refute_0_1345,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y) = least_upper_bound(Y,inverse(least_upper_bound(X_504,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_504)),Y),least_upper_bound(Y,inverse(least_upper_bound(identity,X_504)))) )],[refute_0_1339,refute_0_1344]) ).
cnf(refute_0_1346,plain,
least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) = least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))),
inference(subst,[],[refute_0_1345:[bind(Y,$fot(greatest_lower_bound(identity,X_59))),bind(X_504,$fot(inverse(X_59)))]]) ).
cnf(refute_0_1347,plain,
( least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))) != greatest_lower_bound(identity,X_59)
| least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) != least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity)))
| least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) = greatest_lower_bound(identity,X_59) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))))),bind(Z0,$fot(greatest_lower_bound(identity,X_59)))]]) ).
cnf(refute_0_1348,plain,
( least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))) != greatest_lower_bound(identity,X_59)
| least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) = greatest_lower_bound(identity,X_59) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)),least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity)))) )],[refute_0_1346,refute_0_1347]) ).
cnf(refute_0_1349,plain,
least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) = greatest_lower_bound(identity,X_59),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_59),inverse(least_upper_bound(inverse(X_59),identity))),greatest_lower_bound(identity,X_59)) )],[refute_0_1338,refute_0_1348]) ).
cnf(refute_0_1350,plain,
( inverse(least_upper_bound(identity,inverse(X_59))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))
| least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) != greatest_lower_bound(identity,X_59)
| inverse(least_upper_bound(identity,inverse(X_59))) = greatest_lower_bound(identity,X_59) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)))]]) ).
cnf(refute_0_1351,plain,
( inverse(least_upper_bound(identity,inverse(X_59))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))
| inverse(least_upper_bound(identity,inverse(X_59))) = greatest_lower_bound(identity,X_59) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)),greatest_lower_bound(identity,X_59)) )],[refute_0_1349,refute_0_1350]) ).
cnf(refute_0_1352,plain,
( multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))
| inverse(least_upper_bound(identity,inverse(X_59))) = greatest_lower_bound(identity,X_59) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_59))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))) )],[refute_0_1076,refute_0_1351]) ).
cnf(refute_0_1353,plain,
inverse(least_upper_bound(identity,inverse(X_59))) = greatest_lower_bound(identity,X_59),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X_59),inverse(inverse(least_upper_bound(identity,inverse(X_59)))))),inverse(least_upper_bound(identity,inverse(X_59)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59))) )],[refute_0_435,refute_0_1352]) ).
cnf(refute_0_1354,plain,
( inverse(least_upper_bound(identity,inverse(X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),X_59)
| inverse(least_upper_bound(identity,inverse(X_59))) != greatest_lower_bound(identity,X_59)
| greatest_lower_bound(identity,X_59) = multiply(inverse(least_upper_bound(identity,X_59)),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_59))),multiply(inverse(least_upper_bound(identity,X_59)),X_59)) ),[0],$fot(greatest_lower_bound(identity,X_59))]]) ).
cnf(refute_0_1355,plain,
( inverse(least_upper_bound(identity,inverse(X_59))) != multiply(inverse(least_upper_bound(identity,X_59)),X_59)
| greatest_lower_bound(identity,X_59) = multiply(inverse(least_upper_bound(identity,X_59)),X_59) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_59))),greatest_lower_bound(identity,X_59)) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
greatest_lower_bound(identity,X_59) = multiply(inverse(least_upper_bound(identity,X_59)),X_59),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_59))),multiply(inverse(least_upper_bound(identity,X_59)),X_59)) )],[refute_0_331,refute_0_1355]) ).
cnf(refute_0_1357,plain,
greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) = multiply(inverse(least_upper_bound(identity,multiply(X_65,inverse(X_64)))),multiply(X_65,inverse(X_64))),
inference(subst,[],[refute_0_1356:[bind(X_59,$fot(multiply(X_65,inverse(X_64))))]]) ).
cnf(refute_0_1358,plain,
( multiply(least_upper_bound(X_64,X_65),inverse(X_64)) != least_upper_bound(identity,multiply(X_65,inverse(X_64)))
| least_upper_bound(identity,multiply(X_65,inverse(X_64))) = multiply(least_upper_bound(X_64,X_65),inverse(X_64)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(X_64,X_65),inverse(X_64)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_65,inverse(X_64)))))]]) ).
cnf(refute_0_1359,plain,
least_upper_bound(identity,multiply(X_65,inverse(X_64))) = multiply(least_upper_bound(X_64,X_65),inverse(X_64)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,X_65),inverse(X_64)),least_upper_bound(identity,multiply(X_65,inverse(X_64)))) )],[refute_0_548,refute_0_1358]) ).
cnf(refute_0_1360,plain,
( greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) != multiply(inverse(least_upper_bound(identity,multiply(X_65,inverse(X_64)))),multiply(X_65,inverse(X_64)))
| least_upper_bound(identity,multiply(X_65,inverse(X_64))) != multiply(least_upper_bound(X_64,X_65),inverse(X_64))
| greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) = multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_65,inverse(X_64))),multiply(inverse(least_upper_bound(identity,multiply(X_65,inverse(X_64)))),multiply(X_65,inverse(X_64)))) ),[1,0,0],$fot(multiply(least_upper_bound(X_64,X_65),inverse(X_64)))]]) ).
cnf(refute_0_1361,plain,
( greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) != multiply(inverse(least_upper_bound(identity,multiply(X_65,inverse(X_64)))),multiply(X_65,inverse(X_64)))
| greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) = multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_65,inverse(X_64))),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) )],[refute_0_1359,refute_0_1360]) ).
cnf(refute_0_1362,plain,
greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) = multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_65,inverse(X_64))),multiply(inverse(least_upper_bound(identity,multiply(X_65,inverse(X_64)))),multiply(X_65,inverse(X_64)))) )],[refute_0_1357,refute_0_1361]) ).
cnf(refute_0_1363,plain,
multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))) = least_upper_bound(identity,multiply(X_64,inverse(X_65))),
inference(subst,[],[refute_0_965:[bind(X_51,$fot(X_64)),bind(X_52,$fot(inverse(X_65)))]]) ).
cnf(refute_0_1364,plain,
inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))) = least_upper_bound(inverse(X_65),inverse(X_64)),
inference(subst,[],[refute_0_83:[bind(X_35,$fot(least_upper_bound(inverse(X_65),inverse(X_64))))]]) ).
cnf(refute_0_1365,plain,
inverse(least_upper_bound(inverse(X_261),inverse(X_64))) = multiply(inverse(least_upper_bound(identity,multiply(X_261,inverse(X_64)))),X_261),
inference(subst,[],[refute_0_278:[bind(X_141,$fot(X_261)),bind(X_53,$fot(inverse(X_64)))]]) ).
cnf(refute_0_1366,plain,
multiply(least_upper_bound(X_64,X_261),inverse(X_64)) = least_upper_bound(identity,multiply(X_261,inverse(X_64))),
inference(subst,[],[refute_0_548:[bind(X_65,$fot(X_261))]]) ).
cnf(refute_0_1367,plain,
( multiply(least_upper_bound(X_64,X_261),inverse(X_64)) != least_upper_bound(identity,multiply(X_261,inverse(X_64)))
| least_upper_bound(identity,multiply(X_261,inverse(X_64))) = multiply(least_upper_bound(X_64,X_261),inverse(X_64)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(least_upper_bound(X_64,X_261),inverse(X_64)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_261,inverse(X_64)))))]]) ).
cnf(refute_0_1368,plain,
least_upper_bound(identity,multiply(X_261,inverse(X_64))) = multiply(least_upper_bound(X_64,X_261),inverse(X_64)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_64,X_261),inverse(X_64)),least_upper_bound(identity,multiply(X_261,inverse(X_64)))) )],[refute_0_1366,refute_0_1367]) ).
cnf(refute_0_1369,plain,
( inverse(least_upper_bound(inverse(X_261),inverse(X_64))) != multiply(inverse(least_upper_bound(identity,multiply(X_261,inverse(X_64)))),X_261)
| least_upper_bound(identity,multiply(X_261,inverse(X_64))) != multiply(least_upper_bound(X_64,X_261),inverse(X_64))
| inverse(least_upper_bound(inverse(X_261),inverse(X_64))) = multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_261),inverse(X_64))),multiply(inverse(least_upper_bound(identity,multiply(X_261,inverse(X_64)))),X_261)) ),[1,0,0],$fot(multiply(least_upper_bound(X_64,X_261),inverse(X_64)))]]) ).
cnf(refute_0_1370,plain,
( inverse(least_upper_bound(inverse(X_261),inverse(X_64))) != multiply(inverse(least_upper_bound(identity,multiply(X_261,inverse(X_64)))),X_261)
| inverse(least_upper_bound(inverse(X_261),inverse(X_64))) = multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_261,inverse(X_64))),multiply(least_upper_bound(X_64,X_261),inverse(X_64))) )],[refute_0_1368,refute_0_1369]) ).
cnf(refute_0_1371,plain,
inverse(least_upper_bound(inverse(X_261),inverse(X_64))) = multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_261),inverse(X_64))),multiply(inverse(least_upper_bound(identity,multiply(X_261,inverse(X_64)))),X_261)) )],[refute_0_1365,refute_0_1370]) ).
cnf(refute_0_1372,plain,
multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261) = multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)),
inference(subst,[],[associativity:[bind(X,$fot(X_64)),bind(Y,$fot(inverse(least_upper_bound(X_64,X_261)))),bind(Z,$fot(X_261))]]) ).
cnf(refute_0_1373,plain,
inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))) = multiply(X_64,inverse(least_upper_bound(X_64,X_261))),
inference(subst,[],[refute_0_242:[bind(X_152,$fot(least_upper_bound(X_64,X_261))),bind(X_35,$fot(X_64))]]) ).
cnf(refute_0_1374,plain,
multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) = multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261))]]) ).
cnf(refute_0_1375,plain,
( multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) != multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261)
| inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))) != multiply(X_64,inverse(least_upper_bound(X_64,X_261)))
| multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) = multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261),multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261)) ),[1,0],$fot(multiply(X_64,inverse(least_upper_bound(X_64,X_261))))]]) ).
cnf(refute_0_1376,plain,
( inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))) != multiply(X_64,inverse(least_upper_bound(X_64,X_261)))
| multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) = multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261),multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261)) )],[refute_0_1374,refute_0_1375]) ).
cnf(refute_0_1377,plain,
multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) = multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),multiply(X_64,inverse(least_upper_bound(X_64,X_261)))) )],[refute_0_1373,refute_0_1376]) ).
cnf(refute_0_1378,plain,
( multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261) != multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))
| multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) != multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261)
| multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) = multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261))),bind(Y0,$fot(multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261))),bind(Z0,$fot(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))))]]) ).
cnf(refute_0_1379,plain,
( multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261) != multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))
| multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) = multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261),multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261)) )],[refute_0_1377,refute_0_1378]) ).
cnf(refute_0_1380,plain,
multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) = multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_64,inverse(least_upper_bound(X_64,X_261))),X_261),multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))) )],[refute_0_1372,refute_0_1379]) ).
cnf(refute_0_1381,plain,
( multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261) != multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))
| inverse(least_upper_bound(inverse(X_261),inverse(X_64))) != multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261)
| inverse(least_upper_bound(inverse(X_261),inverse(X_64))) = multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_261),inverse(X_64))),multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261)) ),[1],$fot(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)))]]) ).
cnf(refute_0_1382,plain,
( inverse(least_upper_bound(inverse(X_261),inverse(X_64))) != multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261)
| inverse(least_upper_bound(inverse(X_261),inverse(X_64))) = multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261),multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))) )],[refute_0_1380,refute_0_1381]) ).
cnf(refute_0_1383,plain,
inverse(least_upper_bound(inverse(X_261),inverse(X_64))) = multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_261),inverse(X_64))),multiply(inverse(multiply(least_upper_bound(X_64,X_261),inverse(X_64))),X_261)) )],[refute_0_1371,refute_0_1382]) ).
cnf(refute_0_1384,plain,
( inverse(least_upper_bound(inverse(X_261),inverse(X_64))) != multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))
| multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)) = inverse(least_upper_bound(inverse(X_261),inverse(X_64))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(inverse(X_261),inverse(X_64))))),bind(Y0,$fot(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))))]]) ).
cnf(refute_0_1385,plain,
multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261)) = inverse(least_upper_bound(inverse(X_261),inverse(X_64))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_261),inverse(X_64))),multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_261)),X_261))) )],[refute_0_1383,refute_0_1384]) ).
cnf(refute_0_1386,plain,
multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)) = inverse(least_upper_bound(inverse(X_65),inverse(X_64))),
inference(subst,[],[refute_0_1385:[bind(X_261,$fot(X_65))]]) ).
cnf(refute_0_1387,plain,
inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) = inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))))]]) ).
cnf(refute_0_1388,plain,
( multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)) != inverse(least_upper_bound(inverse(X_65),inverse(X_64)))
| inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) != inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)))
| inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) = inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))),inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)))) ),[1,0],$fot(inverse(least_upper_bound(inverse(X_65),inverse(X_64))))]]) ).
cnf(refute_0_1389,plain,
( multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)) != inverse(least_upper_bound(inverse(X_65),inverse(X_64)))
| inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) = inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))),inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)))) )],[refute_0_1387,refute_0_1388]) ).
cnf(refute_0_1390,plain,
inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) = inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))),
inference(resolve,[$cnf( $equal(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)),inverse(least_upper_bound(inverse(X_65),inverse(X_64)))) )],[refute_0_1386,refute_0_1389]) ).
cnf(refute_0_1391,plain,
( inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) != inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64))))
| inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))) != least_upper_bound(inverse(X_65),inverse(X_64))
| inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) = least_upper_bound(inverse(X_65),inverse(X_64)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))))),bind(Z0,$fot(least_upper_bound(inverse(X_65),inverse(X_64))))]]) ).
cnf(refute_0_1392,plain,
( inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))) != least_upper_bound(inverse(X_65),inverse(X_64))
| inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) = least_upper_bound(inverse(X_65),inverse(X_64)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))),inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64))))) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) = least_upper_bound(inverse(X_65),inverse(X_64)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X_65),inverse(X_64)))),least_upper_bound(inverse(X_65),inverse(X_64))) )],[refute_0_1364,refute_0_1392]) ).
cnf(refute_0_1394,plain,
inverse(multiply(X_30,multiply(inverse(X_323),X_324))) = multiply(inverse(multiply(inverse(X_323),X_324)),inverse(X_30)),
inference(subst,[],[refute_0_238:[bind(X_31,$fot(multiply(inverse(X_323),X_324)))]]) ).
cnf(refute_0_1395,plain,
inverse(multiply(inverse(X_323),X_324)) = multiply(inverse(X_324),X_323),
inference(subst,[],[refute_0_321:[bind(X_141,$fot(X_323)),bind(X_31,$fot(X_324))]]) ).
cnf(refute_0_1396,plain,
( inverse(multiply(X_30,multiply(inverse(X_323),X_324))) != multiply(inverse(multiply(inverse(X_323),X_324)),inverse(X_30))
| inverse(multiply(inverse(X_323),X_324)) != multiply(inverse(X_324),X_323)
| inverse(multiply(X_30,multiply(inverse(X_323),X_324))) = multiply(multiply(inverse(X_324),X_323),inverse(X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_30,multiply(inverse(X_323),X_324))),multiply(inverse(multiply(inverse(X_323),X_324)),inverse(X_30))) ),[1,0],$fot(multiply(inverse(X_324),X_323))]]) ).
cnf(refute_0_1397,plain,
( inverse(multiply(X_30,multiply(inverse(X_323),X_324))) != multiply(inverse(multiply(inverse(X_323),X_324)),inverse(X_30))
| inverse(multiply(X_30,multiply(inverse(X_323),X_324))) = multiply(multiply(inverse(X_324),X_323),inverse(X_30)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_323),X_324)),multiply(inverse(X_324),X_323)) )],[refute_0_1395,refute_0_1396]) ).
cnf(refute_0_1398,plain,
inverse(multiply(X_30,multiply(inverse(X_323),X_324))) = multiply(multiply(inverse(X_324),X_323),inverse(X_30)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,multiply(inverse(X_323),X_324))),multiply(inverse(multiply(inverse(X_323),X_324)),inverse(X_30))) )],[refute_0_1394,refute_0_1397]) ).
cnf(refute_0_1399,plain,
multiply(multiply(inverse(X_324),X_323),inverse(X_30)) = multiply(inverse(X_324),multiply(X_323,inverse(X_30))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_324))),bind(Y,$fot(X_323)),bind(Z,$fot(inverse(X_30)))]]) ).
cnf(refute_0_1400,plain,
( multiply(multiply(inverse(X_324),X_323),inverse(X_30)) != multiply(inverse(X_324),multiply(X_323,inverse(X_30)))
| inverse(multiply(X_30,multiply(inverse(X_323),X_324))) != multiply(multiply(inverse(X_324),X_323),inverse(X_30))
| inverse(multiply(X_30,multiply(inverse(X_323),X_324))) = multiply(inverse(X_324),multiply(X_323,inverse(X_30))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_30,multiply(inverse(X_323),X_324))),multiply(multiply(inverse(X_324),X_323),inverse(X_30))) ),[1],$fot(multiply(inverse(X_324),multiply(X_323,inverse(X_30))))]]) ).
cnf(refute_0_1401,plain,
( inverse(multiply(X_30,multiply(inverse(X_323),X_324))) != multiply(multiply(inverse(X_324),X_323),inverse(X_30))
| inverse(multiply(X_30,multiply(inverse(X_323),X_324))) = multiply(inverse(X_324),multiply(X_323,inverse(X_30))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_324),X_323),inverse(X_30)),multiply(inverse(X_324),multiply(X_323,inverse(X_30)))) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
inverse(multiply(X_30,multiply(inverse(X_323),X_324))) = multiply(inverse(X_324),multiply(X_323,inverse(X_30))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,multiply(inverse(X_323),X_324))),multiply(multiply(inverse(X_324),X_323),inverse(X_30))) )],[refute_0_1398,refute_0_1401]) ).
cnf(refute_0_1403,plain,
( inverse(multiply(X_30,multiply(inverse(X_323),X_324))) != multiply(inverse(X_324),multiply(X_323,inverse(X_30)))
| multiply(inverse(X_324),multiply(X_323,inverse(X_30))) = inverse(multiply(X_30,multiply(inverse(X_323),X_324))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(multiply(X_30,multiply(inverse(X_323),X_324))))),bind(Y0,$fot(multiply(inverse(X_324),multiply(X_323,inverse(X_30)))))]]) ).
cnf(refute_0_1404,plain,
multiply(inverse(X_324),multiply(X_323,inverse(X_30))) = inverse(multiply(X_30,multiply(inverse(X_323),X_324))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_30,multiply(inverse(X_323),X_324))),multiply(inverse(X_324),multiply(X_323,inverse(X_30)))) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) = inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))),
inference(subst,[],[refute_0_1404:[bind(X_30,$fot(X_64)),bind(X_323,$fot(least_upper_bound(X_64,X_65))),bind(X_324,$fot(X_65))]]) ).
cnf(refute_0_1406,plain,
( multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) != inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)))
| inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) != least_upper_bound(inverse(X_65),inverse(X_64))
| multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) = least_upper_bound(inverse(X_65),inverse(X_64)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))),bind(Y0,$fot(inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))))),bind(Z0,$fot(least_upper_bound(inverse(X_65),inverse(X_64))))]]) ).
cnf(refute_0_1407,plain,
( inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))) != least_upper_bound(inverse(X_65),inverse(X_64))
| multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) = least_upper_bound(inverse(X_65),inverse(X_64)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))),inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65)))) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) = least_upper_bound(inverse(X_65),inverse(X_64)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_64,multiply(inverse(least_upper_bound(X_64,X_65)),X_65))),least_upper_bound(inverse(X_65),inverse(X_64))) )],[refute_0_1393,refute_0_1407]) ).
cnf(refute_0_1409,plain,
multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) = multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))),
introduced(tautology,[refl,[$fot(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))))]]) ).
cnf(refute_0_1410,plain,
( multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) != multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))
| multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) != least_upper_bound(inverse(X_65),inverse(X_64))
| multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) = multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))),multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) ),[1,1],$fot(least_upper_bound(inverse(X_65),inverse(X_64)))]]) ).
cnf(refute_0_1411,plain,
( multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))) != least_upper_bound(inverse(X_65),inverse(X_64))
| multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) = multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))) ),
inference(resolve,[$cnf( $equal(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))),multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) )],[refute_0_1409,refute_0_1410]) ).
cnf(refute_0_1412,plain,
multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) = multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))),least_upper_bound(inverse(X_65),inverse(X_64))) )],[refute_0_1408,refute_0_1411]) ).
cnf(refute_0_1413,plain,
( multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) != multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64)))
| multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))) != least_upper_bound(identity,multiply(X_64,inverse(X_65)))
| multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) = least_upper_bound(identity,multiply(X_64,inverse(X_65))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))))),bind(Y0,$fot(multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_64,inverse(X_65)))))]]) ).
cnf(refute_0_1414,plain,
( multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))) != least_upper_bound(identity,multiply(X_64,inverse(X_65)))
| multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) = least_upper_bound(identity,multiply(X_64,inverse(X_65))) ),
inference(resolve,[$cnf( $equal(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))),multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64)))) )],[refute_0_1412,refute_0_1413]) ).
cnf(refute_0_1415,plain,
multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) = least_upper_bound(identity,multiply(X_64,inverse(X_65))),
inference(resolve,[$cnf( $equal(multiply(X_64,least_upper_bound(inverse(X_65),inverse(X_64))),least_upper_bound(identity,multiply(X_64,inverse(X_65)))) )],[refute_0_1363,refute_0_1414]) ).
cnf(refute_0_1416,plain,
inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) = inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))))]]) ).
cnf(refute_0_1417,plain,
( multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) != least_upper_bound(identity,multiply(X_64,inverse(X_65)))
| inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) != inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))))
| inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))),inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_64,inverse(X_65))))]]) ).
cnf(refute_0_1418,plain,
( multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))) != least_upper_bound(identity,multiply(X_64,inverse(X_65)))
| inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))),inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))))) )],[refute_0_1416,refute_0_1417]) ).
cnf(refute_0_1419,plain,
inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),
inference(resolve,[$cnf( $equal(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))),least_upper_bound(identity,multiply(X_64,inverse(X_65)))) )],[refute_0_1415,refute_0_1418]) ).
cnf(refute_0_1420,plain,
multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) = inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))),
inference(subst,[],[refute_0_1404:[bind(X_30,$fot(X_64)),bind(X_323,$fot(X_65)),bind(X_324,$fot(multiply(least_upper_bound(X_64,X_65),inverse(X_64))))]]) ).
cnf(refute_0_1421,plain,
( multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) != inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))))
| inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) != inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))
| multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))))),bind(Y0,$fot(inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))))]]) ).
cnf(refute_0_1422,plain,
( inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))) != inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))
| multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))),inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64)))))) )],[refute_0_1420,refute_0_1421]) ).
cnf(refute_0_1423,plain,
multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),
inference(resolve,[$cnf( $equal(inverse(multiply(X_64,multiply(inverse(X_65),multiply(least_upper_bound(X_64,X_65),inverse(X_64))))),inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))) )],[refute_0_1419,refute_0_1422]) ).
cnf(refute_0_1424,plain,
( multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))) != inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))
| greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) != multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64)))
| greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_65,inverse(X_64))),multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64)))) ),[1],$fot(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))))]]) ).
cnf(refute_0_1425,plain,
( greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) != multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64)))
| greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64))),inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))) )],[refute_0_1423,refute_0_1424]) ).
cnf(refute_0_1426,plain,
greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) = inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_65,inverse(X_64))),multiply(inverse(multiply(least_upper_bound(X_64,X_65),inverse(X_64))),multiply(X_65,inverse(X_64)))) )],[refute_0_1362,refute_0_1425]) ).
cnf(refute_0_1427,plain,
( greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) != inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))
| inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) = greatest_lower_bound(identity,multiply(X_65,inverse(X_64))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_65,inverse(X_64))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))))]]) ).
cnf(refute_0_1428,plain,
inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65)))) = greatest_lower_bound(identity,multiply(X_65,inverse(X_64))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_65,inverse(X_64))),inverse(least_upper_bound(identity,multiply(X_64,inverse(X_65))))) )],[refute_0_1426,refute_0_1427]) ).
cnf(refute_0_1429,plain,
inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) = greatest_lower_bound(identity,multiply(X_70,inverse(X_16))),
inference(subst,[],[refute_0_1428:[bind(X_64,$fot(X_16)),bind(X_65,$fot(X_70))]]) ).
cnf(refute_0_1430,plain,
( multiply(X_70,inverse(least_upper_bound(X_70,X_16))) != inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))
| inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))) != greatest_lower_bound(identity,multiply(X_70,inverse(X_16)))
| multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = greatest_lower_bound(identity,multiply(X_70,inverse(X_16))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_70,inverse(least_upper_bound(X_70,X_16))),greatest_lower_bound(identity,multiply(X_70,inverse(X_16)))) ),[0],$fot(inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))))]]) ).
cnf(refute_0_1431,plain,
( multiply(X_70,inverse(least_upper_bound(X_70,X_16))) != inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))
| multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = greatest_lower_bound(identity,multiply(X_70,inverse(X_16))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70)))),greatest_lower_bound(identity,multiply(X_70,inverse(X_16)))) )],[refute_0_1429,refute_0_1430]) ).
cnf(refute_0_1432,plain,
multiply(X_70,inverse(least_upper_bound(X_70,X_16))) = greatest_lower_bound(identity,multiply(X_70,inverse(X_16))),
inference(resolve,[$cnf( $equal(multiply(X_70,inverse(least_upper_bound(X_70,X_16))),inverse(least_upper_bound(identity,multiply(X_16,inverse(X_70))))) )],[refute_0_287,refute_0_1431]) ).
cnf(refute_0_1433,plain,
multiply(X_30,inverse(least_upper_bound(X_30,X_776))) = greatest_lower_bound(identity,multiply(X_30,inverse(X_776))),
inference(subst,[],[refute_0_1432:[bind(X_16,$fot(X_776)),bind(X_70,$fot(X_30))]]) ).
cnf(refute_0_1434,plain,
( multiply(X_30,inverse(least_upper_bound(X_30,X_776))) != greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))
| inverse(least_upper_bound(X_30,X_776)) != multiply(inverse(X_30),multiply(X_30,inverse(least_upper_bound(X_30,X_776))))
| inverse(least_upper_bound(X_30,X_776)) = multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_30,X_776)),multiply(inverse(X_30),multiply(X_30,inverse(least_upper_bound(X_30,X_776))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_30,inverse(X_776))))]]) ).
cnf(refute_0_1435,plain,
( inverse(least_upper_bound(X_30,X_776)) != multiply(inverse(X_30),multiply(X_30,inverse(least_upper_bound(X_30,X_776))))
| inverse(least_upper_bound(X_30,X_776)) = multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) ),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(least_upper_bound(X_30,X_776))),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) )],[refute_0_1433,refute_0_1434]) ).
cnf(refute_0_1436,plain,
inverse(least_upper_bound(X_30,X_776)) = multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_30,X_776)),multiply(inverse(X_30),multiply(X_30,inverse(least_upper_bound(X_30,X_776))))) )],[refute_0_9,refute_0_1435]) ).
cnf(refute_0_1437,plain,
greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)) = greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)))]]) ).
cnf(refute_0_1438,plain,
( multiply(inverse(X_30),identity) != inverse(X_30)
| greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)) != greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776))
| greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)) = greatest_lower_bound(inverse(X_30),inverse(X_776)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)),greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776))) ),[1,0],$fot(inverse(X_30))]]) ).
cnf(refute_0_1439,plain,
( multiply(inverse(X_30),identity) != inverse(X_30)
| greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)) = greatest_lower_bound(inverse(X_30),inverse(X_776)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)),greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776))) )],[refute_0_1437,refute_0_1438]) ).
cnf(refute_0_1440,plain,
greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)) = greatest_lower_bound(inverse(X_30),inverse(X_776)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),identity),inverse(X_30)) )],[refute_0_421,refute_0_1439]) ).
cnf(refute_0_1441,plain,
multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))) = greatest_lower_bound(multiply(inverse(X_30),X_99),multiply(inverse(X_30),multiply(X_30,X_31))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_30))),bind(Y,$fot(X_99)),bind(Z,$fot(multiply(X_30,X_31)))]]) ).
cnf(refute_0_1442,plain,
( multiply(inverse(X_30),multiply(X_30,X_31)) != X_31
| multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))) != greatest_lower_bound(multiply(inverse(X_30),X_99),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))) = greatest_lower_bound(multiply(inverse(X_30),X_99),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))),greatest_lower_bound(multiply(inverse(X_30),X_99),multiply(inverse(X_30),multiply(X_30,X_31)))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_1443,plain,
( multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))) != greatest_lower_bound(multiply(inverse(X_30),X_99),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))) = greatest_lower_bound(multiply(inverse(X_30),X_99),X_31) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),multiply(X_30,X_31)),X_31) )],[refute_0_235,refute_0_1442]) ).
cnf(refute_0_1444,plain,
multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))) = greatest_lower_bound(multiply(inverse(X_30),X_99),X_31),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),greatest_lower_bound(X_99,multiply(X_30,X_31))),greatest_lower_bound(multiply(inverse(X_30),X_99),multiply(inverse(X_30),multiply(X_30,X_31)))) )],[refute_0_1441,refute_0_1443]) ).
cnf(refute_0_1445,plain,
multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) = greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)),
inference(subst,[],[refute_0_1444:[bind(X_31,$fot(inverse(X_776))),bind(X_99,$fot(identity))]]) ).
cnf(refute_0_1446,plain,
( multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) != greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776))
| greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)) != greatest_lower_bound(inverse(X_30),inverse(X_776))
| multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) = greatest_lower_bound(inverse(X_30),inverse(X_776)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)))),bind(Z0,$fot(greatest_lower_bound(inverse(X_30),inverse(X_776))))]]) ).
cnf(refute_0_1447,plain,
( greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)) != greatest_lower_bound(inverse(X_30),inverse(X_776))
| multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) = greatest_lower_bound(inverse(X_30),inverse(X_776)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))),greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776))) )],[refute_0_1445,refute_0_1446]) ).
cnf(refute_0_1448,plain,
multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) = greatest_lower_bound(inverse(X_30),inverse(X_776)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_30),identity),inverse(X_776)),greatest_lower_bound(inverse(X_30),inverse(X_776))) )],[refute_0_1440,refute_0_1447]) ).
cnf(refute_0_1449,plain,
( multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))) != greatest_lower_bound(inverse(X_30),inverse(X_776))
| inverse(least_upper_bound(X_30,X_776)) != multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776))))
| inverse(least_upper_bound(X_30,X_776)) = greatest_lower_bound(inverse(X_30),inverse(X_776)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_30,X_776)),multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776))))) ),[1],$fot(greatest_lower_bound(inverse(X_30),inverse(X_776)))]]) ).
cnf(refute_0_1450,plain,
( inverse(least_upper_bound(X_30,X_776)) != multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776))))
| inverse(least_upper_bound(X_30,X_776)) = greatest_lower_bound(inverse(X_30),inverse(X_776)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776)))),greatest_lower_bound(inverse(X_30),inverse(X_776))) )],[refute_0_1448,refute_0_1449]) ).
cnf(refute_0_1451,plain,
inverse(least_upper_bound(X_30,X_776)) = greatest_lower_bound(inverse(X_30),inverse(X_776)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_30,X_776)),multiply(inverse(X_30),greatest_lower_bound(identity,multiply(X_30,inverse(X_776))))) )],[refute_0_1436,refute_0_1450]) ).
cnf(refute_0_1452,plain,
( inverse(least_upper_bound(X_30,X_776)) != greatest_lower_bound(inverse(X_30),inverse(X_776))
| greatest_lower_bound(inverse(X_30),inverse(X_776)) = inverse(least_upper_bound(X_30,X_776)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(X_30,X_776)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_30),inverse(X_776))))]]) ).
cnf(refute_0_1453,plain,
greatest_lower_bound(inverse(X_30),inverse(X_776)) = inverse(least_upper_bound(X_30,X_776)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_30,X_776)),greatest_lower_bound(inverse(X_30),inverse(X_776))) )],[refute_0_1451,refute_0_1452]) ).
cnf(refute_0_1454,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(least_upper_bound(a,b)),
inference(subst,[],[refute_0_1453:[bind(X_30,$fot(a)),bind(X_776,$fot(b))]]) ).
cnf(refute_0_1455,plain,
( greatest_lower_bound(inverse(a),inverse(b)) != inverse(least_upper_bound(a,b))
| inverse(least_upper_bound(a,b)) != inverse(least_upper_bound(a,b))
| inverse(least_upper_bound(a,b)) = greatest_lower_bound(inverse(a),inverse(b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(least_upper_bound(a,b)),greatest_lower_bound(inverse(a),inverse(b))) ),[1],$fot(inverse(least_upper_bound(a,b)))]]) ).
cnf(refute_0_1456,plain,
( inverse(least_upper_bound(a,b)) != inverse(least_upper_bound(a,b))
| inverse(least_upper_bound(a,b)) = greatest_lower_bound(inverse(a),inverse(b)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(least_upper_bound(a,b))) )],[refute_0_1454,refute_0_1455]) ).
cnf(refute_0_1457,plain,
inverse(least_upper_bound(a,b)) != inverse(least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,b)),greatest_lower_bound(inverse(a),inverse(b))) )],[refute_0_1456,prove_p10]) ).
cnf(refute_0_1458,plain,
inverse(least_upper_bound(a,b)) = inverse(least_upper_bound(a,b)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(a,b)))]]) ).
cnf(refute_0_1459,plain,
$false,
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,b)),inverse(least_upper_bound(a,b))) )],[refute_0_1458,refute_0_1457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP179-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 09:44:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 222.73/222.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 222.73/222.88
% 222.73/222.88 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 222.81/223.01
%------------------------------------------------------------------------------