TSTP Solution File: GRP186-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP186-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:50 EDT 2022
% Result : Unsatisfiable 14.61s 14.78s
% Output : CNFRefutation 14.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 121
% Number of leaves : 383
% Syntax : Number of clauses : 1845 ( 949 unt; 0 nHn; 897 RR)
% Number of literals : 3134 (3133 equ;1292 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 3369 ( 73 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(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_p23,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_4,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(multiply(a,b),identity) = least_upper_bound(identity,multiply(a,b)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(a,b)))]]) ).
cnf(refute_0_6,plain,
( least_upper_bound(multiply(a,b),identity) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b))))
| least_upper_bound(multiply(a,b),identity) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(multiply(a,b),identity),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) ),[0],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_7,plain,
( least_upper_bound(identity,multiply(a,b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b))))
| least_upper_bound(multiply(a,b),identity) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,b),identity),least_upper_bound(identity,multiply(a,b))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,b),identity),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) )],[refute_0_7,prove_p23]) ).
cnf(refute_0_9,plain,
multiply(X_44,least_upper_bound(X_45,inverse(X_44))) = least_upper_bound(multiply(X_44,X_45),multiply(X_44,inverse(X_44))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(inverse(X_44)))]]) ).
cnf(refute_0_10,plain,
multiply(inverse(inverse(X_33)),inverse(X_33)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_33)))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(inverse(X_28),X_28),X_29) = multiply(inverse(X_28),multiply(X_28,X_29)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_28))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_12,plain,
multiply(inverse(X_28),X_28) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_13,plain,
( multiply(multiply(inverse(X_28),X_28),X_29) != multiply(inverse(X_28),multiply(X_28,X_29))
| multiply(inverse(X_28),X_28) != identity
| multiply(identity,X_29) = multiply(inverse(X_28),multiply(X_28,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_28),X_28),X_29),multiply(inverse(X_28),multiply(X_28,X_29))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_14,plain,
( multiply(multiply(inverse(X_28),X_28),X_29) != multiply(inverse(X_28),multiply(X_28,X_29))
| multiply(identity,X_29) = multiply(inverse(X_28),multiply(X_28,X_29)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),X_28),identity) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(identity,X_29) = multiply(inverse(X_28),multiply(X_28,X_29)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_28),X_28),X_29),multiply(inverse(X_28),multiply(X_28,X_29))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(identity,X_29) = X_29,
inference(subst,[],[left_identity:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_17,plain,
( multiply(identity,X_29) != X_29
| multiply(identity,X_29) != multiply(inverse(X_28),multiply(X_28,X_29))
| X_29 = multiply(inverse(X_28),multiply(X_28,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_29),multiply(inverse(X_28),multiply(X_28,X_29))) ),[0],$fot(X_29)]]) ).
cnf(refute_0_18,plain,
( multiply(identity,X_29) != multiply(inverse(X_28),multiply(X_28,X_29))
| X_29 = multiply(inverse(X_28),multiply(X_28,X_29)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_29),X_29) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
X_29 = multiply(inverse(X_28),multiply(X_28,X_29)),
inference(resolve,[$cnf( $equal(multiply(identity,X_29),multiply(inverse(X_28),multiply(X_28,X_29))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(X_30,X_31) = multiply(inverse(inverse(X_30)),multiply(inverse(X_30),multiply(X_30,X_31))),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(inverse(X_30))),bind(X_29,$fot(multiply(X_30,X_31)))]]) ).
cnf(refute_0_21,plain,
X_31 = multiply(inverse(X_30),multiply(X_30,X_31)),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_22,plain,
( X_31 != multiply(inverse(X_30),multiply(X_30,X_31))
| multiply(inverse(X_30),multiply(X_30,X_31)) = X_31 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(inverse(X_30),multiply(X_30,X_31))))]]) ).
cnf(refute_0_23,plain,
multiply(inverse(X_30),multiply(X_30,X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(X_30),multiply(X_30,X_31))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( multiply(X_30,X_31) != multiply(inverse(inverse(X_30)),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(inverse(X_30),multiply(X_30,X_31)) != X_31
| multiply(X_30,X_31) = multiply(inverse(inverse(X_30)),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_30,X_31),multiply(inverse(inverse(X_30)),multiply(inverse(X_30),multiply(X_30,X_31)))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_25,plain,
( multiply(X_30,X_31) != multiply(inverse(inverse(X_30)),multiply(inverse(X_30),multiply(X_30,X_31)))
| multiply(X_30,X_31) = multiply(inverse(inverse(X_30)),X_31) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_30),multiply(X_30,X_31)),X_31) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(X_30,X_31) = multiply(inverse(inverse(X_30)),X_31),
inference(resolve,[$cnf( $equal(multiply(X_30,X_31),multiply(inverse(inverse(X_30)),multiply(inverse(X_30),multiply(X_30,X_31)))) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_33,inverse(X_33)) = multiply(inverse(inverse(X_33)),inverse(X_33)),
inference(subst,[],[refute_0_26:[bind(X_30,$fot(X_33)),bind(X_31,$fot(inverse(X_33)))]]) ).
cnf(refute_0_28,plain,
( multiply(X_33,inverse(X_33)) != multiply(inverse(inverse(X_33)),inverse(X_33))
| multiply(inverse(inverse(X_33)),inverse(X_33)) = multiply(X_33,inverse(X_33)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_33,inverse(X_33)))),bind(Y0,$fot(multiply(inverse(inverse(X_33)),inverse(X_33))))]]) ).
cnf(refute_0_29,plain,
multiply(inverse(inverse(X_33)),inverse(X_33)) = multiply(X_33,inverse(X_33)),
inference(resolve,[$cnf( $equal(multiply(X_33,inverse(X_33)),multiply(inverse(inverse(X_33)),inverse(X_33))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiply(inverse(inverse(X_33)),inverse(X_33)) != multiply(X_33,inverse(X_33))
| multiply(inverse(inverse(X_33)),inverse(X_33)) != identity
| multiply(X_33,inverse(X_33)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_33)),inverse(X_33)),identity) ),[0],$fot(multiply(X_33,inverse(X_33)))]]) ).
cnf(refute_0_31,plain,
( multiply(inverse(inverse(X_33)),inverse(X_33)) != identity
| multiply(X_33,inverse(X_33)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_33)),inverse(X_33)),multiply(X_33,inverse(X_33))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(X_33,inverse(X_33)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_33)),inverse(X_33)),identity) )],[refute_0_10,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_44,inverse(X_44)) = identity,
inference(subst,[],[refute_0_32:[bind(X_33,$fot(X_44))]]) ).
cnf(refute_0_34,plain,
( multiply(X_44,inverse(X_44)) != identity
| multiply(X_44,least_upper_bound(X_45,inverse(X_44))) != least_upper_bound(multiply(X_44,X_45),multiply(X_44,inverse(X_44)))
| multiply(X_44,least_upper_bound(X_45,inverse(X_44))) = least_upper_bound(multiply(X_44,X_45),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,inverse(X_44))),least_upper_bound(multiply(X_44,X_45),multiply(X_44,inverse(X_44)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_35,plain,
( multiply(X_44,least_upper_bound(X_45,inverse(X_44))) != least_upper_bound(multiply(X_44,X_45),multiply(X_44,inverse(X_44)))
| multiply(X_44,least_upper_bound(X_45,inverse(X_44))) = least_upper_bound(multiply(X_44,X_45),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_44,inverse(X_44)),identity) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(X_44,least_upper_bound(X_45,inverse(X_44))) = least_upper_bound(multiply(X_44,X_45),identity),
inference(resolve,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,inverse(X_44))),least_upper_bound(multiply(X_44,X_45),multiply(X_44,inverse(X_44)))) )],[refute_0_9,refute_0_35]) ).
cnf(refute_0_37,plain,
least_upper_bound(multiply(X_44,X_45),identity) = least_upper_bound(identity,multiply(X_44,X_45)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_44,X_45)))]]) ).
cnf(refute_0_38,plain,
( multiply(X_44,least_upper_bound(X_45,inverse(X_44))) != least_upper_bound(multiply(X_44,X_45),identity)
| least_upper_bound(multiply(X_44,X_45),identity) != least_upper_bound(identity,multiply(X_44,X_45))
| multiply(X_44,least_upper_bound(X_45,inverse(X_44))) = least_upper_bound(identity,multiply(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_44,least_upper_bound(X_45,inverse(X_44))),least_upper_bound(identity,multiply(X_44,X_45))) ),[0],$fot(least_upper_bound(multiply(X_44,X_45),identity))]]) ).
cnf(refute_0_39,plain,
( multiply(X_44,least_upper_bound(X_45,inverse(X_44))) != least_upper_bound(multiply(X_44,X_45),identity)
| multiply(X_44,least_upper_bound(X_45,inverse(X_44))) = least_upper_bound(identity,multiply(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_44,X_45),identity),least_upper_bound(identity,multiply(X_44,X_45))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_44,least_upper_bound(X_45,inverse(X_44))) = least_upper_bound(identity,multiply(X_44,X_45)),
inference(resolve,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,inverse(X_44))),least_upper_bound(multiply(X_44,X_45),identity)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(a,least_upper_bound(b,inverse(a))) = least_upper_bound(identity,multiply(a,b)),
inference(subst,[],[refute_0_40:[bind(X_44,$fot(a)),bind(X_45,$fot(b))]]) ).
cnf(refute_0_42,plain,
X_29 = multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29)),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(greatest_lower_bound(X_101,inverse(X_29))))]]) ).
cnf(refute_0_43,plain,
multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) = greatest_lower_bound(multiply(X_98,X_97),multiply(inverse(X_97),X_97)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_97)),bind(Y,$fot(X_98)),bind(Z,$fot(inverse(X_97)))]]) ).
cnf(refute_0_44,plain,
multiply(inverse(X_97),X_97) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_45,plain,
( multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) != greatest_lower_bound(multiply(X_98,X_97),multiply(inverse(X_97),X_97))
| multiply(inverse(X_97),X_97) != identity
| multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) = greatest_lower_bound(multiply(X_98,X_97),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97),greatest_lower_bound(multiply(X_98,X_97),multiply(inverse(X_97),X_97))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_46,plain,
( multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) != greatest_lower_bound(multiply(X_98,X_97),multiply(inverse(X_97),X_97))
| multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) = greatest_lower_bound(multiply(X_98,X_97),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),X_97),identity) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) = greatest_lower_bound(multiply(X_98,X_97),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97),greatest_lower_bound(multiply(X_98,X_97),multiply(inverse(X_97),X_97))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_49,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_48]) ).
cnf(refute_0_50,plain,
greatest_lower_bound(multiply(X_98,X_97),identity) = greatest_lower_bound(identity,multiply(X_98,X_97)),
inference(subst,[],[refute_0_49:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_98,X_97)))]]) ).
cnf(refute_0_51,plain,
( multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) != greatest_lower_bound(multiply(X_98,X_97),identity)
| greatest_lower_bound(multiply(X_98,X_97),identity) != greatest_lower_bound(identity,multiply(X_98,X_97))
| multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) = greatest_lower_bound(identity,multiply(X_98,X_97)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97),greatest_lower_bound(identity,multiply(X_98,X_97))) ),[0],$fot(greatest_lower_bound(multiply(X_98,X_97),identity))]]) ).
cnf(refute_0_52,plain,
( multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) != greatest_lower_bound(multiply(X_98,X_97),identity)
| multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) = greatest_lower_bound(identity,multiply(X_98,X_97)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_98,X_97),identity),greatest_lower_bound(identity,multiply(X_98,X_97))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97) = greatest_lower_bound(identity,multiply(X_98,X_97)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,inverse(X_97)),X_97),greatest_lower_bound(multiply(X_98,X_97),identity)) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29) = greatest_lower_bound(identity,multiply(X_101,X_29)),
inference(subst,[],[refute_0_53:[bind(X_97,$fot(X_29)),bind(X_98,$fot(X_101))]]) ).
cnf(refute_0_55,plain,
( X_29 != multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29))
| multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29) != greatest_lower_bound(identity,multiply(X_101,X_29))
| X_29 = multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),greatest_lower_bound(identity,multiply(X_101,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(X_29,multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_101,X_29)))]]) ).
cnf(refute_0_56,plain,
( X_29 != multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29))
| X_29 = multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),greatest_lower_bound(identity,multiply(X_101,X_29))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29),greatest_lower_bound(identity,multiply(X_101,X_29))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
X_29 = multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),greatest_lower_bound(identity,multiply(X_101,X_29))),
inference(resolve,[$cnf( $equal(X_29,multiply(inverse(greatest_lower_bound(X_101,inverse(X_29))),multiply(greatest_lower_bound(X_101,inverse(X_29)),X_29))) )],[refute_0_42,refute_0_56]) ).
cnf(refute_0_58,plain,
X_29 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_29)),X_29))),
inference(subst,[],[refute_0_57:[bind(X_101,$fot(inverse(greatest_lower_bound(identity,X_29))))]]) ).
cnf(refute_0_59,plain,
inverse(greatest_lower_bound(identity,inverse(X_203))) = multiply(inverse(greatest_lower_bound(identity,X_203)),multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203))))),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(greatest_lower_bound(identity,X_203))),bind(X_29,$fot(inverse(greatest_lower_bound(identity,inverse(X_203)))))]]) ).
cnf(refute_0_60,plain,
multiply(X_38,inverse(multiply(X_28,X_38))) = multiply(inverse(X_28),multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38))))),
inference(subst,[],[refute_0_19:[bind(X_29,$fot(multiply(X_38,inverse(multiply(X_28,X_38)))))]]) ).
cnf(refute_0_61,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(subst,[],[associativity:[bind(Z,$fot(inverse(multiply(X,Y))))]]) ).
cnf(refute_0_62,plain,
multiply(multiply(X,Y),inverse(multiply(X,Y))) = identity,
inference(subst,[],[refute_0_32:[bind(X_33,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_63,plain,
( multiply(multiply(X,Y),inverse(multiply(X,Y))) != multiply(X,multiply(Y,inverse(multiply(X,Y))))
| multiply(multiply(X,Y),inverse(multiply(X,Y))) != identity
| identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_64,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( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),identity) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
identity = multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))),
inference(subst,[],[refute_0_65:[bind(X,$fot(X_28)),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_67,plain,
( identity != multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38))))
| multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38))))))]]) ).
cnf(refute_0_68,plain,
multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38))))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))) != identity
| multiply(X_38,inverse(multiply(X_28,X_38))) != multiply(inverse(X_28),multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))))
| multiply(X_38,inverse(multiply(X_28,X_38))) = multiply(inverse(X_28),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_38,inverse(multiply(X_28,X_38))),multiply(inverse(X_28),multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_70,plain,
( multiply(X_38,inverse(multiply(X_28,X_38))) != multiply(inverse(X_28),multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))))
| multiply(X_38,inverse(multiply(X_28,X_38))) = multiply(inverse(X_28),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))),identity) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_38,inverse(multiply(X_28,X_38))) = multiply(inverse(X_28),identity),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(multiply(X_28,X_38))),multiply(inverse(X_28),multiply(X_28,multiply(X_38,inverse(multiply(X_28,X_38)))))) )],[refute_0_60,refute_0_70]) ).
cnf(refute_0_72,plain,
X_31 = multiply(inverse(inverse(X_31)),multiply(inverse(X_31),X_31)),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(inverse(X_31))),bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_31),X_31) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_74,plain,
( X_31 != multiply(inverse(inverse(X_31)),multiply(inverse(X_31),X_31))
| multiply(inverse(X_31),X_31) != identity
| X_31 = multiply(inverse(inverse(X_31)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,multiply(inverse(inverse(X_31)),multiply(inverse(X_31),X_31))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_75,plain,
( X_31 != multiply(inverse(inverse(X_31)),multiply(inverse(X_31),X_31))
| X_31 = multiply(inverse(inverse(X_31)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_31),X_31),identity) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
X_31 = multiply(inverse(inverse(X_31)),identity),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(inverse(X_31)),multiply(inverse(X_31),X_31))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( multiply(X_30,X_31) != multiply(inverse(inverse(X_30)),X_31)
| multiply(inverse(inverse(X_30)),X_31) = multiply(X_30,X_31) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_30,X_31))),bind(Y0,$fot(multiply(inverse(inverse(X_30)),X_31)))]]) ).
cnf(refute_0_78,plain,
multiply(inverse(inverse(X_30)),X_31) = multiply(X_30,X_31),
inference(resolve,[$cnf( $equal(multiply(X_30,X_31),multiply(inverse(inverse(X_30)),X_31)) )],[refute_0_26,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(inverse(X_31)),identity) = multiply(X_31,identity),
inference(subst,[],[refute_0_78:[bind(X_30,$fot(X_31)),bind(X_31,$fot(identity))]]) ).
cnf(refute_0_80,plain,
( X_31 != multiply(inverse(inverse(X_31)),identity)
| multiply(inverse(inverse(X_31)),identity) != multiply(X_31,identity)
| X_31 = multiply(X_31,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,multiply(X_31,identity)) ),[0],$fot(multiply(inverse(inverse(X_31)),identity))]]) ).
cnf(refute_0_81,plain,
( X_31 != multiply(inverse(inverse(X_31)),identity)
| X_31 = multiply(X_31,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_31)),identity),multiply(X_31,identity)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
X_31 = multiply(X_31,identity),
inference(resolve,[$cnf( $equal(X_31,multiply(inverse(inverse(X_31)),identity)) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
( X_31 != multiply(X_31,identity)
| multiply(X_31,identity) = X_31 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_31)),bind(Y0,$fot(multiply(X_31,identity)))]]) ).
cnf(refute_0_84,plain,
multiply(X_31,identity) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(X_31,identity)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(inverse(X_28),identity) = inverse(X_28),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(inverse(X_28)))]]) ).
cnf(refute_0_86,plain,
( multiply(X_38,inverse(multiply(X_28,X_38))) != multiply(inverse(X_28),identity)
| multiply(inverse(X_28),identity) != inverse(X_28)
| multiply(X_38,inverse(multiply(X_28,X_38))) = inverse(X_28) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_38,inverse(multiply(X_28,X_38))),inverse(X_28)) ),[0],$fot(multiply(inverse(X_28),identity))]]) ).
cnf(refute_0_87,plain,
( multiply(X_38,inverse(multiply(X_28,X_38))) != multiply(inverse(X_28),identity)
| multiply(X_38,inverse(multiply(X_28,X_38))) = inverse(X_28) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),identity),inverse(X_28)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(X_38,inverse(multiply(X_28,X_38))) = inverse(X_28),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(multiply(X_28,X_38))),multiply(inverse(X_28),identity)) )],[refute_0_71,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(greatest_lower_bound(identity,X_93),inverse(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)))) = inverse(inverse(X_93)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(inverse(X_93))),bind(X_38,$fot(greatest_lower_bound(identity,X_93)))]]) ).
cnf(refute_0_90,plain,
multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(multiply(inverse(X_87),X_86),multiply(inverse(X_87),X_87)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_87))),bind(Y,$fot(X_86)),bind(Z,$fot(X_87))]]) ).
cnf(refute_0_91,plain,
multiply(inverse(X_87),X_87) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_87))]]) ).
cnf(refute_0_92,plain,
( multiply(inverse(X_87),X_87) != identity
| multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) != greatest_lower_bound(multiply(inverse(X_87),X_86),multiply(inverse(X_87),X_87))
| multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(multiply(inverse(X_87),X_86),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(inverse(X_87),X_86),multiply(inverse(X_87),X_87))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_93,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) != greatest_lower_bound(multiply(inverse(X_87),X_86),multiply(inverse(X_87),X_87))
| multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(multiply(inverse(X_87),X_86),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),X_87),identity) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(multiply(inverse(X_87),X_86),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(inverse(X_87),X_86),multiply(inverse(X_87),X_87))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
greatest_lower_bound(multiply(inverse(X_87),X_86),identity) = greatest_lower_bound(identity,multiply(inverse(X_87),X_86)),
inference(subst,[],[refute_0_49:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_87),X_86)))]]) ).
cnf(refute_0_96,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) != greatest_lower_bound(multiply(inverse(X_87),X_86),identity)
| greatest_lower_bound(multiply(inverse(X_87),X_86),identity) != greatest_lower_bound(identity,multiply(inverse(X_87),X_86))
| multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(identity,multiply(inverse(X_87),X_86)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)),greatest_lower_bound(identity,multiply(inverse(X_87),X_86))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_87),X_86),identity))]]) ).
cnf(refute_0_97,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) != greatest_lower_bound(multiply(inverse(X_87),X_86),identity)
| multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(identity,multiply(inverse(X_87),X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_87),X_86),identity),greatest_lower_bound(identity,multiply(inverse(X_87),X_86))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(identity,multiply(inverse(X_87),X_86)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(inverse(X_87),X_86),identity)) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(inverse(X_93),greatest_lower_bound(identity,X_93)) = greatest_lower_bound(identity,multiply(inverse(X_93),identity)),
inference(subst,[],[refute_0_98:[bind(X_86,$fot(identity)),bind(X_87,$fot(X_93))]]) ).
cnf(refute_0_100,plain,
inverse(X_93) = multiply(inverse(X_93),identity),
inference(subst,[],[refute_0_82:[bind(X_31,$fot(inverse(X_93)))]]) ).
cnf(refute_0_101,plain,
( inverse(X_93) != multiply(inverse(X_93),identity)
| multiply(inverse(X_93),identity) = inverse(X_93) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_93))),bind(Y0,$fot(multiply(inverse(X_93),identity)))]]) ).
cnf(refute_0_102,plain,
multiply(inverse(X_93),identity) = inverse(X_93),
inference(resolve,[$cnf( $equal(inverse(X_93),multiply(inverse(X_93),identity)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( multiply(inverse(X_93),greatest_lower_bound(identity,X_93)) != greatest_lower_bound(identity,multiply(inverse(X_93),identity))
| multiply(inverse(X_93),identity) != inverse(X_93)
| multiply(inverse(X_93),greatest_lower_bound(identity,X_93)) = greatest_lower_bound(identity,inverse(X_93)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)),greatest_lower_bound(identity,multiply(inverse(X_93),identity))) ),[1,1],$fot(inverse(X_93))]]) ).
cnf(refute_0_104,plain,
( multiply(inverse(X_93),greatest_lower_bound(identity,X_93)) != greatest_lower_bound(identity,multiply(inverse(X_93),identity))
| multiply(inverse(X_93),greatest_lower_bound(identity,X_93)) = greatest_lower_bound(identity,inverse(X_93)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_93),identity),inverse(X_93)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(inverse(X_93),greatest_lower_bound(identity,X_93)) = greatest_lower_bound(identity,inverse(X_93)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)),greatest_lower_bound(identity,multiply(inverse(X_93),identity))) )],[refute_0_99,refute_0_104]) ).
cnf(refute_0_106,plain,
( multiply(greatest_lower_bound(identity,X_93),inverse(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)))) != inverse(inverse(X_93))
| multiply(inverse(X_93),greatest_lower_bound(identity,X_93)) != greatest_lower_bound(identity,inverse(X_93))
| multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) = inverse(inverse(X_93)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_93),inverse(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)))),inverse(inverse(X_93))) ),[0,1,0],$fot(greatest_lower_bound(identity,inverse(X_93)))]]) ).
cnf(refute_0_107,plain,
( multiply(greatest_lower_bound(identity,X_93),inverse(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)))) != inverse(inverse(X_93))
| multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) = inverse(inverse(X_93)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)),greatest_lower_bound(identity,inverse(X_93))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) = inverse(inverse(X_93)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_93),inverse(multiply(inverse(X_93),greatest_lower_bound(identity,X_93)))),inverse(inverse(X_93))) )],[refute_0_89,refute_0_107]) ).
cnf(refute_0_109,plain,
inverse(inverse(X_33)) = multiply(inverse(inverse(X_33)),identity),
inference(subst,[],[refute_0_82:[bind(X_31,$fot(inverse(inverse(X_33))))]]) ).
cnf(refute_0_110,plain,
multiply(X_33,identity) = multiply(inverse(inverse(X_33)),identity),
inference(subst,[],[refute_0_26:[bind(X_30,$fot(X_33)),bind(X_31,$fot(identity))]]) ).
cnf(refute_0_111,plain,
( multiply(X_33,identity) != multiply(inverse(inverse(X_33)),identity)
| multiply(inverse(inverse(X_33)),identity) = multiply(X_33,identity) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_33,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_33)),identity)))]]) ).
cnf(refute_0_112,plain,
multiply(inverse(inverse(X_33)),identity) = multiply(X_33,identity),
inference(resolve,[$cnf( $equal(multiply(X_33,identity),multiply(inverse(inverse(X_33)),identity)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( multiply(inverse(inverse(X_33)),identity) != multiply(X_33,identity)
| inverse(inverse(X_33)) != multiply(inverse(inverse(X_33)),identity)
| inverse(inverse(X_33)) = multiply(X_33,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_33)),multiply(inverse(inverse(X_33)),identity)) ),[1],$fot(multiply(X_33,identity))]]) ).
cnf(refute_0_114,plain,
( inverse(inverse(X_33)) != multiply(inverse(inverse(X_33)),identity)
| inverse(inverse(X_33)) = multiply(X_33,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_33)),identity),multiply(X_33,identity)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
inverse(inverse(X_33)) = multiply(X_33,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_33)),multiply(inverse(inverse(X_33)),identity)) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(X_33,identity) = X_33,
inference(subst,[],[refute_0_84:[bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_117,plain,
( multiply(X_33,identity) != X_33
| inverse(inverse(X_33)) != multiply(X_33,identity)
| inverse(inverse(X_33)) = X_33 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_33)),multiply(X_33,identity)) ),[1],$fot(X_33)]]) ).
cnf(refute_0_118,plain,
( inverse(inverse(X_33)) != multiply(X_33,identity)
| inverse(inverse(X_33)) = X_33 ),
inference(resolve,[$cnf( $equal(multiply(X_33,identity),X_33) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
inverse(inverse(X_33)) = X_33,
inference(resolve,[$cnf( $equal(inverse(inverse(X_33)),multiply(X_33,identity)) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
inverse(inverse(X_93)) = X_93,
inference(subst,[],[refute_0_119:[bind(X_33,$fot(X_93))]]) ).
cnf(refute_0_121,plain,
( multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) != inverse(inverse(X_93))
| inverse(inverse(X_93)) != X_93
| multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) = X_93 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))),X_93) ),[0],$fot(inverse(inverse(X_93)))]]) ).
cnf(refute_0_122,plain,
( multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) != inverse(inverse(X_93))
| multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) = X_93 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_93)),X_93) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))) = X_93,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_93),inverse(greatest_lower_bound(identity,inverse(X_93)))),inverse(inverse(X_93))) )],[refute_0_108,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203)))) = X_203,
inference(subst,[],[refute_0_123:[bind(X_93,$fot(X_203))]]) ).
cnf(refute_0_125,plain,
( multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203)))) != X_203
| inverse(greatest_lower_bound(identity,inverse(X_203))) != multiply(inverse(greatest_lower_bound(identity,X_203)),multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203)))))
| inverse(greatest_lower_bound(identity,inverse(X_203))) = multiply(inverse(greatest_lower_bound(identity,X_203)),X_203) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_203))),multiply(inverse(greatest_lower_bound(identity,X_203)),multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203)))))) ),[1,1],$fot(X_203)]]) ).
cnf(refute_0_126,plain,
( inverse(greatest_lower_bound(identity,inverse(X_203))) != multiply(inverse(greatest_lower_bound(identity,X_203)),multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203)))))
| inverse(greatest_lower_bound(identity,inverse(X_203))) = multiply(inverse(greatest_lower_bound(identity,X_203)),X_203) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203)))),X_203) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
inverse(greatest_lower_bound(identity,inverse(X_203))) = multiply(inverse(greatest_lower_bound(identity,X_203)),X_203),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_203))),multiply(inverse(greatest_lower_bound(identity,X_203)),multiply(greatest_lower_bound(identity,X_203),inverse(greatest_lower_bound(identity,inverse(X_203)))))) )],[refute_0_59,refute_0_126]) ).
cnf(refute_0_128,plain,
inverse(greatest_lower_bound(identity,inverse(X_29))) = multiply(inverse(greatest_lower_bound(identity,X_29)),X_29),
inference(subst,[],[refute_0_127:[bind(X_203,$fot(X_29))]]) ).
cnf(refute_0_129,plain,
( inverse(greatest_lower_bound(identity,inverse(X_29))) != multiply(inverse(greatest_lower_bound(identity,X_29)),X_29)
| multiply(inverse(greatest_lower_bound(identity,X_29)),X_29) = inverse(greatest_lower_bound(identity,inverse(X_29))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_29))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_29)),X_29)))]]) ).
cnf(refute_0_130,plain,
multiply(inverse(greatest_lower_bound(identity,X_29)),X_29) = inverse(greatest_lower_bound(identity,inverse(X_29))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_29))),multiply(inverse(greatest_lower_bound(identity,X_29)),X_29)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( X_29 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_29)),X_29)))
| multiply(inverse(greatest_lower_bound(identity,X_29)),X_29) != inverse(greatest_lower_bound(identity,inverse(X_29)))
| X_29 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) ),
introduced(tautology,[equality,[$cnf( $equal(X_29,multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_29)),X_29)))) ),[1,1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_29))))]]) ).
cnf(refute_0_132,plain,
( X_29 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_29)),X_29)))
| X_29 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_29)),X_29),inverse(greatest_lower_bound(identity,inverse(X_29)))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
X_29 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),
inference(resolve,[$cnf( $equal(X_29,multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_29)),X_29)))) )],[refute_0_58,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity) = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))))]]) ).
cnf(refute_0_135,plain,
multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_23))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))),
inference(subst,[],[refute_0_105:[bind(X_93,$fot(greatest_lower_bound(identity,X_23)))]]) ).
cnf(refute_0_136,plain,
greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) = X_8,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_137,plain,
least_upper_bound(X_9,X_8) = least_upper_bound(X_8,X_9),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_138,plain,
( least_upper_bound(X_9,X_8) != least_upper_bound(X_8,X_9)
| least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_9,X_8))),bind(Y0,$fot(least_upper_bound(X_8,X_9)))]]) ).
cnf(refute_0_139,plain,
least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_8),least_upper_bound(X_8,X_9)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,X_9) != least_upper_bound(X_9,X_8)
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) ),[0,1],$fot(least_upper_bound(X_9,X_8))]]) ).
cnf(refute_0_141,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,X_9),least_upper_bound(X_9,X_8)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) )],[refute_0_136,refute_0_141]) ).
cnf(refute_0_143,plain,
greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))) = greatest_lower_bound(X_9,X_13),
inference(subst,[],[refute_0_142:[bind(X_8,$fot(greatest_lower_bound(X_9,X_13)))]]) ).
cnf(refute_0_144,plain,
least_upper_bound(X_9,greatest_lower_bound(X_9,X_13)) = X_9,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_9)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_145,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))) != greatest_lower_bound(X_9,X_13)
| least_upper_bound(X_9,greatest_lower_bound(X_9,X_13)) != X_9
| greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))),greatest_lower_bound(X_9,X_13)) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_146,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))) != greatest_lower_bound(X_9,X_13)
| greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,X_13) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,greatest_lower_bound(X_9,X_13)),X_9) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,X_13),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),least_upper_bound(X_9,greatest_lower_bound(X_9,X_13))),greatest_lower_bound(X_9,X_13)) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_149,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_148]) ).
cnf(refute_0_150,plain,
greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) = greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)),
inference(subst,[],[refute_0_149:[bind(X,$fot(X_9)),bind(Y,$fot(X_13)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_151,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) != greatest_lower_bound(X_9,X_13)
| greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) != greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9))
| greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)) = greatest_lower_bound(X_9,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9),greatest_lower_bound(X_9,X_13)) ),[0],$fot(greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)))]]) ).
cnf(refute_0_152,plain,
( greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9) != greatest_lower_bound(X_9,X_13)
| greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)) = greatest_lower_bound(X_9,X_13) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
greatest_lower_bound(X_9,greatest_lower_bound(X_13,X_9)) = greatest_lower_bound(X_9,X_13),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_9,X_13),X_9),greatest_lower_bound(X_9,X_13)) )],[refute_0_147,refute_0_152]) ).
cnf(refute_0_154,plain,
greatest_lower_bound(X_24,greatest_lower_bound(X_23,X_24)) = greatest_lower_bound(X_24,X_23),
inference(subst,[],[refute_0_153:[bind(X_13,$fot(X_23)),bind(X_9,$fot(X_24))]]) ).
cnf(refute_0_155,plain,
greatest_lower_bound(X_24,X_23) = greatest_lower_bound(X_23,X_24),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_24)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_156,plain,
( greatest_lower_bound(X_24,X_23) != greatest_lower_bound(X_23,X_24)
| greatest_lower_bound(X_23,X_24) = greatest_lower_bound(X_24,X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_24,X_23))),bind(Y0,$fot(greatest_lower_bound(X_23,X_24)))]]) ).
cnf(refute_0_157,plain,
greatest_lower_bound(X_23,X_24) = greatest_lower_bound(X_24,X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_24,X_23),greatest_lower_bound(X_23,X_24)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( greatest_lower_bound(X_23,X_24) != greatest_lower_bound(X_24,X_23)
| greatest_lower_bound(X_24,greatest_lower_bound(X_23,X_24)) != greatest_lower_bound(X_24,X_23)
| greatest_lower_bound(X_24,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(X_24,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_24,greatest_lower_bound(X_23,X_24)),greatest_lower_bound(X_24,X_23)) ),[0,1],$fot(greatest_lower_bound(X_24,X_23))]]) ).
cnf(refute_0_159,plain,
( greatest_lower_bound(X_24,greatest_lower_bound(X_23,X_24)) != greatest_lower_bound(X_24,X_23)
| greatest_lower_bound(X_24,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(X_24,X_23) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,X_24),greatest_lower_bound(X_24,X_23)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
greatest_lower_bound(X_24,greatest_lower_bound(X_24,X_23)) = greatest_lower_bound(X_24,X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_24,greatest_lower_bound(X_23,X_24)),greatest_lower_bound(X_24,X_23)) )],[refute_0_154,refute_0_159]) ).
cnf(refute_0_161,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,X_23),
inference(subst,[],[refute_0_160:[bind(X_24,$fot(identity))]]) ).
cnf(refute_0_162,plain,
( multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_23))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,X_23)) != greatest_lower_bound(identity,X_23)
| multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_23))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))) ),[0,1],$fot(greatest_lower_bound(identity,X_23))]]) ).
cnf(refute_0_163,plain,
( multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_23))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))
| multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_23))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))) )],[refute_0_135,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(identity,X_23)))]]) ).
cnf(refute_0_166,plain,
( multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))
| multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) != identity
| identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_167,plain,
( multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))
| identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)),identity) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,X_23)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))))]]) ).
cnf(refute_0_170,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_23)))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))) = identity,
inference(subst,[],[refute_0_170:[bind(X_23,$fot(inverse(X_29)))]]) ).
cnf(refute_0_172,plain,
multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))))]]) ).
cnf(refute_0_173,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) != multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))
| greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))) != identity
| multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_174,plain,
( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))) != identity
| multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))),identity) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(inverse(X_99),inverse(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)))) = inverse(greatest_lower_bound(X_98,X_99)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(greatest_lower_bound(X_98,X_99))),bind(X_38,$fot(inverse(X_99)))]]) ).
cnf(refute_0_177,plain,
multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) = greatest_lower_bound(multiply(X_98,inverse(X_99)),multiply(X_99,inverse(X_99))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_99))),bind(Y,$fot(X_98)),bind(Z,$fot(X_99))]]) ).
cnf(refute_0_178,plain,
multiply(X_99,inverse(X_99)) = identity,
inference(subst,[],[refute_0_32:[bind(X_33,$fot(X_99))]]) ).
cnf(refute_0_179,plain,
( multiply(X_99,inverse(X_99)) != identity
| multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) != greatest_lower_bound(multiply(X_98,inverse(X_99)),multiply(X_99,inverse(X_99)))
| multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) = greatest_lower_bound(multiply(X_98,inverse(X_99)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)),greatest_lower_bound(multiply(X_98,inverse(X_99)),multiply(X_99,inverse(X_99)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_180,plain,
( multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) != greatest_lower_bound(multiply(X_98,inverse(X_99)),multiply(X_99,inverse(X_99)))
| multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) = greatest_lower_bound(multiply(X_98,inverse(X_99)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_99,inverse(X_99)),identity) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) = greatest_lower_bound(multiply(X_98,inverse(X_99)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)),greatest_lower_bound(multiply(X_98,inverse(X_99)),multiply(X_99,inverse(X_99)))) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
greatest_lower_bound(multiply(X_98,inverse(X_99)),identity) = greatest_lower_bound(identity,multiply(X_98,inverse(X_99))),
inference(subst,[],[refute_0_49:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_98,inverse(X_99))))]]) ).
cnf(refute_0_183,plain,
( multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) != greatest_lower_bound(multiply(X_98,inverse(X_99)),identity)
| greatest_lower_bound(multiply(X_98,inverse(X_99)),identity) != greatest_lower_bound(identity,multiply(X_98,inverse(X_99)))
| multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) = greatest_lower_bound(identity,multiply(X_98,inverse(X_99))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)),greatest_lower_bound(identity,multiply(X_98,inverse(X_99)))) ),[0],$fot(greatest_lower_bound(multiply(X_98,inverse(X_99)),identity))]]) ).
cnf(refute_0_184,plain,
( multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) != greatest_lower_bound(multiply(X_98,inverse(X_99)),identity)
| multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) = greatest_lower_bound(identity,multiply(X_98,inverse(X_99))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_98,inverse(X_99)),identity),greatest_lower_bound(identity,multiply(X_98,inverse(X_99)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) = greatest_lower_bound(identity,multiply(X_98,inverse(X_99))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)),greatest_lower_bound(multiply(X_98,inverse(X_99)),identity)) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
( multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)) != greatest_lower_bound(identity,multiply(X_98,inverse(X_99)))
| multiply(inverse(X_99),inverse(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)))) != inverse(greatest_lower_bound(X_98,X_99))
| multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) = inverse(greatest_lower_bound(X_98,X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_99),inverse(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)))),inverse(greatest_lower_bound(X_98,X_99))) ),[0,1,0],$fot(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))]]) ).
cnf(refute_0_187,plain,
( multiply(inverse(X_99),inverse(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)))) != inverse(greatest_lower_bound(X_98,X_99))
| multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) = inverse(greatest_lower_bound(X_98,X_99)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)),greatest_lower_bound(identity,multiply(X_98,inverse(X_99)))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) = inverse(greatest_lower_bound(X_98,X_99)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),inverse(multiply(greatest_lower_bound(X_98,X_99),inverse(X_99)))),inverse(greatest_lower_bound(X_98,X_99))) )],[refute_0_176,refute_0_187]) ).
cnf(refute_0_189,plain,
inverse(inverse(X_99)) = X_99,
inference(subst,[],[refute_0_119:[bind(X_33,$fot(X_99))]]) ).
cnf(refute_0_190,plain,
greatest_lower_bound(inverse(inverse(X_99)),X_98) = greatest_lower_bound(inverse(inverse(X_99)),X_98),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(inverse(X_99)),X_98))]]) ).
cnf(refute_0_191,plain,
( greatest_lower_bound(inverse(inverse(X_99)),X_98) != greatest_lower_bound(inverse(inverse(X_99)),X_98)
| inverse(inverse(X_99)) != X_99
| greatest_lower_bound(inverse(inverse(X_99)),X_98) = greatest_lower_bound(X_99,X_98) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_99)),X_98),greatest_lower_bound(inverse(inverse(X_99)),X_98)) ),[1,0],$fot(X_99)]]) ).
cnf(refute_0_192,plain,
( inverse(inverse(X_99)) != X_99
| greatest_lower_bound(inverse(inverse(X_99)),X_98) = greatest_lower_bound(X_99,X_98) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_99)),X_98),greatest_lower_bound(inverse(inverse(X_99)),X_98)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
greatest_lower_bound(inverse(inverse(X_99)),X_98) = greatest_lower_bound(X_99,X_98),
inference(resolve,[$cnf( $equal(inverse(inverse(X_99)),X_99) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)) = inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)))]]) ).
cnf(refute_0_195,plain,
( greatest_lower_bound(inverse(inverse(X_99)),X_98) != greatest_lower_bound(X_99,X_98)
| inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)) != inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98))
| inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)) = inverse(greatest_lower_bound(X_99,X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)),inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98))) ),[1,0],$fot(greatest_lower_bound(X_99,X_98))]]) ).
cnf(refute_0_196,plain,
( greatest_lower_bound(inverse(inverse(X_99)),X_98) != greatest_lower_bound(X_99,X_98)
| inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)) = inverse(greatest_lower_bound(X_99,X_98)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)),inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)) = inverse(greatest_lower_bound(X_99,X_98)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_99)),X_98),greatest_lower_bound(X_99,X_98)) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
multiply(X_197,inverse(multiply(greatest_lower_bound(inverse(X_197),X_99),X_197))) = inverse(greatest_lower_bound(inverse(X_197),X_99)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(greatest_lower_bound(inverse(X_197),X_99))),bind(X_38,$fot(X_197))]]) ).
cnf(refute_0_199,plain,
multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_97)),bind(Y,$fot(inverse(X_97))),bind(Z,$fot(X_99))]]) ).
cnf(refute_0_200,plain,
( multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) != greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))
| multiply(inverse(X_97),X_97) != identity
| multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(identity,multiply(X_99,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_97),X_99),X_97),greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_201,plain,
( multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) != greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))
| multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(identity,multiply(X_99,X_97)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),X_97),identity) )],[refute_0_44,refute_0_200]) ).
cnf(refute_0_202,plain,
multiply(greatest_lower_bound(inverse(X_97),X_99),X_97) = greatest_lower_bound(identity,multiply(X_99,X_97)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_97),X_99),X_97),greatest_lower_bound(multiply(inverse(X_97),X_97),multiply(X_99,X_97))) )],[refute_0_199,refute_0_201]) ).
cnf(refute_0_203,plain,
multiply(greatest_lower_bound(inverse(X_197),X_99),X_197) = greatest_lower_bound(identity,multiply(X_99,X_197)),
inference(subst,[],[refute_0_202:[bind(X_97,$fot(X_197))]]) ).
cnf(refute_0_204,plain,
( multiply(X_197,inverse(multiply(greatest_lower_bound(inverse(X_197),X_99),X_197))) != inverse(greatest_lower_bound(inverse(X_197),X_99))
| multiply(greatest_lower_bound(inverse(X_197),X_99),X_197) != greatest_lower_bound(identity,multiply(X_99,X_197))
| multiply(X_197,inverse(greatest_lower_bound(identity,multiply(X_99,X_197)))) = inverse(greatest_lower_bound(inverse(X_197),X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_197,inverse(multiply(greatest_lower_bound(inverse(X_197),X_99),X_197))),inverse(greatest_lower_bound(inverse(X_197),X_99))) ),[0,1,0],$fot(greatest_lower_bound(identity,multiply(X_99,X_197)))]]) ).
cnf(refute_0_205,plain,
( multiply(X_197,inverse(multiply(greatest_lower_bound(inverse(X_197),X_99),X_197))) != inverse(greatest_lower_bound(inverse(X_197),X_99))
| multiply(X_197,inverse(greatest_lower_bound(identity,multiply(X_99,X_197)))) = inverse(greatest_lower_bound(inverse(X_197),X_99)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_197),X_99),X_197),greatest_lower_bound(identity,multiply(X_99,X_197))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
multiply(X_197,inverse(greatest_lower_bound(identity,multiply(X_99,X_197)))) = inverse(greatest_lower_bound(inverse(X_197),X_99)),
inference(resolve,[$cnf( $equal(multiply(X_197,inverse(multiply(greatest_lower_bound(inverse(X_197),X_99),X_197))),inverse(greatest_lower_bound(inverse(X_197),X_99))) )],[refute_0_198,refute_0_205]) ).
cnf(refute_0_207,plain,
multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) = inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)),
inference(subst,[],[refute_0_206:[bind(X_197,$fot(inverse(X_99))),bind(X_99,$fot(X_98))]]) ).
cnf(refute_0_208,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_209,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_208]) ).
cnf(refute_0_210,plain,
( multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) != inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98))
| inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)) != inverse(greatest_lower_bound(X_99,X_98))
| multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) = inverse(greatest_lower_bound(X_99,X_98)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_99,X_98))))]]) ).
cnf(refute_0_211,plain,
( inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)) != inverse(greatest_lower_bound(X_99,X_98))
| multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) = inverse(greatest_lower_bound(X_99,X_98)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))),inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98))) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) = inverse(greatest_lower_bound(X_99,X_98)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X_99)),X_98)),inverse(greatest_lower_bound(X_99,X_98))) )],[refute_0_197,refute_0_211]) ).
cnf(refute_0_213,plain,
( multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) != inverse(greatest_lower_bound(X_98,X_99))
| multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) != inverse(greatest_lower_bound(X_99,X_98))
| inverse(greatest_lower_bound(X_99,X_98)) = inverse(greatest_lower_bound(X_98,X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))),inverse(greatest_lower_bound(X_98,X_99))) ),[0],$fot(inverse(greatest_lower_bound(X_99,X_98)))]]) ).
cnf(refute_0_214,plain,
( multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))) != inverse(greatest_lower_bound(X_98,X_99))
| inverse(greatest_lower_bound(X_99,X_98)) = inverse(greatest_lower_bound(X_98,X_99)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))),inverse(greatest_lower_bound(X_99,X_98))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
inverse(greatest_lower_bound(X_99,X_98)) = inverse(greatest_lower_bound(X_98,X_99)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),inverse(greatest_lower_bound(identity,multiply(X_98,inverse(X_99))))),inverse(greatest_lower_bound(X_98,X_99))) )],[refute_0_188,refute_0_214]) ).
cnf(refute_0_216,plain,
( inverse(greatest_lower_bound(X_99,X_98)) != inverse(greatest_lower_bound(X_98,X_99))
| inverse(greatest_lower_bound(X_98,X_99)) = inverse(greatest_lower_bound(X_99,X_98)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(X_99,X_98)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_98,X_99))))]]) ).
cnf(refute_0_217,plain,
inverse(greatest_lower_bound(X_98,X_99)) = inverse(greatest_lower_bound(X_99,X_98)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_99,X_98)),inverse(greatest_lower_bound(X_98,X_99))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))) = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),
inference(subst,[],[refute_0_217:[bind(X_98,$fot(inverse(greatest_lower_bound(identity,X_29)))),bind(X_99,$fot(inverse(X_29)))]]) ).
cnf(refute_0_219,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))))]]) ).
cnf(refute_0_220,plain,
( multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))
| inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))) != inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))) ),[1,0],$fot(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))))]]) ).
cnf(refute_0_221,plain,
( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))) != inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) != multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity)
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) != multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity)))]]) ).
cnf(refute_0_224,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) != multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity)
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity)) )],[refute_0_175,refute_0_224]) ).
cnf(refute_0_226,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity) != inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) != multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity)
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))))]]) ).
cnf(refute_0_227,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity) != inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),identity),inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))) )],[refute_0_134,refute_0_227]) ).
cnf(refute_0_229,plain,
( X_29 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))) != inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))
| X_29 = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_29,inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))))]]) ).
cnf(refute_0_230,plain,
( X_29 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))
| X_29 = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29))))),inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29))))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
X_29 = inverse(greatest_lower_bound(inverse(X_29),inverse(greatest_lower_bound(identity,X_29)))),
inference(resolve,[$cnf( $equal(X_29,multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_29)),inverse(X_29))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_29)))))) )],[refute_0_133,refute_0_230]) ).
cnf(refute_0_232,plain,
least_upper_bound(X_246,X_245) = inverse(greatest_lower_bound(inverse(least_upper_bound(X_246,X_245)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),
inference(subst,[],[refute_0_231:[bind(X_29,$fot(least_upper_bound(X_246,X_245)))]]) ).
cnf(refute_0_233,plain,
multiply(X_38,inverse(multiply(least_upper_bound(X_246,X_245),X_38))) = inverse(least_upper_bound(X_246,X_245)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(least_upper_bound(X_246,X_245)))]]) ).
cnf(refute_0_234,plain,
least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) = least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_61,X_59))),bind(Y,$fot(multiply(X_60,X_59)))]]) ).
cnf(refute_0_235,plain,
multiply(least_upper_bound(X_60,X_61),X_59) = least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_59)),bind(Y,$fot(X_60)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_236,plain,
( multiply(least_upper_bound(X_60,X_61),X_59) != least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59))
| least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59)) = multiply(least_upper_bound(X_60,X_61),X_59) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_60,X_61),X_59))),bind(Y0,$fot(least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59))))]]) ).
cnf(refute_0_237,plain,
least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59)) = multiply(least_upper_bound(X_60,X_61),X_59),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,X_61),X_59),least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
( least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59)) != multiply(least_upper_bound(X_60,X_61),X_59)
| least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) != least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59))
| least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) = multiply(least_upper_bound(X_60,X_61),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)),least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59))) ),[1],$fot(multiply(least_upper_bound(X_60,X_61),X_59))]]) ).
cnf(refute_0_239,plain,
( least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) != least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59))
| least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) = multiply(least_upper_bound(X_60,X_61),X_59) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59)),multiply(least_upper_bound(X_60,X_61),X_59)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) = multiply(least_upper_bound(X_60,X_61),X_59),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)),least_upper_bound(multiply(X_60,X_59),multiply(X_61,X_59))) )],[refute_0_234,refute_0_239]) ).
cnf(refute_0_241,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_242,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_241]) ).
cnf(refute_0_243,plain,
least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) = multiply(least_upper_bound(X_61,X_60),X_59),
inference(subst,[],[refute_0_242:[bind(X,$fot(X_59)),bind(Y,$fot(X_61)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_244,plain,
( least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) != multiply(least_upper_bound(X_60,X_61),X_59)
| least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) != multiply(least_upper_bound(X_61,X_60),X_59)
| multiply(least_upper_bound(X_61,X_60),X_59) = multiply(least_upper_bound(X_60,X_61),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)),multiply(least_upper_bound(X_60,X_61),X_59)) ),[0],$fot(multiply(least_upper_bound(X_61,X_60),X_59))]]) ).
cnf(refute_0_245,plain,
( least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)) != multiply(least_upper_bound(X_60,X_61),X_59)
| multiply(least_upper_bound(X_61,X_60),X_59) = multiply(least_upper_bound(X_60,X_61),X_59) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)),multiply(least_upper_bound(X_61,X_60),X_59)) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
multiply(least_upper_bound(X_61,X_60),X_59) = multiply(least_upper_bound(X_60,X_61),X_59),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_61,X_59),multiply(X_60,X_59)),multiply(least_upper_bound(X_60,X_61),X_59)) )],[refute_0_240,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(least_upper_bound(X_246,X_245),X_38) = multiply(least_upper_bound(X_245,X_246),X_38),
inference(subst,[],[refute_0_246:[bind(X_59,$fot(X_38)),bind(X_60,$fot(X_245)),bind(X_61,$fot(X_246))]]) ).
cnf(refute_0_248,plain,
( multiply(X_38,inverse(multiply(least_upper_bound(X_246,X_245),X_38))) != inverse(least_upper_bound(X_246,X_245))
| multiply(least_upper_bound(X_246,X_245),X_38) != multiply(least_upper_bound(X_245,X_246),X_38)
| multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))) = inverse(least_upper_bound(X_246,X_245)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_38,inverse(multiply(least_upper_bound(X_246,X_245),X_38))),inverse(least_upper_bound(X_246,X_245))) ),[0,1,0],$fot(multiply(least_upper_bound(X_245,X_246),X_38))]]) ).
cnf(refute_0_249,plain,
( multiply(X_38,inverse(multiply(least_upper_bound(X_246,X_245),X_38))) != inverse(least_upper_bound(X_246,X_245))
| multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))) = inverse(least_upper_bound(X_246,X_245)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_246,X_245),X_38),multiply(least_upper_bound(X_245,X_246),X_38)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))) = inverse(least_upper_bound(X_246,X_245)),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(multiply(least_upper_bound(X_246,X_245),X_38))),inverse(least_upper_bound(X_246,X_245))) )],[refute_0_233,refute_0_249]) ).
cnf(refute_0_251,plain,
multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))) = inverse(least_upper_bound(X_245,X_246)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_252,plain,
( multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))) != inverse(least_upper_bound(X_245,X_246))
| multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))) != inverse(least_upper_bound(X_246,X_245))
| inverse(least_upper_bound(X_245,X_246)) = inverse(least_upper_bound(X_246,X_245)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))),inverse(least_upper_bound(X_246,X_245))) ),[0],$fot(inverse(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_253,plain,
( multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))) != inverse(least_upper_bound(X_246,X_245))
| inverse(least_upper_bound(X_245,X_246)) = inverse(least_upper_bound(X_246,X_245)) ),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))),inverse(least_upper_bound(X_245,X_246))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
inverse(least_upper_bound(X_245,X_246)) = inverse(least_upper_bound(X_246,X_245)),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(multiply(least_upper_bound(X_245,X_246),X_38))),inverse(least_upper_bound(X_246,X_245))) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
( inverse(least_upper_bound(X_245,X_246)) != inverse(least_upper_bound(X_246,X_245))
| inverse(least_upper_bound(X_246,X_245)) = inverse(least_upper_bound(X_245,X_246)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_245,X_246)))),bind(Y0,$fot(inverse(least_upper_bound(X_246,X_245))))]]) ).
cnf(refute_0_256,plain,
inverse(least_upper_bound(X_246,X_245)) = inverse(least_upper_bound(X_245,X_246)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_245,X_246)),inverse(least_upper_bound(X_246,X_245))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
( inverse(least_upper_bound(X_246,X_245)) != inverse(least_upper_bound(X_245,X_246))
| least_upper_bound(X_246,X_245) != inverse(greatest_lower_bound(inverse(least_upper_bound(X_246,X_245)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))
| least_upper_bound(X_246,X_245) = inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_246,X_245),inverse(greatest_lower_bound(inverse(least_upper_bound(X_246,X_245)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))) ),[1,0,0],$fot(inverse(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_258,plain,
( least_upper_bound(X_246,X_245) != inverse(greatest_lower_bound(inverse(least_upper_bound(X_246,X_245)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))
| least_upper_bound(X_246,X_245) = inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_246,X_245)),inverse(least_upper_bound(X_245,X_246))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
least_upper_bound(X_246,X_245) = inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_246,X_245),inverse(greatest_lower_bound(inverse(least_upper_bound(X_246,X_245)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))) )],[refute_0_232,refute_0_258]) ).
cnf(refute_0_260,plain,
inverse(inverse(least_upper_bound(X_245,X_246))) = least_upper_bound(X_245,X_246),
inference(subst,[],[refute_0_119:[bind(X_33,$fot(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_261,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_262,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_263,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_2:[bind(X0,$fot(greatest_lower_bound(X_13,X_12))),bind(Y0,$fot(greatest_lower_bound(X_12,X_13)))]]) ).
cnf(refute_0_264,plain,
greatest_lower_bound(X_12,X_13) = greatest_lower_bound(X_13,X_12),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,X_12),greatest_lower_bound(X_12,X_13)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
( greatest_lower_bound(X_12,X_13) != greatest_lower_bound(X_13,X_12)
| least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12 ),
introduced(tautology,[equality,[$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_266,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( $equal(greatest_lower_bound(X_12,X_13),greatest_lower_bound(X_13,X_12)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
least_upper_bound(X_12,greatest_lower_bound(X_13,X_12)) = X_12,
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(X_12,X_13)),X_12) )],[refute_0_261,refute_0_266]) ).
cnf(refute_0_268,plain,
least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)) = X_12,
inference(subst,[],[refute_0_267:[bind(X_13,$fot(greatest_lower_bound(X_39,X_40)))]]) ).
cnf(refute_0_269,plain,
greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12)) = greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_270,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12)) != greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)
| greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12) = greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)))]]) ).
cnf(refute_0_271,plain,
greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12) = greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12)),greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
( greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12) != greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12))
| least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)),X_12) ),[0,1],$fot(greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12)))]]) ).
cnf(refute_0_273,plain,
( least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)) != X_12
| least_upper_bound(X_12,greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12))) = X_12 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12),greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
least_upper_bound(X_12,greatest_lower_bound(X_39,greatest_lower_bound(X_40,X_12))) = X_12,
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,greatest_lower_bound(greatest_lower_bound(X_39,X_40),X_12)),X_12) )],[refute_0_268,refute_0_273]) ).
cnf(refute_0_275,plain,
least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)))) = least_upper_bound(X_136,X_135),
inference(subst,[],[refute_0_274:[bind(X_12,$fot(least_upper_bound(X_136,X_135))),bind(X_40,$fot(least_upper_bound(X_135,X_136)))]]) ).
cnf(refute_0_276,plain,
greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))) = least_upper_bound(X_16,X_9),
inference(subst,[],[refute_0_142:[bind(X_8,$fot(least_upper_bound(X_16,X_9)))]]) ).
cnf(refute_0_277,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_267:[bind(X_12,$fot(least_upper_bound(X_15,Y))),bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_278,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_279,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) != X_15
| least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$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_280,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( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_277,refute_0_280]) ).
cnf(refute_0_282,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_283,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_282]) ).
cnf(refute_0_284,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_285,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$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_286,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( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_281,refute_0_286]) ).
cnf(refute_0_288,plain,
least_upper_bound(X_9,least_upper_bound(X_16,X_9)) = least_upper_bound(X_9,X_16),
inference(subst,[],[refute_0_287:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_9))]]) ).
cnf(refute_0_289,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))) != least_upper_bound(X_16,X_9)
| least_upper_bound(X_9,least_upper_bound(X_16,X_9)) != least_upper_bound(X_9,X_16)
| greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,X_16)) = least_upper_bound(X_16,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))),least_upper_bound(X_16,X_9)) ),[0,1],$fot(least_upper_bound(X_9,X_16))]]) ).
cnf(refute_0_290,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))) != least_upper_bound(X_16,X_9)
| greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,X_16)) = least_upper_bound(X_16,X_9) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,least_upper_bound(X_16,X_9)),least_upper_bound(X_9,X_16)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,X_16)) = least_upper_bound(X_16,X_9),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))),least_upper_bound(X_16,X_9)) )],[refute_0_276,refute_0_290]) ).
cnf(refute_0_292,plain,
greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)) = least_upper_bound(X_135,X_136),
inference(subst,[],[refute_0_291:[bind(X_16,$fot(X_135)),bind(X_9,$fot(X_136))]]) ).
cnf(refute_0_293,plain,
( greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)) != least_upper_bound(X_135,X_136)
| least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)))) != least_upper_bound(X_136,X_135)
| least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))) = least_upper_bound(X_136,X_135) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)))),least_upper_bound(X_136,X_135)) ),[0,1,1],$fot(least_upper_bound(X_135,X_136))]]) ).
cnf(refute_0_294,plain,
( least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)))) != least_upper_bound(X_136,X_135)
| least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))) = least_upper_bound(X_136,X_135) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)),least_upper_bound(X_135,X_136)) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))) = least_upper_bound(X_136,X_135),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_135,X_136),least_upper_bound(X_136,X_135)))),least_upper_bound(X_136,X_135)) )],[refute_0_275,refute_0_294]) ).
cnf(refute_0_296,plain,
least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))) = least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_39,least_upper_bound(X_135,X_136)))),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_136)),bind(Y,$fot(X_135)),bind(Z,$fot(greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))))]]) ).
cnf(refute_0_297,plain,
( least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))) != least_upper_bound(X_136,X_135)
| least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))) != least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))))
| least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_39,least_upper_bound(X_135,X_136)))) = least_upper_bound(X_136,X_135) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))),least_upper_bound(X_136,X_135)) ),[0],$fot(least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_39,least_upper_bound(X_135,X_136)))))]]) ).
cnf(refute_0_298,plain,
( least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))) != least_upper_bound(X_136,X_135)
| least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_39,least_upper_bound(X_135,X_136)))) = least_upper_bound(X_136,X_135) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))),least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
least_upper_bound(X_136,least_upper_bound(X_135,greatest_lower_bound(X_39,least_upper_bound(X_135,X_136)))) = least_upper_bound(X_136,X_135),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_136,X_135),greatest_lower_bound(X_39,least_upper_bound(X_135,X_136))),least_upper_bound(X_136,X_135)) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = least_upper_bound(X_245,X_246),
inference(subst,[],[refute_0_299:[bind(X_135,$fot(X_246)),bind(X_136,$fot(X_245)),bind(X_39,$fot(identity))]]) ).
cnf(refute_0_301,plain,
least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))) = least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_245)),bind(Y,$fot(X_246)),bind(Z,$fot(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))]]) ).
cnf(refute_0_302,plain,
( least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != least_upper_bound(X_245,X_246)
| least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))) != least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))
| least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))) = least_upper_bound(X_245,X_246) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),bind(Y0,$fot(least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))),bind(Z0,$fot(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_303,plain,
( least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != least_upper_bound(X_245,X_246)
| least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))) = least_upper_bound(X_245,X_246) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))),least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))) = least_upper_bound(X_245,X_246),
inference(resolve,[$cnf( $equal(least_upper_bound(X_245,least_upper_bound(X_246,greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),least_upper_bound(X_245,X_246)) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))]]) ).
cnf(refute_0_306,plain,
( inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))
| least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))) != least_upper_bound(X_245,X_246)
| inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(X_245,X_246)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) ),[1,0],$fot(least_upper_bound(X_245,X_246))]]) ).
cnf(refute_0_307,plain,
( least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))) != least_upper_bound(X_245,X_246)
| inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(X_245,X_246)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(X_245,X_246)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))),least_upper_bound(X_245,X_246)) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
inverse(least_upper_bound(X_101,X_324)) = multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,multiply(X_101,inverse(least_upper_bound(X_101,X_324))))),
inference(subst,[],[refute_0_57:[bind(X_29,$fot(inverse(least_upper_bound(X_101,X_324))))]]) ).
cnf(refute_0_310,plain,
inverse(least_upper_bound(X_69,identity)) = multiply(inverse(least_upper_bound(identity,X_69)),multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity)))),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(least_upper_bound(identity,X_69))),bind(X_29,$fot(inverse(least_upper_bound(X_69,identity))))]]) ).
cnf(refute_0_311,plain,
multiply(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(multiply(X_44,X_45),multiply(X_44,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_312,plain,
X_44 = multiply(X_44,identity),
inference(subst,[],[refute_0_82:[bind(X_31,$fot(X_44))]]) ).
cnf(refute_0_313,plain,
( X_44 != multiply(X_44,identity)
| multiply(X_44,identity) = X_44 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_44)),bind(Y0,$fot(multiply(X_44,identity)))]]) ).
cnf(refute_0_314,plain,
multiply(X_44,identity) = X_44,
inference(resolve,[$cnf( $equal(X_44,multiply(X_44,identity)) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
( multiply(X_44,identity) != X_44
| multiply(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(multiply(X_44,X_45),multiply(X_44,identity))
| multiply(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(multiply(X_44,X_45),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,identity)),least_upper_bound(multiply(X_44,X_45),multiply(X_44,identity))) ),[1,1],$fot(X_44)]]) ).
cnf(refute_0_316,plain,
( multiply(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(multiply(X_44,X_45),multiply(X_44,identity))
| multiply(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(multiply(X_44,X_45),X_44) ),
inference(resolve,[$cnf( $equal(multiply(X_44,identity),X_44) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
multiply(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(multiply(X_44,X_45),X_44),
inference(resolve,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,identity)),least_upper_bound(multiply(X_44,X_45),multiply(X_44,identity))) )],[refute_0_311,refute_0_316]) ).
cnf(refute_0_318,plain,
least_upper_bound(multiply(X_44,X_45),X_44) = least_upper_bound(X_44,multiply(X_44,X_45)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_44)),bind(Y,$fot(multiply(X_44,X_45)))]]) ).
cnf(refute_0_319,plain,
( multiply(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(multiply(X_44,X_45),X_44)
| least_upper_bound(multiply(X_44,X_45),X_44) != least_upper_bound(X_44,multiply(X_44,X_45))
| multiply(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(X_44,multiply(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_44,least_upper_bound(X_45,identity)),least_upper_bound(X_44,multiply(X_44,X_45))) ),[0],$fot(least_upper_bound(multiply(X_44,X_45),X_44))]]) ).
cnf(refute_0_320,plain,
( multiply(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(multiply(X_44,X_45),X_44)
| multiply(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(X_44,multiply(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_44,X_45),X_44),least_upper_bound(X_44,multiply(X_44,X_45))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
multiply(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(X_44,multiply(X_44,X_45)),
inference(resolve,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,identity)),least_upper_bound(multiply(X_44,X_45),X_44)) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
multiply(identity,least_upper_bound(inverse(X_65),identity)) = least_upper_bound(identity,multiply(identity,inverse(X_65))),
inference(subst,[],[refute_0_321:[bind(X_44,$fot(identity)),bind(X_45,$fot(inverse(X_65)))]]) ).
cnf(refute_0_323,plain,
multiply(least_upper_bound(X_60,X_61),inverse(X_61)) = least_upper_bound(multiply(X_60,inverse(X_61)),multiply(X_61,inverse(X_61))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_61))),bind(Y,$fot(X_60)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_324,plain,
multiply(X_61,inverse(X_61)) = identity,
inference(subst,[],[refute_0_32:[bind(X_33,$fot(X_61))]]) ).
cnf(refute_0_325,plain,
( multiply(X_61,inverse(X_61)) != identity
| multiply(least_upper_bound(X_60,X_61),inverse(X_61)) != least_upper_bound(multiply(X_60,inverse(X_61)),multiply(X_61,inverse(X_61)))
| multiply(least_upper_bound(X_60,X_61),inverse(X_61)) = least_upper_bound(multiply(X_60,inverse(X_61)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_60,X_61),inverse(X_61)),least_upper_bound(multiply(X_60,inverse(X_61)),multiply(X_61,inverse(X_61)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_326,plain,
( multiply(least_upper_bound(X_60,X_61),inverse(X_61)) != least_upper_bound(multiply(X_60,inverse(X_61)),multiply(X_61,inverse(X_61)))
| multiply(least_upper_bound(X_60,X_61),inverse(X_61)) = least_upper_bound(multiply(X_60,inverse(X_61)),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_61,inverse(X_61)),identity) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
multiply(least_upper_bound(X_60,X_61),inverse(X_61)) = least_upper_bound(multiply(X_60,inverse(X_61)),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,X_61),inverse(X_61)),least_upper_bound(multiply(X_60,inverse(X_61)),multiply(X_61,inverse(X_61)))) )],[refute_0_323,refute_0_326]) ).
cnf(refute_0_328,plain,
least_upper_bound(multiply(X_60,inverse(X_61)),identity) = least_upper_bound(identity,multiply(X_60,inverse(X_61))),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_60,inverse(X_61))))]]) ).
cnf(refute_0_329,plain,
( multiply(least_upper_bound(X_60,X_61),inverse(X_61)) != least_upper_bound(multiply(X_60,inverse(X_61)),identity)
| least_upper_bound(multiply(X_60,inverse(X_61)),identity) != least_upper_bound(identity,multiply(X_60,inverse(X_61)))
| multiply(least_upper_bound(X_60,X_61),inverse(X_61)) = least_upper_bound(identity,multiply(X_60,inverse(X_61))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_60,X_61),inverse(X_61)),least_upper_bound(identity,multiply(X_60,inverse(X_61)))) ),[0],$fot(least_upper_bound(multiply(X_60,inverse(X_61)),identity))]]) ).
cnf(refute_0_330,plain,
( multiply(least_upper_bound(X_60,X_61),inverse(X_61)) != least_upper_bound(multiply(X_60,inverse(X_61)),identity)
| multiply(least_upper_bound(X_60,X_61),inverse(X_61)) = least_upper_bound(identity,multiply(X_60,inverse(X_61))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_60,inverse(X_61)),identity),least_upper_bound(identity,multiply(X_60,inverse(X_61)))) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
multiply(least_upper_bound(X_60,X_61),inverse(X_61)) = least_upper_bound(identity,multiply(X_60,inverse(X_61))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,X_61),inverse(X_61)),least_upper_bound(multiply(X_60,inverse(X_61)),identity)) )],[refute_0_327,refute_0_330]) ).
cnf(refute_0_332,plain,
multiply(least_upper_bound(identity,X_65),inverse(X_65)) = least_upper_bound(identity,multiply(identity,inverse(X_65))),
inference(subst,[],[refute_0_331:[bind(X_60,$fot(identity)),bind(X_61,$fot(X_65))]]) ).
cnf(refute_0_333,plain,
( multiply(least_upper_bound(identity,X_65),inverse(X_65)) != least_upper_bound(identity,multiply(identity,inverse(X_65)))
| least_upper_bound(identity,multiply(identity,inverse(X_65))) = multiply(least_upper_bound(identity,X_65),inverse(X_65)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,X_65),inverse(X_65)))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,inverse(X_65)))))]]) ).
cnf(refute_0_334,plain,
least_upper_bound(identity,multiply(identity,inverse(X_65))) = multiply(least_upper_bound(identity,X_65),inverse(X_65)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_65),inverse(X_65)),least_upper_bound(identity,multiply(identity,inverse(X_65)))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
( multiply(identity,least_upper_bound(inverse(X_65),identity)) != least_upper_bound(identity,multiply(identity,inverse(X_65)))
| least_upper_bound(identity,multiply(identity,inverse(X_65))) != multiply(least_upper_bound(identity,X_65),inverse(X_65))
| multiply(identity,least_upper_bound(inverse(X_65),identity)) = multiply(least_upper_bound(identity,X_65),inverse(X_65)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,least_upper_bound(inverse(X_65),identity)),multiply(least_upper_bound(identity,X_65),inverse(X_65))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(X_65))))]]) ).
cnf(refute_0_336,plain,
( multiply(identity,least_upper_bound(inverse(X_65),identity)) != least_upper_bound(identity,multiply(identity,inverse(X_65)))
| multiply(identity,least_upper_bound(inverse(X_65),identity)) = multiply(least_upper_bound(identity,X_65),inverse(X_65)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(X_65))),multiply(least_upper_bound(identity,X_65),inverse(X_65))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
multiply(identity,least_upper_bound(inverse(X_65),identity)) = multiply(least_upper_bound(identity,X_65),inverse(X_65)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_65),identity)),least_upper_bound(identity,multiply(identity,inverse(X_65)))) )],[refute_0_322,refute_0_336]) ).
cnf(refute_0_338,plain,
multiply(identity,least_upper_bound(identity,inverse(X_65))) = least_upper_bound(identity,inverse(X_65)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(X_65))))]]) ).
cnf(refute_0_339,plain,
least_upper_bound(X_17,least_upper_bound(X_16,X_17)) = least_upper_bound(X_17,X_16),
inference(subst,[],[refute_0_287:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_340,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_341,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_2:[bind(X0,$fot(least_upper_bound(X_17,X_16))),bind(Y0,$fot(least_upper_bound(X_16,X_17)))]]) ).
cnf(refute_0_342,plain,
least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),least_upper_bound(X_16,X_17)) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
( least_upper_bound(X_16,X_17) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
introduced(tautology,[equality,[$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_344,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( $equal(least_upper_bound(X_16,X_17),least_upper_bound(X_17,X_16)) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) )],[refute_0_339,refute_0_344]) ).
cnf(refute_0_346,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_55))) = least_upper_bound(X_17,multiply(X_17,X_55)),
inference(subst,[],[refute_0_345:[bind(X_16,$fot(multiply(X_17,X_55)))]]) ).
cnf(refute_0_347,plain,
multiply(X_17,least_upper_bound(X_55,identity)) = least_upper_bound(X_17,multiply(X_17,X_55)),
inference(subst,[],[refute_0_321:[bind(X_44,$fot(X_17)),bind(X_45,$fot(X_55))]]) ).
cnf(refute_0_348,plain,
( multiply(X_17,least_upper_bound(X_55,identity)) != least_upper_bound(X_17,multiply(X_17,X_55))
| least_upper_bound(X_17,multiply(X_17,X_55)) = multiply(X_17,least_upper_bound(X_55,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,least_upper_bound(X_55,identity)))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_17,X_55))))]]) ).
cnf(refute_0_349,plain,
least_upper_bound(X_17,multiply(X_17,X_55)) = multiply(X_17,least_upper_bound(X_55,identity)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(X_55,identity)),least_upper_bound(X_17,multiply(X_17,X_55))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
( least_upper_bound(X_17,multiply(X_17,X_55)) != multiply(X_17,least_upper_bound(X_55,identity))
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_55))) != least_upper_bound(X_17,multiply(X_17,X_55))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = least_upper_bound(X_17,multiply(X_17,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_55))),least_upper_bound(X_17,multiply(X_17,X_55))) ),[0,1],$fot(multiply(X_17,least_upper_bound(X_55,identity)))]]) ).
cnf(refute_0_351,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_55))) != least_upper_bound(X_17,multiply(X_17,X_55))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = least_upper_bound(X_17,multiply(X_17,X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,X_55)),multiply(X_17,least_upper_bound(X_55,identity))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = least_upper_bound(X_17,multiply(X_17,X_55)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_55))),least_upper_bound(X_17,multiply(X_17,X_55))) )],[refute_0_346,refute_0_351]) ).
cnf(refute_0_353,plain,
least_upper_bound(identity,least_upper_bound(X_55,identity)) = least_upper_bound(identity,X_55),
inference(subst,[],[refute_0_287:[bind(Y,$fot(X_55)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_354,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))),
introduced(tautology,[refl,[$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))))]]) ).
cnf(refute_0_355,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))
| least_upper_bound(identity,least_upper_bound(X_55,identity)) != least_upper_bound(identity,X_55)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_55))]]) ).
cnf(refute_0_356,plain,
( least_upper_bound(identity,least_upper_bound(X_55,identity)) != least_upper_bound(identity,X_55)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,X_55)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,X_55)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_55,identity)),least_upper_bound(identity,X_55)) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) = least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_44,X_46))),bind(Y,$fot(multiply(X_44,X_45)))]]) ).
cnf(refute_0_359,plain,
multiply(X_44,least_upper_bound(X_45,X_46)) = least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_360,plain,
( multiply(X_44,least_upper_bound(X_45,X_46)) != least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46))
| least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46)) = multiply(X_44,least_upper_bound(X_45,X_46)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_44,least_upper_bound(X_45,X_46)))),bind(Y0,$fot(least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46))))]]) ).
cnf(refute_0_361,plain,
least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46)) = multiply(X_44,least_upper_bound(X_45,X_46)),
inference(resolve,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,X_46)),least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
( least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46)) != multiply(X_44,least_upper_bound(X_45,X_46))
| least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) != least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46))
| least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) = multiply(X_44,least_upper_bound(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)),least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46))) ),[1],$fot(multiply(X_44,least_upper_bound(X_45,X_46)))]]) ).
cnf(refute_0_363,plain,
( least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) != least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46))
| least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) = multiply(X_44,least_upper_bound(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46)),multiply(X_44,least_upper_bound(X_45,X_46))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) = multiply(X_44,least_upper_bound(X_45,X_46)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)),least_upper_bound(multiply(X_44,X_45),multiply(X_44,X_46))) )],[refute_0_358,refute_0_363]) ).
cnf(refute_0_365,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_366,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_365]) ).
cnf(refute_0_367,plain,
least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) = multiply(X_44,least_upper_bound(X_46,X_45)),
inference(subst,[],[refute_0_366:[bind(X,$fot(X_44)),bind(Y,$fot(X_46)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_368,plain,
( least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) != multiply(X_44,least_upper_bound(X_45,X_46))
| least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) != multiply(X_44,least_upper_bound(X_46,X_45))
| multiply(X_44,least_upper_bound(X_46,X_45)) = multiply(X_44,least_upper_bound(X_45,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)),multiply(X_44,least_upper_bound(X_45,X_46))) ),[0],$fot(multiply(X_44,least_upper_bound(X_46,X_45)))]]) ).
cnf(refute_0_369,plain,
( least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)) != multiply(X_44,least_upper_bound(X_45,X_46))
| multiply(X_44,least_upper_bound(X_46,X_45)) = multiply(X_44,least_upper_bound(X_45,X_46)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)),multiply(X_44,least_upper_bound(X_46,X_45))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
multiply(X_44,least_upper_bound(X_46,X_45)) = multiply(X_44,least_upper_bound(X_45,X_46)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_44,X_46),multiply(X_44,X_45)),multiply(X_44,least_upper_bound(X_45,X_46))) )],[refute_0_364,refute_0_369]) ).
cnf(refute_0_371,plain,
( multiply(X_44,least_upper_bound(X_46,X_45)) != multiply(X_44,least_upper_bound(X_45,X_46))
| multiply(X_44,least_upper_bound(X_45,X_46)) = multiply(X_44,least_upper_bound(X_46,X_45)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_44,least_upper_bound(X_46,X_45)))),bind(Y0,$fot(multiply(X_44,least_upper_bound(X_45,X_46))))]]) ).
cnf(refute_0_372,plain,
multiply(X_44,least_upper_bound(X_45,X_46)) = multiply(X_44,least_upper_bound(X_46,X_45)),
inference(resolve,[$cnf( $equal(multiply(X_44,least_upper_bound(X_46,X_45)),multiply(X_44,least_upper_bound(X_45,X_46))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity)) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))),
inference(subst,[],[refute_0_372:[bind(X_44,$fot(X_17)),bind(X_45,$fot(least_upper_bound(X_55,identity))),bind(X_46,$fot(identity))]]) ).
cnf(refute_0_374,plain,
( multiply(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(X_44,multiply(X_44,X_45))
| least_upper_bound(X_44,multiply(X_44,X_45)) = multiply(X_44,least_upper_bound(X_45,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_44,least_upper_bound(X_45,identity)))),bind(Y0,$fot(least_upper_bound(X_44,multiply(X_44,X_45))))]]) ).
cnf(refute_0_375,plain,
least_upper_bound(X_44,multiply(X_44,X_45)) = multiply(X_44,least_upper_bound(X_45,identity)),
inference(resolve,[$cnf( $equal(multiply(X_44,least_upper_bound(X_45,identity)),least_upper_bound(X_44,multiply(X_44,X_45))) )],[refute_0_321,refute_0_374]) ).
cnf(refute_0_376,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity)),
inference(subst,[],[refute_0_375:[bind(X_44,$fot(X_17)),bind(X_45,$fot(least_upper_bound(X_55,identity)))]]) ).
cnf(refute_0_377,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) != multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))))),bind(Y0,$fot(multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity)))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))))]]) ).
cnf(refute_0_378,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))),multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(least_upper_bound(X_55,identity),identity)),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))) )],[refute_0_373,refute_0_378]) ).
cnf(refute_0_380,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) != multiply(X_17,least_upper_bound(identity,X_55))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,X_55)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))))),bind(Y0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,X_55))))]]) ).
cnf(refute_0_381,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))) != multiply(X_17,least_upper_bound(identity,X_55))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity)))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) = multiply(X_17,least_upper_bound(identity,X_55)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_55,identity))),multiply(X_17,least_upper_bound(identity,X_55))) )],[refute_0_357,refute_0_381]) ).
cnf(refute_0_383,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) != multiply(X_17,least_upper_bound(identity,X_55))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) != least_upper_bound(X_17,multiply(X_17,X_55))
| multiply(X_17,least_upper_bound(identity,X_55)) = least_upper_bound(X_17,multiply(X_17,X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))),least_upper_bound(X_17,multiply(X_17,X_55))) ),[0],$fot(multiply(X_17,least_upper_bound(identity,X_55)))]]) ).
cnf(refute_0_384,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) != least_upper_bound(X_17,multiply(X_17,X_55))
| multiply(X_17,least_upper_bound(identity,X_55)) = least_upper_bound(X_17,multiply(X_17,X_55)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))),multiply(X_17,least_upper_bound(identity,X_55))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
( multiply(X_17,least_upper_bound(identity,X_55)) != least_upper_bound(X_17,multiply(X_17,X_55))
| least_upper_bound(X_17,multiply(X_17,X_55)) != multiply(X_17,least_upper_bound(X_55,identity))
| multiply(X_17,least_upper_bound(identity,X_55)) = multiply(X_17,least_upper_bound(X_55,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_17,least_upper_bound(identity,X_55)),multiply(X_17,least_upper_bound(X_55,identity))) ),[0],$fot(least_upper_bound(X_17,multiply(X_17,X_55)))]]) ).
cnf(refute_0_386,plain,
( multiply(X_17,least_upper_bound(identity,X_55)) != least_upper_bound(X_17,multiply(X_17,X_55))
| multiply(X_17,least_upper_bound(identity,X_55)) = multiply(X_17,least_upper_bound(X_55,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,X_55)),multiply(X_17,least_upper_bound(X_55,identity))) )],[refute_0_349,refute_0_385]) ).
cnf(refute_0_387,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))) != least_upper_bound(X_17,multiply(X_17,X_55))
| multiply(X_17,least_upper_bound(identity,X_55)) = multiply(X_17,least_upper_bound(X_55,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,X_55)),least_upper_bound(X_17,multiply(X_17,X_55))) )],[refute_0_384,refute_0_386]) ).
cnf(refute_0_388,plain,
multiply(X_17,least_upper_bound(identity,X_55)) = multiply(X_17,least_upper_bound(X_55,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_55,identity))),least_upper_bound(X_17,multiply(X_17,X_55))) )],[refute_0_352,refute_0_387]) ).
cnf(refute_0_389,plain,
( multiply(X_17,least_upper_bound(identity,X_55)) != multiply(X_17,least_upper_bound(X_55,identity))
| multiply(X_17,least_upper_bound(X_55,identity)) = multiply(X_17,least_upper_bound(identity,X_55)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,least_upper_bound(identity,X_55)))),bind(Y0,$fot(multiply(X_17,least_upper_bound(X_55,identity))))]]) ).
cnf(refute_0_390,plain,
multiply(X_17,least_upper_bound(X_55,identity)) = multiply(X_17,least_upper_bound(identity,X_55)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,X_55)),multiply(X_17,least_upper_bound(X_55,identity))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
multiply(identity,least_upper_bound(inverse(X_65),identity)) = multiply(identity,least_upper_bound(identity,inverse(X_65))),
inference(subst,[],[refute_0_390:[bind(X_17,$fot(identity)),bind(X_55,$fot(inverse(X_65)))]]) ).
cnf(refute_0_392,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_65))) != least_upper_bound(identity,inverse(X_65))
| multiply(identity,least_upper_bound(inverse(X_65),identity)) != multiply(identity,least_upper_bound(identity,inverse(X_65)))
| multiply(identity,least_upper_bound(inverse(X_65),identity)) = least_upper_bound(identity,inverse(X_65)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(X_65),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(X_65))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_65))))]]) ).
cnf(refute_0_393,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_65))) != least_upper_bound(identity,inverse(X_65))
| multiply(identity,least_upper_bound(inverse(X_65),identity)) = least_upper_bound(identity,inverse(X_65)) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_65),identity)),multiply(identity,least_upper_bound(identity,inverse(X_65)))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
multiply(identity,least_upper_bound(inverse(X_65),identity)) = least_upper_bound(identity,inverse(X_65)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(X_65))),least_upper_bound(identity,inverse(X_65))) )],[refute_0_338,refute_0_393]) ).
cnf(refute_0_395,plain,
( multiply(identity,least_upper_bound(inverse(X_65),identity)) != multiply(least_upper_bound(identity,X_65),inverse(X_65))
| multiply(identity,least_upper_bound(inverse(X_65),identity)) != least_upper_bound(identity,inverse(X_65))
| least_upper_bound(identity,inverse(X_65)) = multiply(least_upper_bound(identity,X_65),inverse(X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_65),identity)),multiply(least_upper_bound(identity,X_65),inverse(X_65))) ),[0],$fot(least_upper_bound(identity,inverse(X_65)))]]) ).
cnf(refute_0_396,plain,
( multiply(identity,least_upper_bound(inverse(X_65),identity)) != multiply(least_upper_bound(identity,X_65),inverse(X_65))
| least_upper_bound(identity,inverse(X_65)) = multiply(least_upper_bound(identity,X_65),inverse(X_65)) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_65),identity)),least_upper_bound(identity,inverse(X_65))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
least_upper_bound(identity,inverse(X_65)) = multiply(least_upper_bound(identity,X_65),inverse(X_65)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_65),identity)),multiply(least_upper_bound(identity,X_65),inverse(X_65))) )],[refute_0_337,refute_0_396]) ).
cnf(refute_0_398,plain,
least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) = multiply(least_upper_bound(identity,least_upper_bound(Y,identity)),inverse(least_upper_bound(Y,identity))),
inference(subst,[],[refute_0_397:[bind(X_65,$fot(least_upper_bound(Y,identity)))]]) ).
cnf(refute_0_399,plain,
least_upper_bound(identity,least_upper_bound(Y,identity)) = least_upper_bound(identity,Y),
inference(subst,[],[refute_0_287:[bind(X_15,$fot(identity))]]) ).
cnf(refute_0_400,plain,
( least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) != multiply(least_upper_bound(identity,least_upper_bound(Y,identity)),inverse(least_upper_bound(Y,identity)))
| least_upper_bound(identity,least_upper_bound(Y,identity)) != least_upper_bound(identity,Y)
| least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) = multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),multiply(least_upper_bound(identity,least_upper_bound(Y,identity)),inverse(least_upper_bound(Y,identity)))) ),[1,0],$fot(least_upper_bound(identity,Y))]]) ).
cnf(refute_0_401,plain,
( least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) != multiply(least_upper_bound(identity,least_upper_bound(Y,identity)),inverse(least_upper_bound(Y,identity)))
| least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) = multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,identity)),least_upper_bound(identity,Y)) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) = multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),multiply(least_upper_bound(identity,least_upper_bound(Y,identity)),inverse(least_upper_bound(Y,identity)))) )],[refute_0_398,refute_0_401]) ).
cnf(refute_0_403,plain,
multiply(inverse(X_45),least_upper_bound(X_45,X_46)) = least_upper_bound(multiply(inverse(X_45),X_45),multiply(inverse(X_45),X_46)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).
cnf(refute_0_404,plain,
multiply(inverse(X_45),X_45) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_45))]]) ).
cnf(refute_0_405,plain,
( multiply(inverse(X_45),X_45) != identity
| multiply(inverse(X_45),least_upper_bound(X_45,X_46)) != least_upper_bound(multiply(inverse(X_45),X_45),multiply(inverse(X_45),X_46))
| multiply(inverse(X_45),least_upper_bound(X_45,X_46)) = least_upper_bound(identity,multiply(inverse(X_45),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_45),least_upper_bound(X_45,X_46)),least_upper_bound(multiply(inverse(X_45),X_45),multiply(inverse(X_45),X_46))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_406,plain,
( multiply(inverse(X_45),least_upper_bound(X_45,X_46)) != least_upper_bound(multiply(inverse(X_45),X_45),multiply(inverse(X_45),X_46))
| multiply(inverse(X_45),least_upper_bound(X_45,X_46)) = least_upper_bound(identity,multiply(inverse(X_45),X_46)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),X_45),identity) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
multiply(inverse(X_45),least_upper_bound(X_45,X_46)) = least_upper_bound(identity,multiply(inverse(X_45),X_46)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_45),least_upper_bound(X_45,X_46)),least_upper_bound(multiply(inverse(X_45),X_45),multiply(inverse(X_45),X_46))) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
multiply(inverse(X_51),least_upper_bound(X_51,identity)) = least_upper_bound(identity,multiply(inverse(X_51),identity)),
inference(subst,[],[refute_0_407:[bind(X_45,$fot(X_51)),bind(X_46,$fot(identity))]]) ).
cnf(refute_0_409,plain,
inverse(X_51) = multiply(inverse(X_51),identity),
inference(subst,[],[refute_0_82:[bind(X_31,$fot(inverse(X_51)))]]) ).
cnf(refute_0_410,plain,
( inverse(X_51) != multiply(inverse(X_51),identity)
| multiply(inverse(X_51),identity) = inverse(X_51) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_51))),bind(Y0,$fot(multiply(inverse(X_51),identity)))]]) ).
cnf(refute_0_411,plain,
multiply(inverse(X_51),identity) = inverse(X_51),
inference(resolve,[$cnf( $equal(inverse(X_51),multiply(inverse(X_51),identity)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
( multiply(inverse(X_51),identity) != inverse(X_51)
| multiply(inverse(X_51),least_upper_bound(X_51,identity)) != least_upper_bound(identity,multiply(inverse(X_51),identity))
| multiply(inverse(X_51),least_upper_bound(X_51,identity)) = least_upper_bound(identity,inverse(X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(X_51,identity)),least_upper_bound(identity,multiply(inverse(X_51),identity))) ),[1,1],$fot(inverse(X_51))]]) ).
cnf(refute_0_413,plain,
( multiply(inverse(X_51),least_upper_bound(X_51,identity)) != least_upper_bound(identity,multiply(inverse(X_51),identity))
| multiply(inverse(X_51),least_upper_bound(X_51,identity)) = least_upper_bound(identity,inverse(X_51)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),identity),inverse(X_51)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
multiply(inverse(X_51),least_upper_bound(X_51,identity)) = least_upper_bound(identity,inverse(X_51)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(X_51,identity)),least_upper_bound(identity,multiply(inverse(X_51),identity))) )],[refute_0_408,refute_0_413]) ).
cnf(refute_0_415,plain,
multiply(inverse(X_53),least_upper_bound(X_53,identity)) = least_upper_bound(identity,inverse(X_53)),
inference(subst,[],[refute_0_414:[bind(X_51,$fot(X_53))]]) ).
cnf(refute_0_416,plain,
least_upper_bound(identity,X_53) = least_upper_bound(X_53,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_53))]]) ).
cnf(refute_0_417,plain,
( least_upper_bound(identity,X_53) != least_upper_bound(X_53,identity)
| least_upper_bound(X_53,identity) = least_upper_bound(identity,X_53) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,X_53))),bind(Y0,$fot(least_upper_bound(X_53,identity)))]]) ).
cnf(refute_0_418,plain,
least_upper_bound(X_53,identity) = least_upper_bound(identity,X_53),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_53),least_upper_bound(X_53,identity)) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
( multiply(inverse(X_53),least_upper_bound(X_53,identity)) != least_upper_bound(identity,inverse(X_53))
| least_upper_bound(X_53,identity) != least_upper_bound(identity,X_53)
| multiply(inverse(X_53),least_upper_bound(identity,X_53)) = least_upper_bound(identity,inverse(X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_53),least_upper_bound(X_53,identity)),least_upper_bound(identity,inverse(X_53))) ),[0,1],$fot(least_upper_bound(identity,X_53))]]) ).
cnf(refute_0_420,plain,
( multiply(inverse(X_53),least_upper_bound(X_53,identity)) != least_upper_bound(identity,inverse(X_53))
| multiply(inverse(X_53),least_upper_bound(identity,X_53)) = least_upper_bound(identity,inverse(X_53)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,identity),least_upper_bound(identity,X_53)) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
multiply(inverse(X_53),least_upper_bound(identity,X_53)) = least_upper_bound(identity,inverse(X_53)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_53),least_upper_bound(X_53,identity)),least_upper_bound(identity,inverse(X_53))) )],[refute_0_415,refute_0_420]) ).
cnf(refute_0_422,plain,
multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))),
inference(subst,[],[refute_0_421:[bind(X_53,$fot(least_upper_bound(identity,X_16)))]]) ).
cnf(refute_0_423,plain,
least_upper_bound(identity,least_upper_bound(identity,X_16)) = least_upper_bound(identity,X_16),
inference(subst,[],[refute_0_345:[bind(X_17,$fot(identity))]]) ).
cnf(refute_0_424,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| least_upper_bound(identity,least_upper_bound(identity,X_16)) != least_upper_bound(identity,X_16)
| multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) ),[0,1],$fot(least_upper_bound(identity,X_16))]]) ).
cnf(refute_0_425,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) )],[refute_0_422,refute_0_425]) ).
cnf(refute_0_427,plain,
multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(identity,X_16)))]]) ).
cnf(refute_0_428,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) != identity
| multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_429,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)),identity) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) )],[refute_0_426,refute_0_429]) ).
cnf(refute_0_431,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(identity,X_45)))),
inference(subst,[],[refute_0_430:[bind(X_16,$fot(multiply(identity,X_45)))]]) ).
cnf(refute_0_432,plain,
multiply(identity,least_upper_bound(X_45,identity)) = least_upper_bound(identity,multiply(identity,X_45)),
inference(subst,[],[refute_0_321:[bind(X_44,$fot(identity))]]) ).
cnf(refute_0_433,plain,
( multiply(identity,least_upper_bound(X_45,identity)) != least_upper_bound(identity,multiply(identity,X_45))
| least_upper_bound(identity,multiply(identity,X_45)) = multiply(identity,least_upper_bound(X_45,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(identity,least_upper_bound(X_45,identity)))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,X_45))))]]) ).
cnf(refute_0_434,plain,
least_upper_bound(identity,multiply(identity,X_45)) = multiply(identity,least_upper_bound(X_45,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_45,identity)),least_upper_bound(identity,multiply(identity,X_45))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(identity,X_45))))
| least_upper_bound(identity,multiply(identity,X_45)) != multiply(identity,least_upper_bound(X_45,identity))
| identity = least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(identity,X_45))))) ),[1,1,0],$fot(multiply(identity,least_upper_bound(X_45,identity)))]]) ).
cnf(refute_0_436,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(identity,X_45))))
| identity = least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_45)),multiply(identity,least_upper_bound(X_45,identity))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
identity = least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(identity,X_45))))) )],[refute_0_431,refute_0_436]) ).
cnf(refute_0_438,plain,
multiply(identity,least_upper_bound(X_45,identity)) = least_upper_bound(X_45,identity),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_45,identity)))]]) ).
cnf(refute_0_439,plain,
inverse(multiply(identity,least_upper_bound(X_45,identity))) = inverse(multiply(identity,least_upper_bound(X_45,identity))),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,least_upper_bound(X_45,identity))))]]) ).
cnf(refute_0_440,plain,
( multiply(identity,least_upper_bound(X_45,identity)) != least_upper_bound(X_45,identity)
| inverse(multiply(identity,least_upper_bound(X_45,identity))) != inverse(multiply(identity,least_upper_bound(X_45,identity)))
| inverse(multiply(identity,least_upper_bound(X_45,identity))) = inverse(least_upper_bound(X_45,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_45,identity))),inverse(multiply(identity,least_upper_bound(X_45,identity)))) ),[1,0],$fot(least_upper_bound(X_45,identity))]]) ).
cnf(refute_0_441,plain,
( multiply(identity,least_upper_bound(X_45,identity)) != least_upper_bound(X_45,identity)
| inverse(multiply(identity,least_upper_bound(X_45,identity))) = inverse(least_upper_bound(X_45,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_45,identity))),inverse(multiply(identity,least_upper_bound(X_45,identity)))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
inverse(multiply(identity,least_upper_bound(X_45,identity))) = inverse(least_upper_bound(X_45,identity)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_45,identity)),least_upper_bound(X_45,identity)) )],[refute_0_438,refute_0_441]) ).
cnf(refute_0_443,plain,
least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) = least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))))]]) ).
cnf(refute_0_444,plain,
( inverse(multiply(identity,least_upper_bound(X_45,identity))) != inverse(least_upper_bound(X_45,identity))
| least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) != least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity))))
| least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) = least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))),least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity))))) ),[1,1],$fot(inverse(least_upper_bound(X_45,identity)))]]) ).
cnf(refute_0_445,plain,
( inverse(multiply(identity,least_upper_bound(X_45,identity))) != inverse(least_upper_bound(X_45,identity))
| least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) = least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))),least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity))))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) = least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_45,identity))) )],[refute_0_442,refute_0_445]) ).
cnf(refute_0_447,plain,
( identity != least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity))))
| least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))) != least_upper_bound(identity,inverse(least_upper_bound(X_45,identity)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(X_45,identity)))) ),[0],$fot(least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))))]]) ).
cnf(refute_0_448,plain,
( identity != least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity))))
| identity = least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity)))),least_upper_bound(identity,inverse(least_upper_bound(X_45,identity)))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(multiply(identity,least_upper_bound(X_45,identity))))) )],[refute_0_437,refute_0_448]) ).
cnf(refute_0_450,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(X_45,identity)))
| least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(X_45,identity)))))]]) ).
cnf(refute_0_451,plain,
least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(X_45,identity)))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) = identity,
inference(subst,[],[refute_0_451:[bind(X_45,$fot(Y))]]) ).
cnf(refute_0_453,plain,
( least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) != multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity)))
| least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) != identity
| identity = multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_454,plain,
( least_upper_bound(identity,inverse(least_upper_bound(Y,identity))) != multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity)))
| identity = multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),identity) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
identity = multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(Y,identity))),multiply(least_upper_bound(identity,Y),inverse(least_upper_bound(Y,identity)))) )],[refute_0_402,refute_0_454]) ).
cnf(refute_0_456,plain,
identity = multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))),
inference(subst,[],[refute_0_455:[bind(Y,$fot(X_69))]]) ).
cnf(refute_0_457,plain,
( identity != multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity)))
| multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity)))))]]) ).
cnf(refute_0_458,plain,
multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity)))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
( multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))) != identity
| inverse(least_upper_bound(X_69,identity)) != multiply(inverse(least_upper_bound(identity,X_69)),multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))))
| inverse(least_upper_bound(X_69,identity)) = multiply(inverse(least_upper_bound(identity,X_69)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_69,identity)),multiply(inverse(least_upper_bound(identity,X_69)),multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_460,plain,
( inverse(least_upper_bound(X_69,identity)) != multiply(inverse(least_upper_bound(identity,X_69)),multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))))
| inverse(least_upper_bound(X_69,identity)) = multiply(inverse(least_upper_bound(identity,X_69)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))),identity) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
inverse(least_upper_bound(X_69,identity)) = multiply(inverse(least_upper_bound(identity,X_69)),identity),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_69,identity)),multiply(inverse(least_upper_bound(identity,X_69)),multiply(least_upper_bound(identity,X_69),inverse(least_upper_bound(X_69,identity))))) )],[refute_0_310,refute_0_460]) ).
cnf(refute_0_462,plain,
multiply(inverse(least_upper_bound(identity,X_69)),identity) = inverse(least_upper_bound(identity,X_69)),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(inverse(least_upper_bound(identity,X_69))))]]) ).
cnf(refute_0_463,plain,
( multiply(inverse(least_upper_bound(identity,X_69)),identity) != inverse(least_upper_bound(identity,X_69))
| inverse(least_upper_bound(X_69,identity)) != multiply(inverse(least_upper_bound(identity,X_69)),identity)
| inverse(least_upper_bound(X_69,identity)) = inverse(least_upper_bound(identity,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_69,identity)),multiply(inverse(least_upper_bound(identity,X_69)),identity)) ),[1],$fot(inverse(least_upper_bound(identity,X_69)))]]) ).
cnf(refute_0_464,plain,
( inverse(least_upper_bound(X_69,identity)) != multiply(inverse(least_upper_bound(identity,X_69)),identity)
| inverse(least_upper_bound(X_69,identity)) = inverse(least_upper_bound(identity,X_69)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_69)),identity),inverse(least_upper_bound(identity,X_69))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
inverse(least_upper_bound(X_69,identity)) = inverse(least_upper_bound(identity,X_69)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_69,identity)),multiply(inverse(least_upper_bound(identity,X_69)),identity)) )],[refute_0_461,refute_0_464]) ).
cnf(refute_0_466,plain,
inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) = inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))),
inference(subst,[],[refute_0_465:[bind(X_69,$fot(multiply(X_181,inverse(X_180))))]]) ).
cnf(refute_0_467,plain,
multiply(least_upper_bound(X_60,X_61),inverse(X_60)) = least_upper_bound(multiply(X_60,inverse(X_60)),multiply(X_61,inverse(X_60))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_60))),bind(Y,$fot(X_60)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_468,plain,
multiply(X_60,inverse(X_60)) = identity,
inference(subst,[],[refute_0_32:[bind(X_33,$fot(X_60))]]) ).
cnf(refute_0_469,plain,
( multiply(X_60,inverse(X_60)) != identity
| multiply(least_upper_bound(X_60,X_61),inverse(X_60)) != least_upper_bound(multiply(X_60,inverse(X_60)),multiply(X_61,inverse(X_60)))
| multiply(least_upper_bound(X_60,X_61),inverse(X_60)) = least_upper_bound(identity,multiply(X_61,inverse(X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_60,X_61),inverse(X_60)),least_upper_bound(multiply(X_60,inverse(X_60)),multiply(X_61,inverse(X_60)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_470,plain,
( multiply(least_upper_bound(X_60,X_61),inverse(X_60)) != least_upper_bound(multiply(X_60,inverse(X_60)),multiply(X_61,inverse(X_60)))
| multiply(least_upper_bound(X_60,X_61),inverse(X_60)) = least_upper_bound(identity,multiply(X_61,inverse(X_60))) ),
inference(resolve,[$cnf( $equal(multiply(X_60,inverse(X_60)),identity) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
multiply(least_upper_bound(X_60,X_61),inverse(X_60)) = least_upper_bound(identity,multiply(X_61,inverse(X_60))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,X_61),inverse(X_60)),least_upper_bound(multiply(X_60,inverse(X_60)),multiply(X_61,inverse(X_60)))) )],[refute_0_467,refute_0_470]) ).
cnf(refute_0_472,plain,
multiply(least_upper_bound(X_180,X_181),inverse(X_180)) = least_upper_bound(identity,multiply(X_181,inverse(X_180))),
inference(subst,[],[refute_0_471:[bind(X_60,$fot(X_180)),bind(X_61,$fot(X_181))]]) ).
cnf(refute_0_473,plain,
( multiply(least_upper_bound(X_180,X_181),inverse(X_180)) != least_upper_bound(identity,multiply(X_181,inverse(X_180)))
| least_upper_bound(identity,multiply(X_181,inverse(X_180))) = multiply(least_upper_bound(X_180,X_181),inverse(X_180)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_181,inverse(X_180)))))]]) ).
cnf(refute_0_474,plain,
least_upper_bound(identity,multiply(X_181,inverse(X_180))) = multiply(least_upper_bound(X_180,X_181),inverse(X_180)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,X_181),inverse(X_180)),least_upper_bound(identity,multiply(X_181,inverse(X_180)))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
( inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) != inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180))))
| least_upper_bound(identity,multiply(X_181,inverse(X_180))) != multiply(least_upper_bound(X_180,X_181),inverse(X_180))
| inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) = inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)),inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180))))) ),[1,0],$fot(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))]]) ).
cnf(refute_0_476,plain,
( inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) != inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180))))
| inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) = inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_181,inverse(X_180))),multiply(least_upper_bound(X_180,X_181),inverse(X_180))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) = inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)),inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180))))) )],[refute_0_466,refute_0_476]) ).
cnf(refute_0_478,plain,
( inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) != inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))
| inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) != inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180))))
| inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) = inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)),inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))) ),[0],$fot(inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))))]]) ).
cnf(refute_0_479,plain,
( inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)) != inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))
| inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) = inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)),inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180))))) )],[refute_0_466,refute_0_478]) ).
cnf(refute_0_480,plain,
inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) = inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X_181,inverse(X_180)),identity)),inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))) )],[refute_0_477,refute_0_479]) ).
cnf(refute_0_481,plain,
X_29 = multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29)),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(inverse(X_33)))]]) ).
cnf(refute_0_482,plain,
multiply(X_33,multiply(inverse(X_33),X_29)) = multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29)),
inference(subst,[],[refute_0_26:[bind(X_30,$fot(X_33)),bind(X_31,$fot(multiply(inverse(X_33),X_29)))]]) ).
cnf(refute_0_483,plain,
( multiply(X_33,multiply(inverse(X_33),X_29)) != multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29))
| multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29)) = multiply(X_33,multiply(inverse(X_33),X_29)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_33,multiply(inverse(X_33),X_29)))),bind(Y0,$fot(multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29))))]]) ).
cnf(refute_0_484,plain,
multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29)) = multiply(X_33,multiply(inverse(X_33),X_29)),
inference(resolve,[$cnf( $equal(multiply(X_33,multiply(inverse(X_33),X_29)),multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
( X_29 != multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29))
| multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29)) != multiply(X_33,multiply(inverse(X_33),X_29))
| X_29 = multiply(X_33,multiply(inverse(X_33),X_29)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_29,multiply(X_33,multiply(inverse(X_33),X_29))) ),[0],$fot(multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29)))]]) ).
cnf(refute_0_486,plain,
( X_29 != multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29))
| X_29 = multiply(X_33,multiply(inverse(X_33),X_29)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29)),multiply(X_33,multiply(inverse(X_33),X_29))) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
X_29 = multiply(X_33,multiply(inverse(X_33),X_29)),
inference(resolve,[$cnf( $equal(X_29,multiply(inverse(inverse(X_33)),multiply(inverse(X_33),X_29))) )],[refute_0_481,refute_0_486]) ).
cnf(refute_0_488,plain,
inverse(multiply(X_196,inverse(X_33))) = multiply(X_33,multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33))))),
inference(subst,[],[refute_0_487:[bind(X_29,$fot(inverse(multiply(X_196,inverse(X_33)))))]]) ).
cnf(refute_0_489,plain,
multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33)))) = inverse(X_196),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(X_196)),bind(X_38,$fot(inverse(X_33)))]]) ).
cnf(refute_0_490,plain,
( multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33)))) != inverse(X_196)
| inverse(multiply(X_196,inverse(X_33))) != multiply(X_33,multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33)))))
| inverse(multiply(X_196,inverse(X_33))) = multiply(X_33,inverse(X_196)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_196,inverse(X_33))),multiply(X_33,multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33)))))) ),[1,1],$fot(inverse(X_196))]]) ).
cnf(refute_0_491,plain,
( inverse(multiply(X_196,inverse(X_33))) != multiply(X_33,multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33)))))
| inverse(multiply(X_196,inverse(X_33))) = multiply(X_33,inverse(X_196)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33)))),inverse(X_196)) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
inverse(multiply(X_196,inverse(X_33))) = multiply(X_33,inverse(X_196)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_196,inverse(X_33))),multiply(X_33,multiply(inverse(X_33),inverse(multiply(X_196,inverse(X_33)))))) )],[refute_0_488,refute_0_491]) ).
cnf(refute_0_493,plain,
inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))) = multiply(X_180,inverse(least_upper_bound(X_180,X_181))),
inference(subst,[],[refute_0_492:[bind(X_196,$fot(least_upper_bound(X_180,X_181))),bind(X_33,$fot(X_180))]]) ).
cnf(refute_0_494,plain,
( inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))) != multiply(X_180,inverse(least_upper_bound(X_180,X_181)))
| inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) != inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))
| inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) = multiply(X_180,inverse(least_upper_bound(X_180,X_181))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))),inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))) ),[1],$fot(multiply(X_180,inverse(least_upper_bound(X_180,X_181))))]]) ).
cnf(refute_0_495,plain,
( inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) != inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))
| inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) = multiply(X_180,inverse(least_upper_bound(X_180,X_181))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180))),multiply(X_180,inverse(least_upper_bound(X_180,X_181)))) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) = multiply(X_180,inverse(least_upper_bound(X_180,X_181))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))),inverse(multiply(least_upper_bound(X_180,X_181),inverse(X_180)))) )],[refute_0_480,refute_0_495]) ).
cnf(refute_0_497,plain,
inverse(multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))) = multiply(greatest_lower_bound(identity,X_196),inverse(X_196)),
inference(subst,[],[refute_0_492:[bind(X_33,$fot(greatest_lower_bound(identity,X_196)))]]) ).
cnf(refute_0_498,plain,
inverse(multiply(greatest_lower_bound(identity,X_202),inverse(X_202))) = multiply(X_202,inverse(greatest_lower_bound(identity,X_202))),
inference(subst,[],[refute_0_492:[bind(X_196,$fot(greatest_lower_bound(identity,X_202))),bind(X_33,$fot(X_202))]]) ).
cnf(refute_0_499,plain,
multiply(greatest_lower_bound(identity,X_105),inverse(X_105)) = greatest_lower_bound(identity,multiply(identity,inverse(X_105))),
inference(subst,[],[refute_0_185:[bind(X_98,$fot(identity)),bind(X_99,$fot(X_105))]]) ).
cnf(refute_0_500,plain,
multiply(identity,inverse(X_105)) = inverse(X_105),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_105)))]]) ).
cnf(refute_0_501,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(X_105)) != greatest_lower_bound(identity,multiply(identity,inverse(X_105)))
| multiply(identity,inverse(X_105)) != inverse(X_105)
| multiply(greatest_lower_bound(identity,X_105),inverse(X_105)) = greatest_lower_bound(identity,inverse(X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)),greatest_lower_bound(identity,multiply(identity,inverse(X_105)))) ),[1,1],$fot(inverse(X_105))]]) ).
cnf(refute_0_502,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(X_105)) != greatest_lower_bound(identity,multiply(identity,inverse(X_105)))
| multiply(greatest_lower_bound(identity,X_105),inverse(X_105)) = greatest_lower_bound(identity,inverse(X_105)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_105)),inverse(X_105)) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
multiply(greatest_lower_bound(identity,X_105),inverse(X_105)) = greatest_lower_bound(identity,inverse(X_105)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)),greatest_lower_bound(identity,multiply(identity,inverse(X_105)))) )],[refute_0_499,refute_0_502]) ).
cnf(refute_0_504,plain,
multiply(greatest_lower_bound(identity,X_202),inverse(X_202)) = greatest_lower_bound(identity,inverse(X_202)),
inference(subst,[],[refute_0_503:[bind(X_105,$fot(X_202))]]) ).
cnf(refute_0_505,plain,
( multiply(greatest_lower_bound(identity,X_202),inverse(X_202)) != greatest_lower_bound(identity,inverse(X_202))
| inverse(multiply(greatest_lower_bound(identity,X_202),inverse(X_202))) != multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))
| inverse(greatest_lower_bound(identity,inverse(X_202))) = multiply(X_202,inverse(greatest_lower_bound(identity,X_202))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_202),inverse(X_202))),multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_202)))]]) ).
cnf(refute_0_506,plain,
( inverse(multiply(greatest_lower_bound(identity,X_202),inverse(X_202))) != multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))
| inverse(greatest_lower_bound(identity,inverse(X_202))) = multiply(X_202,inverse(greatest_lower_bound(identity,X_202))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_202),inverse(X_202)),greatest_lower_bound(identity,inverse(X_202))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
inverse(greatest_lower_bound(identity,inverse(X_202))) = multiply(X_202,inverse(greatest_lower_bound(identity,X_202))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_202),inverse(X_202))),multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))) )],[refute_0_498,refute_0_506]) ).
cnf(refute_0_508,plain,
X_29 = multiply(inverse(least_upper_bound(X_63,inverse(X_29))),multiply(least_upper_bound(X_63,inverse(X_29)),X_29)),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(least_upper_bound(X_63,inverse(X_29))))]]) ).
cnf(refute_0_509,plain,
multiply(least_upper_bound(X_60,inverse(X_59)),X_59) = least_upper_bound(multiply(X_60,X_59),multiply(inverse(X_59),X_59)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_59)),bind(Y,$fot(X_60)),bind(Z,$fot(inverse(X_59)))]]) ).
cnf(refute_0_510,plain,
multiply(inverse(X_59),X_59) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_511,plain,
( multiply(inverse(X_59),X_59) != identity
| multiply(least_upper_bound(X_60,inverse(X_59)),X_59) != least_upper_bound(multiply(X_60,X_59),multiply(inverse(X_59),X_59))
| multiply(least_upper_bound(X_60,inverse(X_59)),X_59) = least_upper_bound(multiply(X_60,X_59),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_60,inverse(X_59)),X_59),least_upper_bound(multiply(X_60,X_59),multiply(inverse(X_59),X_59))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_512,plain,
( multiply(least_upper_bound(X_60,inverse(X_59)),X_59) != least_upper_bound(multiply(X_60,X_59),multiply(inverse(X_59),X_59))
| multiply(least_upper_bound(X_60,inverse(X_59)),X_59) = least_upper_bound(multiply(X_60,X_59),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),X_59),identity) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
multiply(least_upper_bound(X_60,inverse(X_59)),X_59) = least_upper_bound(multiply(X_60,X_59),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,inverse(X_59)),X_59),least_upper_bound(multiply(X_60,X_59),multiply(inverse(X_59),X_59))) )],[refute_0_509,refute_0_512]) ).
cnf(refute_0_514,plain,
least_upper_bound(multiply(X_60,X_59),identity) = least_upper_bound(identity,multiply(X_60,X_59)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_60,X_59)))]]) ).
cnf(refute_0_515,plain,
( multiply(least_upper_bound(X_60,inverse(X_59)),X_59) != least_upper_bound(multiply(X_60,X_59),identity)
| least_upper_bound(multiply(X_60,X_59),identity) != least_upper_bound(identity,multiply(X_60,X_59))
| multiply(least_upper_bound(X_60,inverse(X_59)),X_59) = least_upper_bound(identity,multiply(X_60,X_59)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_60,inverse(X_59)),X_59),least_upper_bound(identity,multiply(X_60,X_59))) ),[0],$fot(least_upper_bound(multiply(X_60,X_59),identity))]]) ).
cnf(refute_0_516,plain,
( multiply(least_upper_bound(X_60,inverse(X_59)),X_59) != least_upper_bound(multiply(X_60,X_59),identity)
| multiply(least_upper_bound(X_60,inverse(X_59)),X_59) = least_upper_bound(identity,multiply(X_60,X_59)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_60,X_59),identity),least_upper_bound(identity,multiply(X_60,X_59))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
multiply(least_upper_bound(X_60,inverse(X_59)),X_59) = least_upper_bound(identity,multiply(X_60,X_59)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,inverse(X_59)),X_59),least_upper_bound(multiply(X_60,X_59),identity)) )],[refute_0_513,refute_0_516]) ).
cnf(refute_0_518,plain,
multiply(least_upper_bound(X_63,inverse(X_29)),X_29) = least_upper_bound(identity,multiply(X_63,X_29)),
inference(subst,[],[refute_0_517:[bind(X_59,$fot(X_29)),bind(X_60,$fot(X_63))]]) ).
cnf(refute_0_519,plain,
( X_29 != multiply(inverse(least_upper_bound(X_63,inverse(X_29))),multiply(least_upper_bound(X_63,inverse(X_29)),X_29))
| multiply(least_upper_bound(X_63,inverse(X_29)),X_29) != least_upper_bound(identity,multiply(X_63,X_29))
| X_29 = multiply(inverse(least_upper_bound(X_63,inverse(X_29))),least_upper_bound(identity,multiply(X_63,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(X_29,multiply(inverse(least_upper_bound(X_63,inverse(X_29))),multiply(least_upper_bound(X_63,inverse(X_29)),X_29))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_63,X_29)))]]) ).
cnf(refute_0_520,plain,
( X_29 != multiply(inverse(least_upper_bound(X_63,inverse(X_29))),multiply(least_upper_bound(X_63,inverse(X_29)),X_29))
| X_29 = multiply(inverse(least_upper_bound(X_63,inverse(X_29))),least_upper_bound(identity,multiply(X_63,X_29))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_63,inverse(X_29)),X_29),least_upper_bound(identity,multiply(X_63,X_29))) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
X_29 = multiply(inverse(least_upper_bound(X_63,inverse(X_29))),least_upper_bound(identity,multiply(X_63,X_29))),
inference(resolve,[$cnf( $equal(X_29,multiply(inverse(least_upper_bound(X_63,inverse(X_29))),multiply(least_upper_bound(X_63,inverse(X_29)),X_29))) )],[refute_0_508,refute_0_520]) ).
cnf(refute_0_522,plain,
inverse(greatest_lower_bound(identity,inverse(X_232))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232)))))),
inference(subst,[],[refute_0_521:[bind(X_29,$fot(inverse(greatest_lower_bound(identity,inverse(X_232))))),bind(X_63,$fot(greatest_lower_bound(X_232,identity)))]]) ).
cnf(refute_0_523,plain,
multiply(greatest_lower_bound(X_87,identity),inverse(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)))) = inverse(inverse(X_87)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(inverse(X_87))),bind(X_38,$fot(greatest_lower_bound(X_87,identity)))]]) ).
cnf(refute_0_524,plain,
multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = greatest_lower_bound(identity,multiply(inverse(X_87),greatest_lower_bound(identity,X_87))),
inference(subst,[],[refute_0_98:[bind(X_86,$fot(greatest_lower_bound(identity,X_87)))]]) ).
cnf(refute_0_525,plain,
multiply(inverse(X_87),greatest_lower_bound(identity,X_87)) = greatest_lower_bound(identity,inverse(X_87)),
inference(subst,[],[refute_0_105:[bind(X_93,$fot(X_87))]]) ).
cnf(refute_0_526,plain,
( multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) != greatest_lower_bound(identity,multiply(inverse(X_87),greatest_lower_bound(identity,X_87)))
| multiply(inverse(X_87),greatest_lower_bound(identity,X_87)) != greatest_lower_bound(identity,inverse(X_87))
| multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)),greatest_lower_bound(identity,multiply(inverse(X_87),greatest_lower_bound(identity,X_87)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_87)))]]) ).
cnf(refute_0_527,plain,
( multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) != greatest_lower_bound(identity,multiply(inverse(X_87),greatest_lower_bound(identity,X_87)))
| multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(identity,X_87)),greatest_lower_bound(identity,inverse(X_87))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)),greatest_lower_bound(identity,multiply(inverse(X_87),greatest_lower_bound(identity,X_87)))) )],[refute_0_524,refute_0_527]) ).
cnf(refute_0_529,plain,
greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)) = greatest_lower_bound(X_87,identity),
inference(subst,[],[refute_0_153:[bind(X_13,$fot(identity)),bind(X_9,$fot(X_87))]]) ).
cnf(refute_0_530,plain,
multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))) = multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))))]]) ).
cnf(refute_0_531,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))) != multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)))
| greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)) != greatest_lower_bound(X_87,identity)
| multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))) = multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))),multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)))) ),[1,1],$fot(greatest_lower_bound(X_87,identity))]]) ).
cnf(refute_0_532,plain,
( greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)) != greatest_lower_bound(X_87,identity)
| multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))) = multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))),multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))) = multiply(inverse(X_87),greatest_lower_bound(X_87,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)),greatest_lower_bound(X_87,identity)) )],[refute_0_529,refute_0_532]) ).
cnf(refute_0_534,plain,
least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13))) = greatest_lower_bound(X_23,X_13),
inference(subst,[],[refute_0_267:[bind(X_12,$fot(greatest_lower_bound(X_23,X_13)))]]) ).
cnf(refute_0_535,plain,
greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13)) = greatest_lower_bound(X_13,X_23),
inference(subst,[],[refute_0_153:[bind(X_13,$fot(X_23)),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_536,plain,
( greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13)) != greatest_lower_bound(X_13,X_23)
| least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13))) != greatest_lower_bound(X_23,X_13)
| least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23)) = greatest_lower_bound(X_23,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13))),greatest_lower_bound(X_23,X_13)) ),[0,1],$fot(greatest_lower_bound(X_13,X_23))]]) ).
cnf(refute_0_537,plain,
( least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13))) != greatest_lower_bound(X_23,X_13)
| least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23)) = greatest_lower_bound(X_23,X_13) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13)),greatest_lower_bound(X_13,X_23)) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23)) = greatest_lower_bound(X_23,X_13),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,greatest_lower_bound(X_23,X_13))),greatest_lower_bound(X_23,X_13)) )],[refute_0_534,refute_0_537]) ).
cnf(refute_0_539,plain,
least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))) = greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),
inference(subst,[],[refute_0_538:[bind(X_13,$fot(multiply(X_85,X_86))),bind(X_23,$fot(multiply(X_85,X_87)))]]) ).
cnf(refute_0_540,plain,
multiply(X_85,greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_85)),bind(Y,$fot(X_86)),bind(Z,$fot(X_87))]]) ).
cnf(refute_0_541,plain,
( multiply(X_85,greatest_lower_bound(X_86,X_87)) != greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))
| greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87)) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_85,greatest_lower_bound(X_86,X_87)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))))]]) ).
cnf(refute_0_542,plain,
greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87)) = multiply(X_85,greatest_lower_bound(X_86,X_87)),
inference(resolve,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
( greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87)) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))) != greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))
| least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) = greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) ),[0,1],$fot(multiply(X_85,greatest_lower_bound(X_86,X_87)))]]) ).
cnf(refute_0_544,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))) != greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))
| least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) = greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87)),multiply(X_85,greatest_lower_bound(X_86,X_87))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) = greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,X_87))),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) )],[refute_0_539,refute_0_544]) ).
cnf(refute_0_546,plain,
least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)) = greatest_lower_bound(X_86,X_87),
inference(subst,[],[refute_0_538:[bind(X_13,$fot(X_87)),bind(X_23,$fot(X_86))]]) ).
cnf(refute_0_547,plain,
multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))) = multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))),
introduced(tautology,[refl,[$fot(multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))))]]) ).
cnf(refute_0_548,plain,
( multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))) != multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)))
| least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)) != greatest_lower_bound(X_86,X_87)
| multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))),multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)))) ),[1,1],$fot(greatest_lower_bound(X_86,X_87))]]) ).
cnf(refute_0_549,plain,
( least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)) != greatest_lower_bound(X_86,X_87)
| multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(resolve,[$cnf( $equal(multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))),multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)),greatest_lower_bound(X_86,X_87)) )],[refute_0_546,refute_0_549]) ).
cnf(refute_0_551,plain,
least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) = multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))),
inference(subst,[],[refute_0_366:[bind(X,$fot(X_85)),bind(Y,$fot(greatest_lower_bound(X_86,X_87))),bind(Z,$fot(greatest_lower_bound(X_87,X_86)))]]) ).
cnf(refute_0_552,plain,
( multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) != multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))))),bind(Y0,$fot(multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))))),bind(Z0,$fot(multiply(X_85,greatest_lower_bound(X_86,X_87))))]]) ).
cnf(refute_0_553,plain,
( multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))),multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86)))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)),
inference(resolve,[$cnf( $equal(multiply(X_85,least_upper_bound(greatest_lower_bound(X_86,X_87),greatest_lower_bound(X_87,X_86))),multiply(X_85,greatest_lower_bound(X_86,X_87))) )],[refute_0_550,refute_0_553]) ).
cnf(refute_0_555,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_556,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_555]) ).
cnf(refute_0_557,plain,
greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) = multiply(X_85,greatest_lower_bound(X_87,X_86)),
inference(subst,[],[refute_0_556:[bind(X,$fot(X_85)),bind(Y,$fot(X_87)),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_558,plain,
least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) = least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))))]]) ).
cnf(refute_0_559,plain,
( greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) != multiply(X_85,greatest_lower_bound(X_87,X_86))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) != least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) = least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))),least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)))) ),[1,1],$fot(multiply(X_85,greatest_lower_bound(X_87,X_86)))]]) ).
cnf(refute_0_560,plain,
( greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) != multiply(X_85,greatest_lower_bound(X_87,X_86))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) = least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))),least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) = least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_87,X_86))) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
( least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) != least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86)))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))))),bind(Y0,$fot(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))))),bind(Z0,$fot(multiply(X_85,greatest_lower_bound(X_86,X_87))))]]) ).
cnf(refute_0_563,plain,
( least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))),least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86)))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) = multiply(X_85,greatest_lower_bound(X_86,X_87)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))),multiply(X_85,greatest_lower_bound(X_86,X_87))) )],[refute_0_554,refute_0_563]) ).
cnf(refute_0_565,plain,
least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) = least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(X_85,greatest_lower_bound(X_86,X_87)))),bind(Y,$fot(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))))]]) ).
cnf(refute_0_566,plain,
( least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) != least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)))
| least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))))),bind(Y0,$fot(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))))),bind(Z0,$fot(multiply(X_85,greatest_lower_bound(X_86,X_87))))]]) ).
cnf(refute_0_567,plain,
( least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))),least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) = multiply(X_85,greatest_lower_bound(X_86,X_87)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))),multiply(X_85,greatest_lower_bound(X_86,X_87))) )],[refute_0_564,refute_0_567]) ).
cnf(refute_0_569,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) != multiply(X_85,greatest_lower_bound(X_86,X_87))
| least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) != greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))
| multiply(X_85,greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) ),[0],$fot(multiply(X_85,greatest_lower_bound(X_86,X_87)))]]) ).
cnf(refute_0_570,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) != greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))
| multiply(X_85,greatest_lower_bound(X_86,X_87)) = greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))),multiply(X_85,greatest_lower_bound(X_86,X_87))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
( multiply(X_85,greatest_lower_bound(X_86,X_87)) != greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))
| greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)) != multiply(X_85,greatest_lower_bound(X_87,X_86))
| multiply(X_85,greatest_lower_bound(X_86,X_87)) = multiply(X_85,greatest_lower_bound(X_87,X_86)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) ),[0],$fot(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)))]]) ).
cnf(refute_0_572,plain,
( multiply(X_85,greatest_lower_bound(X_86,X_87)) != greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))
| multiply(X_85,greatest_lower_bound(X_86,X_87)) = multiply(X_85,greatest_lower_bound(X_87,X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_87,X_86))) )],[refute_0_557,refute_0_571]) ).
cnf(refute_0_573,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))) != greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))
| multiply(X_85,greatest_lower_bound(X_86,X_87)) = multiply(X_85,greatest_lower_bound(X_87,X_86)) ),
inference(resolve,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,X_87)),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) )],[refute_0_570,refute_0_572]) ).
cnf(refute_0_574,plain,
multiply(X_85,greatest_lower_bound(X_86,X_87)) = multiply(X_85,greatest_lower_bound(X_87,X_86)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86)),multiply(X_85,greatest_lower_bound(X_86,X_87))),greatest_lower_bound(multiply(X_85,X_87),multiply(X_85,X_86))) )],[refute_0_545,refute_0_573]) ).
cnf(refute_0_575,plain,
( multiply(X_85,greatest_lower_bound(X_86,X_87)) != multiply(X_85,greatest_lower_bound(X_87,X_86))
| multiply(X_85,greatest_lower_bound(X_87,X_86)) = multiply(X_85,greatest_lower_bound(X_86,X_87)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_85,greatest_lower_bound(X_86,X_87)))),bind(Y0,$fot(multiply(X_85,greatest_lower_bound(X_87,X_86))))]]) ).
cnf(refute_0_576,plain,
multiply(X_85,greatest_lower_bound(X_87,X_86)) = multiply(X_85,greatest_lower_bound(X_86,X_87)),
inference(resolve,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,X_87)),multiply(X_85,greatest_lower_bound(X_87,X_86))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))),
inference(subst,[],[refute_0_576:[bind(X_85,$fot(inverse(X_87))),bind(X_86,$fot(X_87)),bind(X_87,$fot(greatest_lower_bound(identity,X_87)))]]) ).
cnf(refute_0_578,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))) != multiply(inverse(X_87),greatest_lower_bound(X_87,identity))
| multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) != multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)))
| multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)))),bind(Y0,$fot(multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))))),bind(Z0,$fot(multiply(inverse(X_87),greatest_lower_bound(X_87,identity))))]]) ).
cnf(refute_0_579,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))) != multiply(inverse(X_87),greatest_lower_bound(X_87,identity))
| multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)),multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87)))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) = multiply(inverse(X_87),greatest_lower_bound(X_87,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_87,greatest_lower_bound(identity,X_87))),multiply(inverse(X_87),greatest_lower_bound(X_87,identity))) )],[refute_0_533,refute_0_579]) ).
cnf(refute_0_581,plain,
( multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) != multiply(inverse(X_87),greatest_lower_bound(X_87,identity))
| multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))
| multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) ),[0],$fot(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)))]]) ).
cnf(refute_0_582,plain,
( multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))
| multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)),multiply(inverse(X_87),greatest_lower_bound(X_87,identity))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))) = greatest_lower_bound(identity,inverse(X_87)),
inference(subst,[],[refute_0_160:[bind(X_23,$fot(inverse(X_87))),bind(X_24,$fot(identity))]]) ).
cnf(refute_0_584,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))) != greatest_lower_bound(identity,inverse(X_87))
| multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) = greatest_lower_bound(identity,inverse(X_87)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)),greatest_lower_bound(identity,inverse(X_87))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))))]]) ).
cnf(refute_0_585,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))
| multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) = greatest_lower_bound(identity,inverse(X_87)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87))),greatest_lower_bound(identity,inverse(X_87))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
( multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))
| multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) = greatest_lower_bound(identity,inverse(X_87)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) )],[refute_0_582,refute_0_585]) ).
cnf(refute_0_587,plain,
multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) = greatest_lower_bound(identity,inverse(X_87)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(greatest_lower_bound(identity,X_87),X_87)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) )],[refute_0_528,refute_0_586]) ).
cnf(refute_0_588,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)))) != inverse(inverse(X_87))
| multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) != greatest_lower_bound(identity,inverse(X_87))
| multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) = inverse(inverse(X_87)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),inverse(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)))),inverse(inverse(X_87))) ),[0,1,0],$fot(greatest_lower_bound(identity,inverse(X_87)))]]) ).
cnf(refute_0_589,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)))) != inverse(inverse(X_87))
| multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) = inverse(inverse(X_87)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)),greatest_lower_bound(identity,inverse(X_87))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) = inverse(inverse(X_87)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),inverse(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)))),inverse(inverse(X_87))) )],[refute_0_523,refute_0_589]) ).
cnf(refute_0_591,plain,
inverse(inverse(X_87)) = X_87,
inference(subst,[],[refute_0_119:[bind(X_33,$fot(X_87))]]) ).
cnf(refute_0_592,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) != inverse(inverse(X_87))
| inverse(inverse(X_87)) != X_87
| multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) = X_87 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))),X_87) ),[0],$fot(inverse(inverse(X_87)))]]) ).
cnf(refute_0_593,plain,
( multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) != inverse(inverse(X_87))
| multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) = X_87 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_87)),X_87) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))) = X_87,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_87,identity),inverse(greatest_lower_bound(identity,inverse(X_87)))),inverse(inverse(X_87))) )],[refute_0_590,refute_0_593]) ).
cnf(refute_0_595,plain,
multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232)))) = X_232,
inference(subst,[],[refute_0_594:[bind(X_87,$fot(X_232))]]) ).
cnf(refute_0_596,plain,
( multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232)))) != X_232
| inverse(greatest_lower_bound(identity,inverse(X_232))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232))))))
| inverse(greatest_lower_bound(identity,inverse(X_232))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_232))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232))))))) ),[1,1,1],$fot(X_232)]]) ).
cnf(refute_0_597,plain,
( inverse(greatest_lower_bound(identity,inverse(X_232))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232))))))
| inverse(greatest_lower_bound(identity,inverse(X_232))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232)))),X_232) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
inverse(greatest_lower_bound(identity,inverse(X_232))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_232))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_232,identity),inverse(greatest_lower_bound(identity,inverse(X_232))))))) )],[refute_0_522,refute_0_597]) ).
cnf(refute_0_599,plain,
multiply(least_upper_bound(X_60,identity),X_59) = least_upper_bound(multiply(X_60,X_59),multiply(identity,X_59)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_59)),bind(Y,$fot(X_60)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_600,plain,
multiply(identity,X_59) = X_59,
inference(subst,[],[left_identity:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_601,plain,
( multiply(identity,X_59) != X_59
| multiply(least_upper_bound(X_60,identity),X_59) != least_upper_bound(multiply(X_60,X_59),multiply(identity,X_59))
| multiply(least_upper_bound(X_60,identity),X_59) = least_upper_bound(multiply(X_60,X_59),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_60,identity),X_59),least_upper_bound(multiply(X_60,X_59),multiply(identity,X_59))) ),[1,1],$fot(X_59)]]) ).
cnf(refute_0_602,plain,
( multiply(least_upper_bound(X_60,identity),X_59) != least_upper_bound(multiply(X_60,X_59),multiply(identity,X_59))
| multiply(least_upper_bound(X_60,identity),X_59) = least_upper_bound(multiply(X_60,X_59),X_59) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_59),X_59) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
multiply(least_upper_bound(X_60,identity),X_59) = least_upper_bound(multiply(X_60,X_59),X_59),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,identity),X_59),least_upper_bound(multiply(X_60,X_59),multiply(identity,X_59))) )],[refute_0_599,refute_0_602]) ).
cnf(refute_0_604,plain,
least_upper_bound(multiply(X_60,X_59),X_59) = least_upper_bound(X_59,multiply(X_60,X_59)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_59)),bind(Y,$fot(multiply(X_60,X_59)))]]) ).
cnf(refute_0_605,plain,
( multiply(least_upper_bound(X_60,identity),X_59) != least_upper_bound(multiply(X_60,X_59),X_59)
| least_upper_bound(multiply(X_60,X_59),X_59) != least_upper_bound(X_59,multiply(X_60,X_59))
| multiply(least_upper_bound(X_60,identity),X_59) = least_upper_bound(X_59,multiply(X_60,X_59)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_60,identity),X_59),least_upper_bound(X_59,multiply(X_60,X_59))) ),[0],$fot(least_upper_bound(multiply(X_60,X_59),X_59))]]) ).
cnf(refute_0_606,plain,
( multiply(least_upper_bound(X_60,identity),X_59) != least_upper_bound(multiply(X_60,X_59),X_59)
| multiply(least_upper_bound(X_60,identity),X_59) = least_upper_bound(X_59,multiply(X_60,X_59)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_60,X_59),X_59),least_upper_bound(X_59,multiply(X_60,X_59))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
multiply(least_upper_bound(X_60,identity),X_59) = least_upper_bound(X_59,multiply(X_60,X_59)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,identity),X_59),least_upper_bound(multiply(X_60,X_59),X_59)) )],[refute_0_603,refute_0_606]) ).
cnf(refute_0_608,plain,
multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) = least_upper_bound(greatest_lower_bound(X_164,identity),multiply(inverse(X_164),greatest_lower_bound(X_164,identity))),
inference(subst,[],[refute_0_607:[bind(X_59,$fot(greatest_lower_bound(X_164,identity))),bind(X_60,$fot(inverse(X_164)))]]) ).
cnf(refute_0_609,plain,
multiply(inverse(X_164),greatest_lower_bound(X_164,identity)) = greatest_lower_bound(identity,inverse(X_164)),
inference(subst,[],[refute_0_587:[bind(X_87,$fot(X_164))]]) ).
cnf(refute_0_610,plain,
( multiply(inverse(X_164),greatest_lower_bound(X_164,identity)) != greatest_lower_bound(identity,inverse(X_164))
| multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) != least_upper_bound(greatest_lower_bound(X_164,identity),multiply(inverse(X_164),greatest_lower_bound(X_164,identity)))
| multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)),least_upper_bound(greatest_lower_bound(X_164,identity),multiply(inverse(X_164),greatest_lower_bound(X_164,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_164)))]]) ).
cnf(refute_0_611,plain,
( multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) != least_upper_bound(greatest_lower_bound(X_164,identity),multiply(inverse(X_164),greatest_lower_bound(X_164,identity)))
| multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_164),greatest_lower_bound(X_164,identity)),greatest_lower_bound(identity,inverse(X_164))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)),least_upper_bound(greatest_lower_bound(X_164,identity),multiply(inverse(X_164),greatest_lower_bound(X_164,identity)))) )],[refute_0_608,refute_0_611]) ).
cnf(refute_0_613,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_291:[bind(X_16,$fot(multiply(Z,X))),bind(X_9,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_614,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$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_615,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( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_242,refute_0_614]) ).
cnf(refute_0_616,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_613,refute_0_615]) ).
cnf(refute_0_617,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_291:[bind(X_16,$fot(Y)),bind(X_9,$fot(Z))]]) ).
cnf(refute_0_618,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))]]) ).
cnf(refute_0_619,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_620,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( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_617,refute_0_620]) ).
cnf(refute_0_622,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_623,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_622]) ).
cnf(refute_0_624,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
inference(subst,[],[refute_0_623:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_625,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_209:[bind(X0,$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_626,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( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_621,refute_0_626]) ).
cnf(refute_0_628,plain,
least_upper_bound(multiply(Z,X),multiply(Y,X)) = multiply(least_upper_bound(Z,Y),X),
inference(subst,[],[refute_0_242:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_629,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_630,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_631,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( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_628,refute_0_631]) ).
cnf(refute_0_633,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_209:[bind(X0,$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_634,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( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_627,refute_0_634]) ).
cnf(refute_0_636,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_49:[bind(X,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y,$fot(least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_637,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_209:[bind(X0,$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_638,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( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_635,refute_0_638]) ).
cnf(refute_0_640,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$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_641,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( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
introduced(tautology,[equality,[$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_643,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( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_628,refute_0_642]) ).
cnf(refute_0_644,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_641,refute_0_643]) ).
cnf(refute_0_645,plain,
multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_616,refute_0_644]) ).
cnf(refute_0_646,plain,
( multiply(least_upper_bound(Y,Z),X) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(multiply(least_upper_bound(Z,Y),X)))]]) ).
cnf(refute_0_647,plain,
multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) = multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)),
inference(subst,[],[refute_0_647:[bind(X,$fot(greatest_lower_bound(X_164,identity))),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_164)))]]) ).
cnf(refute_0_649,plain,
( multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) != multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity))
| multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) != least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))
| multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)),least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)))]]) ).
cnf(refute_0_650,plain,
( multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)) != least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))
| multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)),multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_164),identity),greatest_lower_bound(X_164,identity)),least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))) )],[refute_0_612,refute_0_650]) ).
cnf(refute_0_652,plain,
multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) = least_upper_bound(greatest_lower_bound(X_189,identity),multiply(greatest_lower_bound(X_189,identity),inverse(X_189))),
inference(subst,[],[refute_0_321:[bind(X_44,$fot(greatest_lower_bound(X_189,identity))),bind(X_45,$fot(inverse(X_189)))]]) ).
cnf(refute_0_653,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_99),inverse(X_99))),
inference(subst,[],[refute_0_185:[bind(X_98,$fot(greatest_lower_bound(identity,X_99)))]]) ).
cnf(refute_0_654,plain,
multiply(greatest_lower_bound(identity,X_99),inverse(X_99)) = greatest_lower_bound(identity,inverse(X_99)),
inference(subst,[],[refute_0_503:[bind(X_105,$fot(X_99))]]) ).
cnf(refute_0_655,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_99),inverse(X_99)))
| multiply(greatest_lower_bound(identity,X_99),inverse(X_99)) != greatest_lower_bound(identity,inverse(X_99))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_99),inverse(X_99)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_99)))]]) ).
cnf(refute_0_656,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_99),inverse(X_99)))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_99),inverse(X_99)),greatest_lower_bound(identity,inverse(X_99))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_99),inverse(X_99)))) )],[refute_0_653,refute_0_656]) ).
cnf(refute_0_658,plain,
greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)) = greatest_lower_bound(X_99,identity),
inference(subst,[],[refute_0_153:[bind(X_13,$fot(identity)),bind(X_9,$fot(X_99))]]) ).
cnf(refute_0_659,plain,
multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)) = multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)))]]) ).
cnf(refute_0_660,plain,
( multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)) != multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99))
| greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)) != greatest_lower_bound(X_99,identity)
| multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)) = multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)),multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99))) ),[1,0],$fot(greatest_lower_bound(X_99,identity))]]) ).
cnf(refute_0_661,plain,
( greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)) != greatest_lower_bound(X_99,identity)
| multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)) = multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)),multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99))) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)) = multiply(greatest_lower_bound(X_99,identity),inverse(X_99)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),greatest_lower_bound(X_99,identity)) )],[refute_0_658,refute_0_661]) ).
cnf(refute_0_663,plain,
least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))) = greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),
inference(subst,[],[refute_0_538:[bind(X_13,$fot(multiply(X_98,X_97))),bind(X_23,$fot(multiply(X_99,X_97)))]]) ).
cnf(refute_0_664,plain,
multiply(greatest_lower_bound(X_98,X_99),X_97) = greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_97)),bind(Y,$fot(X_98)),bind(Z,$fot(X_99))]]) ).
cnf(refute_0_665,plain,
( multiply(greatest_lower_bound(X_98,X_99),X_97) != greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))
| greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_98,X_99),X_97))),bind(Y0,$fot(greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))))]]) ).
cnf(refute_0_666,plain,
greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))) )],[refute_0_664,refute_0_665]) ).
cnf(refute_0_667,plain,
( greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97)) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))) != greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))
| least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) = greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) ),[0,1],$fot(multiply(greatest_lower_bound(X_98,X_99),X_97))]]) ).
cnf(refute_0_668,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))) != greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))
| least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) = greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) = greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),greatest_lower_bound(multiply(X_98,X_97),multiply(X_99,X_97))),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) )],[refute_0_663,refute_0_668]) ).
cnf(refute_0_670,plain,
least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)) = greatest_lower_bound(X_98,X_99),
inference(subst,[],[refute_0_538:[bind(X_13,$fot(X_99)),bind(X_23,$fot(X_98))]]) ).
cnf(refute_0_671,plain,
multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97) = multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97))]]) ).
cnf(refute_0_672,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97) != multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97)
| least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)) != greatest_lower_bound(X_98,X_99)
| multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97),multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97)) ),[1,0],$fot(greatest_lower_bound(X_98,X_99))]]) ).
cnf(refute_0_673,plain,
( least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)) != greatest_lower_bound(X_98,X_99)
| multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97),multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97)) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97) = multiply(greatest_lower_bound(X_98,X_99),X_97),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),greatest_lower_bound(X_98,X_99)) )],[refute_0_670,refute_0_673]) ).
cnf(refute_0_675,plain,
least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) = multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97),
inference(subst,[],[refute_0_242:[bind(X,$fot(X_97)),bind(Y,$fot(greatest_lower_bound(X_98,X_99))),bind(Z,$fot(greatest_lower_bound(X_99,X_98)))]]) ).
cnf(refute_0_676,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) != multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97)
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97))),bind(Z0,$fot(multiply(greatest_lower_bound(X_98,X_99),X_97)))]]) ).
cnf(refute_0_677,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)),multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97)) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_98,X_99),greatest_lower_bound(X_99,X_98)),X_97),multiply(greatest_lower_bound(X_98,X_99),X_97)) )],[refute_0_674,refute_0_677]) ).
cnf(refute_0_679,plain,
greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) = multiply(greatest_lower_bound(X_99,X_98),X_97),
inference(subst,[],[refute_0_623:[bind(X,$fot(X_97)),bind(Y,$fot(X_99)),bind(Z,$fot(X_98))]]) ).
cnf(refute_0_680,plain,
least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) = least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))))]]) ).
cnf(refute_0_681,plain,
( greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) != multiply(greatest_lower_bound(X_99,X_98),X_97)
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) != least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)))
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) = least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))),least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_99,X_98),X_97))]]) ).
cnf(refute_0_682,plain,
( greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) != multiply(greatest_lower_bound(X_99,X_98),X_97)
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) = least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))),least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) = least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_99,X_98),X_97)) )],[refute_0_679,refute_0_682]) ).
cnf(refute_0_684,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) != least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97))
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_98,X_99),X_97)))]]) ).
cnf(refute_0_685,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))),least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) = multiply(greatest_lower_bound(X_98,X_99),X_97),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) )],[refute_0_678,refute_0_685]) ).
cnf(refute_0_687,plain,
least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) = least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(greatest_lower_bound(X_98,X_99),X_97))),bind(Y,$fot(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))))]]) ).
cnf(refute_0_688,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) != least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)))
| least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_98,X_99),X_97)))]]) ).
cnf(refute_0_689,plain,
( least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)),least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)))) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) = multiply(greatest_lower_bound(X_98,X_99),X_97),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))),multiply(greatest_lower_bound(X_98,X_99),X_97)) )],[refute_0_686,refute_0_689]) ).
cnf(refute_0_691,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) != multiply(greatest_lower_bound(X_98,X_99),X_97)
| least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) != greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))
| multiply(greatest_lower_bound(X_98,X_99),X_97) = greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) ),[0],$fot(multiply(greatest_lower_bound(X_98,X_99),X_97))]]) ).
cnf(refute_0_692,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) != greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))
| multiply(greatest_lower_bound(X_98,X_99),X_97) = greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
( multiply(greatest_lower_bound(X_98,X_99),X_97) != greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))
| greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)) != multiply(greatest_lower_bound(X_99,X_98),X_97)
| multiply(greatest_lower_bound(X_98,X_99),X_97) = multiply(greatest_lower_bound(X_99,X_98),X_97) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) ),[0],$fot(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)))]]) ).
cnf(refute_0_694,plain,
( multiply(greatest_lower_bound(X_98,X_99),X_97) != greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))
| multiply(greatest_lower_bound(X_98,X_99),X_97) = multiply(greatest_lower_bound(X_99,X_98),X_97) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_99,X_98),X_97)) )],[refute_0_679,refute_0_693]) ).
cnf(refute_0_695,plain,
( least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)) != greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))
| multiply(greatest_lower_bound(X_98,X_99),X_97) = multiply(greatest_lower_bound(X_99,X_98),X_97) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,X_99),X_97),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) )],[refute_0_692,refute_0_694]) ).
cnf(refute_0_696,plain,
multiply(greatest_lower_bound(X_98,X_99),X_97) = multiply(greatest_lower_bound(X_99,X_98),X_97),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97)),multiply(greatest_lower_bound(X_98,X_99),X_97)),greatest_lower_bound(multiply(X_99,X_97),multiply(X_98,X_97))) )],[refute_0_669,refute_0_695]) ).
cnf(refute_0_697,plain,
( multiply(greatest_lower_bound(X_98,X_99),X_97) != multiply(greatest_lower_bound(X_99,X_98),X_97)
| multiply(greatest_lower_bound(X_99,X_98),X_97) = multiply(greatest_lower_bound(X_98,X_99),X_97) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_98,X_99),X_97))),bind(Y0,$fot(multiply(greatest_lower_bound(X_99,X_98),X_97)))]]) ).
cnf(refute_0_698,plain,
multiply(greatest_lower_bound(X_99,X_98),X_97) = multiply(greatest_lower_bound(X_98,X_99),X_97),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,X_99),X_97),multiply(greatest_lower_bound(X_99,X_98),X_97)) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)),
inference(subst,[],[refute_0_698:[bind(X_97,$fot(inverse(X_99))),bind(X_98,$fot(X_99)),bind(X_99,$fot(greatest_lower_bound(identity,X_99)))]]) ).
cnf(refute_0_700,plain,
( multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)) != multiply(greatest_lower_bound(X_99,identity),inverse(X_99))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) != multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_99,identity),inverse(X_99))))]]) ).
cnf(refute_0_701,plain,
( multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)) != multiply(greatest_lower_bound(X_99,identity),inverse(X_99))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)),multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) = multiply(greatest_lower_bound(X_99,identity),inverse(X_99)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_99,greatest_lower_bound(identity,X_99)),inverse(X_99)),multiply(greatest_lower_bound(X_99,identity),inverse(X_99))) )],[refute_0_662,refute_0_701]) ).
cnf(refute_0_703,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) != multiply(greatest_lower_bound(X_99,identity),inverse(X_99))
| multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))
| multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))) ),[0],$fot(multiply(greatest_lower_bound(X_99,identity),inverse(X_99)))]]) ).
cnf(refute_0_704,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))
| multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) = greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)),multiply(greatest_lower_bound(X_99,identity),inverse(X_99))) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))) = greatest_lower_bound(identity,inverse(X_99)),
inference(subst,[],[refute_0_160:[bind(X_23,$fot(inverse(X_99))),bind(X_24,$fot(identity))]]) ).
cnf(refute_0_706,plain,
( multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))
| greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))) != greatest_lower_bound(identity,inverse(X_99))
| multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) = greatest_lower_bound(identity,inverse(X_99)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_99,identity),inverse(X_99)),greatest_lower_bound(identity,inverse(X_99))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))))]]) ).
cnf(refute_0_707,plain,
( multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))
| multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) = greatest_lower_bound(identity,inverse(X_99)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99))),greatest_lower_bound(identity,inverse(X_99))) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)) != greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))
| multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) = greatest_lower_bound(identity,inverse(X_99)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_99,identity),inverse(X_99)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))) )],[refute_0_704,refute_0_707]) ).
cnf(refute_0_709,plain,
multiply(greatest_lower_bound(X_99,identity),inverse(X_99)) = greatest_lower_bound(identity,inverse(X_99)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,X_99),X_99),inverse(X_99)),greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_99)))) )],[refute_0_657,refute_0_708]) ).
cnf(refute_0_710,plain,
multiply(greatest_lower_bound(X_189,identity),inverse(X_189)) = greatest_lower_bound(identity,inverse(X_189)),
inference(subst,[],[refute_0_709:[bind(X_99,$fot(X_189))]]) ).
cnf(refute_0_711,plain,
( multiply(greatest_lower_bound(X_189,identity),inverse(X_189)) != greatest_lower_bound(identity,inverse(X_189))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) != least_upper_bound(greatest_lower_bound(X_189,identity),multiply(greatest_lower_bound(X_189,identity),inverse(X_189)))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) = least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)),least_upper_bound(greatest_lower_bound(X_189,identity),multiply(greatest_lower_bound(X_189,identity),inverse(X_189)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_189)))]]) ).
cnf(refute_0_712,plain,
( multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) != least_upper_bound(greatest_lower_bound(X_189,identity),multiply(greatest_lower_bound(X_189,identity),inverse(X_189)))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) = least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),inverse(X_189)),greatest_lower_bound(identity,inverse(X_189))) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) = least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)),least_upper_bound(greatest_lower_bound(X_189,identity),multiply(greatest_lower_bound(X_189,identity),inverse(X_189)))) )],[refute_0_652,refute_0_712]) ).
cnf(refute_0_714,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_291:[bind(X_16,$fot(multiply(X,Z))),bind(X_9,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_715,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_716,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_366,refute_0_715]) ).
cnf(refute_0_717,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_714,refute_0_716]) ).
cnf(refute_0_718,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_719,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_720,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_617,refute_0_720]) ).
cnf(refute_0_722,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
inference(subst,[],[refute_0_556:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_723,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_724,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_366:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_727,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_728,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_729,plain,
( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_726,refute_0_729]) ).
cnf(refute_0_731,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_732,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_725,refute_0_732]) ).
cnf(refute_0_734,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_49:[bind(X,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_735,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_736,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_739,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_741,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_726,refute_0_740]) ).
cnf(refute_0_742,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_739,refute_0_741]) ).
cnf(refute_0_743,plain,
multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_717,refute_0_742]) ).
cnf(refute_0_744,plain,
( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_745,plain,
multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) = multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))),
inference(subst,[],[refute_0_745:[bind(X,$fot(greatest_lower_bound(X_189,identity))),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_189)))]]) ).
cnf(refute_0_747,plain,
( multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) != multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) != least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) = least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)),least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) ),[0],$fot(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))))]]) ).
cnf(refute_0_748,plain,
( multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) != least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) = least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)),multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) )],[refute_0_746,refute_0_747]) ).
cnf(refute_0_749,plain,
( multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) != least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))
| least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) = multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))))]]) ).
cnf(refute_0_750,plain,
least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) = multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)),least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))) )],[refute_0_651,refute_0_749]) ).
cnf(refute_0_751,plain,
least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) = multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity)),
inference(subst,[],[refute_0_750:[bind(X_164,$fot(X_189))]]) ).
cnf(refute_0_752,plain,
( multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) != least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))
| least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) != multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) = multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))),multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))]]) ).
cnf(refute_0_753,plain,
( multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) != least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) = multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))),multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity))) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
( multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)) != least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))
| multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) = multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))),least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) )],[refute_0_748,refute_0_753]) ).
cnf(refute_0_755,plain,
multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) = multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(inverse(X_189),identity)),least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) )],[refute_0_713,refute_0_754]) ).
cnf(refute_0_756,plain,
( multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) != multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity))
| multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity)) = multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity))))]]) ).
cnf(refute_0_757,plain,
multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity)) = multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))),multiply(least_upper_bound(identity,inverse(X_189)),greatest_lower_bound(X_189,identity))) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) = multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))),
inference(subst,[],[refute_0_757:[bind(X_189,$fot(X_164))]]) ).
cnf(refute_0_759,plain,
( multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) != multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164)))
| multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) != least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))
| multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)),least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))) ),[0],$fot(multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))))]]) ).
cnf(refute_0_760,plain,
( multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)) != least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))
| multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)),multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164)))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))) = least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_164)),greatest_lower_bound(X_164,identity)),least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))) )],[refute_0_651,refute_0_760]) ).
cnf(refute_0_762,plain,
( multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))) != least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))
| least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) = multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))))]]) ).
cnf(refute_0_763,plain,
least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164))) = multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_164,identity),least_upper_bound(identity,inverse(X_164))),least_upper_bound(greatest_lower_bound(X_164,identity),greatest_lower_bound(identity,inverse(X_164)))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))) = multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))),
inference(subst,[],[refute_0_763:[bind(X_164,$fot(X_232))]]) ).
cnf(refute_0_765,plain,
inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))) = greatest_lower_bound(identity,inverse(X_232)),
inference(subst,[],[refute_0_119:[bind(X_33,$fot(greatest_lower_bound(identity,inverse(X_232))))]]) ).
cnf(refute_0_766,plain,
least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) = least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))))]]) ).
cnf(refute_0_767,plain,
( inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))) != greatest_lower_bound(identity,inverse(X_232))
| least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) != least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))
| least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) = least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))),least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_232)))]]) ).
cnf(refute_0_768,plain,
( inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))) != greatest_lower_bound(identity,inverse(X_232))
| least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) = least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))),least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) = least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))),greatest_lower_bound(identity,inverse(X_232))) )],[refute_0_765,refute_0_768]) ).
cnf(refute_0_770,plain,
( least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))) != multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))
| least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) != least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232)))
| least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) = multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))))]]) ).
cnf(refute_0_771,plain,
( least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))) != multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))
| least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) = multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))),least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232)))) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) = multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_232,identity),greatest_lower_bound(identity,inverse(X_232))),multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) )],[refute_0_764,refute_0_771]) ).
cnf(refute_0_773,plain,
inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) = inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))))]]) ).
cnf(refute_0_774,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) != inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))))
| least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) != multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))
| inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) = inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))))) ),[1,0],$fot(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))))]]) ).
cnf(refute_0_775,plain,
( least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))) != multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))
| inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) = inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) = inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232))))),multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) )],[refute_0_772,refute_0_775]) ).
cnf(refute_0_777,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)))]]) ).
cnf(refute_0_778,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232))
| inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) != inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) = multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232))) ),[1,0],$fot(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))))]]) ).
cnf(refute_0_779,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))) != inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) = multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232))) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) = multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))))) )],[refute_0_776,refute_0_779]) ).
cnf(refute_0_781,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)) != multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))
| inverse(greatest_lower_bound(identity,inverse(X_232))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232))
| inverse(greatest_lower_bound(identity,inverse(X_232))) = multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_232))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232))) ),[1],$fot(multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)))]]) ).
cnf(refute_0_782,plain,
( inverse(greatest_lower_bound(identity,inverse(X_232))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232))
| inverse(greatest_lower_bound(identity,inverse(X_232))) = multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232)),multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
inverse(greatest_lower_bound(identity,inverse(X_232))) = multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_232))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_232,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_232)))))),least_upper_bound(identity,X_232))) )],[refute_0_598,refute_0_782]) ).
cnf(refute_0_784,plain,
multiply(identity,least_upper_bound(identity,X_232)) = least_upper_bound(identity,X_232),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,X_232)))]]) ).
cnf(refute_0_785,plain,
multiply(inverse(identity),identity) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_786,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_82:[bind(X_31,$fot(inverse(identity)))]]) ).
cnf(refute_0_787,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_788,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
( multiply(inverse(identity),identity) != identity
| multiply(inverse(identity),identity) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_790,plain,
( multiply(inverse(identity),identity) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_785,refute_0_790]) ).
cnf(refute_0_792,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))) = multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),
inference(subst,[],[refute_0_142:[bind(X_8,$fot(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_793,plain,
multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = least_upper_bound(X_81,multiply(least_upper_bound(X_60,inverse(X_81)),X_81)),
inference(subst,[],[refute_0_607:[bind(X_59,$fot(X_81)),bind(X_60,$fot(least_upper_bound(X_60,inverse(X_81))))]]) ).
cnf(refute_0_794,plain,
multiply(least_upper_bound(X_60,inverse(X_81)),X_81) = least_upper_bound(identity,multiply(X_60,X_81)),
inference(subst,[],[refute_0_517:[bind(X_59,$fot(X_81))]]) ).
cnf(refute_0_795,plain,
( multiply(least_upper_bound(X_60,inverse(X_81)),X_81) != least_upper_bound(identity,multiply(X_60,X_81))
| multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) != least_upper_bound(X_81,multiply(least_upper_bound(X_60,inverse(X_81)),X_81))
| multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81),least_upper_bound(X_81,multiply(least_upper_bound(X_60,inverse(X_81)),X_81))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_60,X_81)))]]) ).
cnf(refute_0_796,plain,
( multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) != least_upper_bound(X_81,multiply(least_upper_bound(X_60,inverse(X_81)),X_81))
| multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,inverse(X_81)),X_81),least_upper_bound(identity,multiply(X_60,X_81))) )],[refute_0_794,refute_0_795]) ).
cnf(refute_0_797,plain,
multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81),least_upper_bound(X_81,multiply(least_upper_bound(X_60,inverse(X_81)),X_81))) )],[refute_0_793,refute_0_796]) ).
cnf(refute_0_798,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_63,inverse(X)),X)),
inference(subst,[],[monotony_lub2:[bind(Z,$fot(least_upper_bound(X_63,inverse(X))))]]) ).
cnf(refute_0_799,plain,
multiply(least_upper_bound(X_63,inverse(X)),X) = least_upper_bound(identity,multiply(X_63,X)),
inference(subst,[],[refute_0_517:[bind(X_59,$fot(X)),bind(X_60,$fot(X_63))]]) ).
cnf(refute_0_800,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_63,inverse(X)),X))
| multiply(least_upper_bound(X_63,inverse(X)),X) != least_upper_bound(identity,multiply(X_63,X))
| multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_63,inverse(X)),X))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_63,X)))]]) ).
cnf(refute_0_801,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_63,inverse(X)),X))
| multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_63,inverse(X)),X),least_upper_bound(identity,multiply(X_63,X))) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_63,inverse(X)),X))) )],[refute_0_798,refute_0_801]) ).
cnf(refute_0_803,plain,
least_upper_bound(multiply(Y,X),multiply(X_63,X)) = multiply(least_upper_bound(Y,X_63),X),
inference(subst,[],[refute_0_242:[bind(Z,$fot(X_63))]]) ).
cnf(refute_0_804,plain,
least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))) = least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))))]]) ).
cnf(refute_0_805,plain,
( least_upper_bound(multiply(Y,X),multiply(X_63,X)) != multiply(least_upper_bound(Y,X_63),X)
| least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))) != least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X)))
| least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))),least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X)))) ),[1,1],$fot(multiply(least_upper_bound(Y,X_63),X))]]) ).
cnf(refute_0_806,plain,
( least_upper_bound(multiply(Y,X),multiply(X_63,X)) != multiply(least_upper_bound(Y,X_63),X)
| least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))),least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X)))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(X_63,X)),multiply(least_upper_bound(Y,X_63),X)) )],[refute_0_803,refute_0_806]) ).
cnf(refute_0_808,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(least_upper_bound(Y,X_18))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_809,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_18)) = least_upper_bound(X_18,Y),
inference(subst,[],[refute_0_287:[bind(X_15,$fot(X_18))]]) ).
cnf(refute_0_810,plain,
( least_upper_bound(X_18,least_upper_bound(Y,X_18)) != least_upper_bound(X_18,Y)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$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_811,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( $equal(least_upper_bound(X_18,least_upper_bound(Y,X_18)),least_upper_bound(X_18,Y)) )],[refute_0_809,refute_0_810]) ).
cnf(refute_0_812,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,least_upper_bound(Y,X_18)),X_20)) )],[refute_0_808,refute_0_811]) ).
cnf(refute_0_813,plain,
least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(least_upper_bound(Y,X_19)))]]) ).
cnf(refute_0_814,plain,
least_upper_bound(X_19,least_upper_bound(Y,X_19)) = least_upper_bound(X_19,Y),
inference(subst,[],[refute_0_287:[bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_815,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(X_19,least_upper_bound(Y,X_19)) != least_upper_bound(X_19,Y)
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) ),
introduced(tautology,[equality,[$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_816,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( $equal(least_upper_bound(X_19,least_upper_bound(Y,X_19)),least_upper_bound(X_19,Y)) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,least_upper_bound(Y,X_19))),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_813,refute_0_816]) ).
cnf(refute_0_818,plain,
least_upper_bound(least_upper_bound(X_18,X_19),Y) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_819,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,[$fot(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)))]]) ).
cnf(refute_0_820,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))
| least_upper_bound(least_upper_bound(X_18,X_19),Y) != least_upper_bound(X_18,least_upper_bound(X_19,Y))
| least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$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_821,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( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),Y),least_upper_bound(X_18,least_upper_bound(X_19,Y))) )],[refute_0_818,refute_0_821]) ).
cnf(refute_0_823,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_824,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,$fot(X))]]) ).
cnf(refute_0_825,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),X)))]]) ).
cnf(refute_0_826,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_824,refute_0_825]) ).
cnf(refute_0_827,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(least_upper_bound(X_18,X_19),X)
| least_upper_bound(least_upper_bound(X_18,X_19),X) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)) ),
introduced(tautology,[equality,[$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_828,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( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X)) )],[refute_0_823,refute_0_828]) ).
cnf(refute_0_830,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(X_18,least_upper_bound(X_19,X))
| least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_18,X_19)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X))))]]) ).
cnf(refute_0_831,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_829,refute_0_830]) ).
cnf(refute_0_832,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),
inference(subst,[],[refute_0_831:[bind(X,$fot(X_19)),bind(X_18,$fot(least_upper_bound(X_18,X_19))),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_833,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_209:[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,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_834,plain,
( least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y))) )],[refute_0_832,refute_0_833]) ).
cnf(refute_0_835,plain,
least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(least_upper_bound(X_18,X_19),Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_822,refute_0_834]) ).
cnf(refute_0_836,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))
| least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) ),
introduced(tautology,[equality,[$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_837,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( $equal(least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
least_upper_bound(X_18,least_upper_bound(X_19,Y)) = least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(least_upper_bound(X_18,X_19),least_upper_bound(Y,X_19))) )],[refute_0_817,refute_0_837]) ).
cnf(refute_0_839,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,Y)) != least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))
| least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,Y)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))))]]) ).
cnf(refute_0_840,plain,
least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y))) = least_upper_bound(X_18,least_upper_bound(X_19,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,Y)),least_upper_bound(X_19,least_upper_bound(X_18,least_upper_bound(X_19,Y)))) )],[refute_0_838,refute_0_839]) ).
cnf(refute_0_841,plain,
least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(subst,[],[refute_0_840:[bind(Y,$fot(X_20)),bind(X_18,$fot(Y)),bind(X_19,$fot(X_18))]]) ).
cnf(refute_0_842,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_283:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_843,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)))]]) ).
cnf(refute_0_844,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_845,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( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_18),X_20),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_842,refute_0_845]) ).
cnf(refute_0_847,plain,
( least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(subst,[],[refute_0_209:[bind(X0,$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_848,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( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20)))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(Y,least_upper_bound(X_18,X_20))),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_841,refute_0_848]) ).
cnf(refute_0_850,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(Y,least_upper_bound(X_18,X_20))
| least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(least_upper_bound(X_18,Y),X_20) ),
introduced(tautology,[equality,[$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_851,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( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(Y,least_upper_bound(X_18,X_20))) )],[refute_0_849,refute_0_850]) ).
cnf(refute_0_852,plain,
least_upper_bound(least_upper_bound(X_18,Y),X_20) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_18)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_853,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(least_upper_bound(X_18,Y),X_20) != least_upper_bound(X_18,least_upper_bound(Y,X_20))
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
introduced(tautology,[equality,[$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_854,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( $equal(least_upper_bound(least_upper_bound(X_18,Y),X_20),least_upper_bound(X_18,least_upper_bound(Y,X_20))) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
( least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)) != least_upper_bound(least_upper_bound(X_18,Y),X_20)
| least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_851,refute_0_854]) ).
cnf(refute_0_856,plain,
least_upper_bound(Y,least_upper_bound(X_18,X_20)) = least_upper_bound(X_18,least_upper_bound(Y,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(least_upper_bound(Y,X_18),X_20)),least_upper_bound(least_upper_bound(X_18,Y),X_20)) )],[refute_0_812,refute_0_855]) ).
cnf(refute_0_857,plain,
( least_upper_bound(Y,least_upper_bound(X_18,X_20)) != least_upper_bound(X_18,least_upper_bound(Y,X_20))
| least_upper_bound(X_18,least_upper_bound(Y,X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_18,X_20)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(Y,X_20))))]]) ).
cnf(refute_0_858,plain,
least_upper_bound(X_18,least_upper_bound(Y,X_20)) = least_upper_bound(Y,least_upper_bound(X_18,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_18,X_20)),least_upper_bound(X_18,least_upper_bound(Y,X_20))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) = least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))),
inference(subst,[],[refute_0_858:[bind(Y,$fot(identity)),bind(X_18,$fot(multiply(Y,X))),bind(X_20,$fot(multiply(X_63,X)))]]) ).
cnf(refute_0_860,plain,
( least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) != least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X)))
| least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X))
| least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X))))]]) ).
cnf(refute_0_861,plain,
( least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X))
| least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))),least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X)))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,X),multiply(X_63,X))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X))) )],[refute_0_807,refute_0_861]) ).
cnf(refute_0_863,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) != least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X)))
| least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X))
| multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X),least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X))) ),[0],$fot(least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))))]]) ).
cnf(refute_0_864,plain,
( multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) != least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X)))
| multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X))) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_63),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_63,inverse(X))),X),least_upper_bound(multiply(Y,X),least_upper_bound(identity,multiply(X_63,X)))) )],[refute_0_802,refute_0_864]) ).
cnf(refute_0_866,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)),
inference(subst,[],[refute_0_865:[bind(X,$fot(X_81)),bind(Y,$fot(identity)),bind(X_63,$fot(X_60))]]) ).
cnf(refute_0_867,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_82,X_17))) = least_upper_bound(X_17,multiply(X_82,X_17)),
inference(subst,[],[refute_0_345:[bind(X_16,$fot(multiply(X_82,X_17)))]]) ).
cnf(refute_0_868,plain,
multiply(least_upper_bound(X_82,identity),X_17) = least_upper_bound(X_17,multiply(X_82,X_17)),
inference(subst,[],[refute_0_607:[bind(X_59,$fot(X_17)),bind(X_60,$fot(X_82))]]) ).
cnf(refute_0_869,plain,
( multiply(least_upper_bound(X_82,identity),X_17) != least_upper_bound(X_17,multiply(X_82,X_17))
| least_upper_bound(X_17,multiply(X_82,X_17)) = multiply(least_upper_bound(X_82,identity),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_82,identity),X_17))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_82,X_17))))]]) ).
cnf(refute_0_870,plain,
least_upper_bound(X_17,multiply(X_82,X_17)) = multiply(least_upper_bound(X_82,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_82,identity),X_17),least_upper_bound(X_17,multiply(X_82,X_17))) )],[refute_0_868,refute_0_869]) ).
cnf(refute_0_871,plain,
( least_upper_bound(X_17,multiply(X_82,X_17)) != multiply(least_upper_bound(X_82,identity),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_82,X_17))) != least_upper_bound(X_17,multiply(X_82,X_17))
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = least_upper_bound(X_17,multiply(X_82,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_82,X_17))),least_upper_bound(X_17,multiply(X_82,X_17))) ),[0,1],$fot(multiply(least_upper_bound(X_82,identity),X_17))]]) ).
cnf(refute_0_872,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_82,X_17))) != least_upper_bound(X_17,multiply(X_82,X_17))
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = least_upper_bound(X_17,multiply(X_82,X_17)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_82,X_17)),multiply(least_upper_bound(X_82,identity),X_17)) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = least_upper_bound(X_17,multiply(X_82,X_17)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_82,X_17))),least_upper_bound(X_17,multiply(X_82,X_17))) )],[refute_0_867,refute_0_872]) ).
cnf(refute_0_874,plain,
least_upper_bound(identity,least_upper_bound(X_82,identity)) = least_upper_bound(identity,X_82),
inference(subst,[],[refute_0_287:[bind(Y,$fot(X_82)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_875,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17))]]) ).
cnf(refute_0_876,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)
| least_upper_bound(identity,least_upper_bound(X_82,identity)) != least_upper_bound(identity,X_82)
| multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) = multiply(least_upper_bound(identity,X_82),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)) ),[1,0],$fot(least_upper_bound(identity,X_82))]]) ).
cnf(refute_0_877,plain,
( least_upper_bound(identity,least_upper_bound(X_82,identity)) != least_upper_bound(identity,X_82)
| multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) = multiply(least_upper_bound(identity,X_82),X_17) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) = multiply(least_upper_bound(identity,X_82),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_82,identity)),least_upper_bound(identity,X_82)) )],[refute_0_874,refute_0_877]) ).
cnf(refute_0_879,plain,
( multiply(least_upper_bound(X_61,X_60),X_59) != multiply(least_upper_bound(X_60,X_61),X_59)
| multiply(least_upper_bound(X_60,X_61),X_59) = multiply(least_upper_bound(X_61,X_60),X_59) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_61,X_60),X_59))),bind(Y0,$fot(multiply(least_upper_bound(X_60,X_61),X_59)))]]) ).
cnf(refute_0_880,plain,
multiply(least_upper_bound(X_60,X_61),X_59) = multiply(least_upper_bound(X_61,X_60),X_59),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_61,X_60),X_59),multiply(least_upper_bound(X_60,X_61),X_59)) )],[refute_0_246,refute_0_879]) ).
cnf(refute_0_881,plain,
multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17),
inference(subst,[],[refute_0_880:[bind(X_59,$fot(X_17)),bind(X_60,$fot(least_upper_bound(X_82,identity))),bind(X_61,$fot(identity))]]) ).
cnf(refute_0_882,plain,
( multiply(least_upper_bound(X_60,identity),X_59) != least_upper_bound(X_59,multiply(X_60,X_59))
| least_upper_bound(X_59,multiply(X_60,X_59)) = multiply(least_upper_bound(X_60,identity),X_59) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_60,identity),X_59))),bind(Y0,$fot(least_upper_bound(X_59,multiply(X_60,X_59))))]]) ).
cnf(refute_0_883,plain,
least_upper_bound(X_59,multiply(X_60,X_59)) = multiply(least_upper_bound(X_60,identity),X_59),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,identity),X_59),least_upper_bound(X_59,multiply(X_60,X_59))) )],[refute_0_607,refute_0_882]) ).
cnf(refute_0_884,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17),
inference(subst,[],[refute_0_883:[bind(X_59,$fot(X_17)),bind(X_60,$fot(least_upper_bound(X_82,identity)))]]) ).
cnf(refute_0_885,plain,
( multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) != multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)))]]) ).
cnf(refute_0_886,plain,
( multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)),multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17)) )],[refute_0_884,refute_0_885]) ).
cnf(refute_0_887,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_82,identity),identity),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)) )],[refute_0_881,refute_0_886]) ).
cnf(refute_0_888,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) != multiply(least_upper_bound(identity,X_82),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) != multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = multiply(least_upper_bound(identity,X_82),X_17) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_82),X_17)))]]) ).
cnf(refute_0_889,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17) != multiply(least_upper_bound(identity,X_82),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = multiply(least_upper_bound(identity,X_82),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)),multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17)) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) = multiply(least_upper_bound(identity,X_82),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_82,identity)),X_17),multiply(least_upper_bound(identity,X_82),X_17)) )],[refute_0_878,refute_0_889]) ).
cnf(refute_0_891,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) != multiply(least_upper_bound(identity,X_82),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) != least_upper_bound(X_17,multiply(X_82,X_17))
| multiply(least_upper_bound(identity,X_82),X_17) = least_upper_bound(X_17,multiply(X_82,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)),least_upper_bound(X_17,multiply(X_82,X_17))) ),[0],$fot(multiply(least_upper_bound(identity,X_82),X_17))]]) ).
cnf(refute_0_892,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) != least_upper_bound(X_17,multiply(X_82,X_17))
| multiply(least_upper_bound(identity,X_82),X_17) = least_upper_bound(X_17,multiply(X_82,X_17)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)),multiply(least_upper_bound(identity,X_82),X_17)) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
( multiply(least_upper_bound(identity,X_82),X_17) != least_upper_bound(X_17,multiply(X_82,X_17))
| least_upper_bound(X_17,multiply(X_82,X_17)) != multiply(least_upper_bound(X_82,identity),X_17)
| multiply(least_upper_bound(identity,X_82),X_17) = multiply(least_upper_bound(X_82,identity),X_17) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_82),X_17),multiply(least_upper_bound(X_82,identity),X_17)) ),[0],$fot(least_upper_bound(X_17,multiply(X_82,X_17)))]]) ).
cnf(refute_0_894,plain,
( multiply(least_upper_bound(identity,X_82),X_17) != least_upper_bound(X_17,multiply(X_82,X_17))
| multiply(least_upper_bound(identity,X_82),X_17) = multiply(least_upper_bound(X_82,identity),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_82,X_17)),multiply(least_upper_bound(X_82,identity),X_17)) )],[refute_0_870,refute_0_893]) ).
cnf(refute_0_895,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)) != least_upper_bound(X_17,multiply(X_82,X_17))
| multiply(least_upper_bound(identity,X_82),X_17) = multiply(least_upper_bound(X_82,identity),X_17) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_82),X_17),least_upper_bound(X_17,multiply(X_82,X_17))) )],[refute_0_892,refute_0_894]) ).
cnf(refute_0_896,plain,
multiply(least_upper_bound(identity,X_82),X_17) = multiply(least_upper_bound(X_82,identity),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_82,identity),X_17)),least_upper_bound(X_17,multiply(X_82,X_17))) )],[refute_0_873,refute_0_895]) ).
cnf(refute_0_897,plain,
( multiply(least_upper_bound(identity,X_82),X_17) != multiply(least_upper_bound(X_82,identity),X_17)
| multiply(least_upper_bound(X_82,identity),X_17) = multiply(least_upper_bound(identity,X_82),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,X_82),X_17))),bind(Y0,$fot(multiply(least_upper_bound(X_82,identity),X_17)))]]) ).
cnf(refute_0_898,plain,
multiply(least_upper_bound(X_82,identity),X_17) = multiply(least_upper_bound(identity,X_82),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_82),X_17),multiply(least_upper_bound(X_82,identity),X_17)) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81),
inference(subst,[],[refute_0_898:[bind(X_17,$fot(X_81)),bind(X_82,$fot(least_upper_bound(X_60,inverse(X_81))))]]) ).
cnf(refute_0_900,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81))
| multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) != multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81)
| multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81))))]]) ).
cnf(refute_0_901,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81))
| multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81),multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81)) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_60,inverse(X_81))),X_81),least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81))) )],[refute_0_866,refute_0_901]) ).
cnf(refute_0_903,plain,
( multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) != least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81)))
| multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81))
| least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)) = least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81),least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81)))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)))]]) ).
cnf(refute_0_904,plain,
( multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81) != least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81)))
| least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)) = least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81),least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,X_60),X_81)) = least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_60,inverse(X_81)),identity),X_81),least_upper_bound(X_81,least_upper_bound(identity,multiply(X_60,X_81)))) )],[refute_0_797,refute_0_904]) ).
cnf(refute_0_906,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,multiply(inverse(X_87),greatest_lower_bound(X_87,identity)))),
inference(subst,[],[refute_0_905:[bind(X_60,$fot(inverse(X_87))),bind(X_81,$fot(greatest_lower_bound(X_87,identity)))]]) ).
cnf(refute_0_907,plain,
( multiply(inverse(X_87),greatest_lower_bound(X_87,identity)) != greatest_lower_bound(identity,inverse(X_87))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) != least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,multiply(inverse(X_87),greatest_lower_bound(X_87,identity))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,multiply(inverse(X_87),greatest_lower_bound(X_87,identity))))) ),[1,1,1],$fot(greatest_lower_bound(identity,inverse(X_87)))]]) ).
cnf(refute_0_908,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) != least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,multiply(inverse(X_87),greatest_lower_bound(X_87,identity))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_87),greatest_lower_bound(X_87,identity)),greatest_lower_bound(identity,inverse(X_87))) )],[refute_0_587,refute_0_907]) ).
cnf(refute_0_909,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,multiply(inverse(X_87),greatest_lower_bound(X_87,identity))))) )],[refute_0_906,refute_0_908]) ).
cnf(refute_0_910,plain,
multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity)) = multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87))),
inference(subst,[],[refute_0_757:[bind(X_189,$fot(X_87))]]) ).
cnf(refute_0_911,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))))]]) ).
cnf(refute_0_912,plain,
( multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity)) != multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) != least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity)))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87))))]]) ).
cnf(refute_0_913,plain,
( multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity)) != multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity)))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity)),multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) )],[refute_0_910,refute_0_913]) ).
cnf(refute_0_915,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) != least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) = least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))) ),[0],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))))]]) ).
cnf(refute_0_916,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) != least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) = least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87))))) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
least_upper_bound(identity,greatest_lower_bound(X_87,identity)) = identity,
inference(subst,[],[refute_0_267:[bind(X_12,$fot(identity)),bind(X_13,$fot(X_87))]]) ).
cnf(refute_0_918,plain,
least_upper_bound(X_216,identity) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity)))),
inference(subst,[],[refute_0_521:[bind(X_29,$fot(least_upper_bound(X_216,identity))),bind(X_63,$fot(least_upper_bound(identity,inverse(X_216))))]]) ).
cnf(refute_0_919,plain,
multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) = least_upper_bound(least_upper_bound(X_51,identity),multiply(inverse(X_51),least_upper_bound(X_51,identity))),
inference(subst,[],[refute_0_607:[bind(X_59,$fot(least_upper_bound(X_51,identity))),bind(X_60,$fot(inverse(X_51)))]]) ).
cnf(refute_0_920,plain,
( multiply(inverse(X_51),least_upper_bound(X_51,identity)) != least_upper_bound(identity,inverse(X_51))
| multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) != least_upper_bound(least_upper_bound(X_51,identity),multiply(inverse(X_51),least_upper_bound(X_51,identity)))
| multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) = least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)),least_upper_bound(least_upper_bound(X_51,identity),multiply(inverse(X_51),least_upper_bound(X_51,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_51)))]]) ).
cnf(refute_0_921,plain,
( multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) != least_upper_bound(least_upper_bound(X_51,identity),multiply(inverse(X_51),least_upper_bound(X_51,identity)))
| multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) = least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_51),least_upper_bound(X_51,identity)),least_upper_bound(identity,inverse(X_51))) )],[refute_0_414,refute_0_920]) ).
cnf(refute_0_922,plain,
multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) = least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)),least_upper_bound(least_upper_bound(X_51,identity),multiply(inverse(X_51),least_upper_bound(X_51,identity)))) )],[refute_0_919,refute_0_921]) ).
cnf(refute_0_923,plain,
multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) = multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)),
inference(subst,[],[refute_0_898:[bind(X_17,$fot(least_upper_bound(X_51,identity))),bind(X_82,$fot(inverse(X_51)))]]) ).
cnf(refute_0_924,plain,
( multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) != multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity))
| multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) != least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) = least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)),least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)))]]) ).
cnf(refute_0_925,plain,
( multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) != least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) = least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)),multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X_20)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_927,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_928,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_2:[bind(X0,$fot(least_upper_bound(X_20,X_19))),bind(Y0,$fot(least_upper_bound(X_19,X_20)))]]) ).
cnf(refute_0_929,plain,
least_upper_bound(X_19,X_20) = least_upper_bound(X_20,X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,X_19),least_upper_bound(X_19,X_20)) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X_20)) != least_upper_bound(least_upper_bound(X_18,X_19),X_20)
| least_upper_bound(X_19,X_20) != least_upper_bound(X_20,X_19)
| least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20) ),
introduced(tautology,[equality,[$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_931,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( $equal(least_upper_bound(X_19,X_20),least_upper_bound(X_20,X_19)) )],[refute_0_929,refute_0_930]) ).
cnf(refute_0_932,plain,
least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(least_upper_bound(X_18,X_19),X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X_20)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) )],[refute_0_926,refute_0_931]) ).
cnf(refute_0_933,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X_20) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_934,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_935,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( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X_20),least_upper_bound(X_18,least_upper_bound(X_19,X_20))) )],[refute_0_933,refute_0_934]) ).
cnf(refute_0_936,plain,
least_upper_bound(X_18,least_upper_bound(X_20,X_19)) = least_upper_bound(X_18,least_upper_bound(X_19,X_20)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_20,X_19)),least_upper_bound(least_upper_bound(X_18,X_19),X_20)) )],[refute_0_932,refute_0_935]) ).
cnf(refute_0_937,plain,
( least_upper_bound(X_18,least_upper_bound(X_20,X_19)) != least_upper_bound(X_18,least_upper_bound(X_19,X_20))
| least_upper_bound(X_18,least_upper_bound(X_19,X_20)) = least_upper_bound(X_18,least_upper_bound(X_20,X_19)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_20,X_19)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X_20))))]]) ).
cnf(refute_0_938,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X_20)) = least_upper_bound(X_18,least_upper_bound(X_20,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_20,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X_20))) )],[refute_0_936,refute_0_937]) ).
cnf(refute_0_939,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51)) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))),
inference(subst,[],[refute_0_938:[bind(X_18,$fot(identity)),bind(X_19,$fot(inverse(X_51))),bind(X_20,$fot(X_51))]]) ).
cnf(refute_0_940,plain,
least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_18,X_19),X_15)) = least_upper_bound(X_15,least_upper_bound(X_18,X_19)),
inference(subst,[],[refute_0_287:[bind(Y,$fot(least_upper_bound(X_18,X_19)))]]) ).
cnf(refute_0_941,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X_15)) = least_upper_bound(least_upper_bound(X_18,X_19),X_15),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_942,plain,
( least_upper_bound(X_18,least_upper_bound(X_19,X_15)) != least_upper_bound(least_upper_bound(X_18,X_19),X_15)
| least_upper_bound(least_upper_bound(X_18,X_19),X_15) = least_upper_bound(X_18,least_upper_bound(X_19,X_15)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_18,least_upper_bound(X_19,X_15)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_18,X_19),X_15)))]]) ).
cnf(refute_0_943,plain,
least_upper_bound(least_upper_bound(X_18,X_19),X_15) = least_upper_bound(X_18,least_upper_bound(X_19,X_15)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X_15)),least_upper_bound(least_upper_bound(X_18,X_19),X_15)) )],[refute_0_941,refute_0_942]) ).
cnf(refute_0_944,plain,
( least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_18,X_19),X_15)) != least_upper_bound(X_15,least_upper_bound(X_18,X_19))
| least_upper_bound(least_upper_bound(X_18,X_19),X_15) != least_upper_bound(X_18,least_upper_bound(X_19,X_15))
| least_upper_bound(X_15,least_upper_bound(X_18,least_upper_bound(X_19,X_15))) = least_upper_bound(X_15,least_upper_bound(X_18,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_18,X_19),X_15)),least_upper_bound(X_15,least_upper_bound(X_18,X_19))) ),[0,1],$fot(least_upper_bound(X_18,least_upper_bound(X_19,X_15)))]]) ).
cnf(refute_0_945,plain,
( least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_18,X_19),X_15)) != least_upper_bound(X_15,least_upper_bound(X_18,X_19))
| least_upper_bound(X_15,least_upper_bound(X_18,least_upper_bound(X_19,X_15))) = least_upper_bound(X_15,least_upper_bound(X_18,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_18,X_19),X_15),least_upper_bound(X_18,least_upper_bound(X_19,X_15))) )],[refute_0_943,refute_0_944]) ).
cnf(refute_0_946,plain,
least_upper_bound(X_15,least_upper_bound(X_18,least_upper_bound(X_19,X_15))) = least_upper_bound(X_15,least_upper_bound(X_18,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_18,X_19),X_15)),least_upper_bound(X_15,least_upper_bound(X_18,X_19))) )],[refute_0_940,refute_0_945]) ).
cnf(refute_0_947,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))) = least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51)),
inference(subst,[],[refute_0_946:[bind(X_15,$fot(identity)),bind(X_18,$fot(inverse(X_51))),bind(X_19,$fot(X_51))]]) ).
cnf(refute_0_948,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51)) != least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))
| least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))) != least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51))
| least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))))]]) ).
cnf(refute_0_949,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51)) != least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))
| least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))),least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51))) )],[refute_0_947,refute_0_948]) ).
cnf(refute_0_950,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_51),X_51)),least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))) )],[refute_0_939,refute_0_949]) ).
cnf(refute_0_951,plain,
least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))) = least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))),
inference(subst,[],[refute_0_938:[bind(X_18,$fot(identity)),bind(X_19,$fot(least_upper_bound(X_51,identity))),bind(X_20,$fot(inverse(X_51)))]]) ).
cnf(refute_0_952,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))) != least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))) != least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))))]]) ).
cnf(refute_0_953,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))) != least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))),least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity)))) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_51),least_upper_bound(X_51,identity))),least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))) )],[refute_0_950,refute_0_953]) ).
cnf(refute_0_955,plain,
least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))),
inference(subst,[],[refute_0_858:[bind(Y,$fot(identity)),bind(X_18,$fot(least_upper_bound(X_51,identity))),bind(X_20,$fot(inverse(X_51)))]]) ).
cnf(refute_0_956,plain,
( least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))) != least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))
| least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51)))
| least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))))]]) ).
cnf(refute_0_957,plain,
( least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))) != least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))
| least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51)))) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_51,identity),inverse(X_51))),least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))) )],[refute_0_954,refute_0_957]) ).
cnf(refute_0_959,plain,
( multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) != least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))
| least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))) != least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)),least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))))]]) ).
cnf(refute_0_960,plain,
( multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) != least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51))),least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51)))) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
( multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)) != least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))
| multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)),least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))) )],[refute_0_925,refute_0_960]) ).
cnf(refute_0_962,plain,
multiply(least_upper_bound(identity,inverse(X_51)),least_upper_bound(X_51,identity)) = least_upper_bound(identity,least_upper_bound(X_51,inverse(X_51))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_51),identity),least_upper_bound(X_51,identity)),least_upper_bound(least_upper_bound(X_51,identity),least_upper_bound(identity,inverse(X_51)))) )],[refute_0_922,refute_0_961]) ).
cnf(refute_0_963,plain,
multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity)) = least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))),
inference(subst,[],[refute_0_962:[bind(X_51,$fot(X_216))]]) ).
cnf(refute_0_964,plain,
( multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity)) != least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))
| least_upper_bound(X_216,identity) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity))))
| least_upper_bound(X_216,identity) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_216,identity),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity))))) ),[1,1,1],$fot(least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))]]) ).
cnf(refute_0_965,plain,
( least_upper_bound(X_216,identity) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity))))
| least_upper_bound(X_216,identity) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity)),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
least_upper_bound(X_216,identity) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_216,identity),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_216)),least_upper_bound(X_216,identity))))) )],[refute_0_918,refute_0_965]) ).
cnf(refute_0_967,plain,
inverse(inverse(X_216)) = X_216,
inference(subst,[],[refute_0_119:[bind(X_33,$fot(X_216))]]) ).
cnf(refute_0_968,plain,
least_upper_bound(identity,inverse(inverse(X_216))) = least_upper_bound(identity,inverse(inverse(X_216))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(inverse(X_216))))]]) ).
cnf(refute_0_969,plain,
( inverse(inverse(X_216)) != X_216
| least_upper_bound(identity,inverse(inverse(X_216))) != least_upper_bound(identity,inverse(inverse(X_216)))
| least_upper_bound(identity,inverse(inverse(X_216))) = least_upper_bound(identity,X_216) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_216))),least_upper_bound(identity,inverse(inverse(X_216)))) ),[1,1],$fot(X_216)]]) ).
cnf(refute_0_970,plain,
( inverse(inverse(X_216)) != X_216
| least_upper_bound(identity,inverse(inverse(X_216))) = least_upper_bound(identity,X_216) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_216))),least_upper_bound(identity,inverse(inverse(X_216)))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
least_upper_bound(identity,inverse(inverse(X_216))) = least_upper_bound(identity,X_216),
inference(resolve,[$cnf( $equal(inverse(inverse(X_216)),X_216) )],[refute_0_967,refute_0_970]) ).
cnf(refute_0_972,plain,
inverse(least_upper_bound(identity,inverse(inverse(X_216)))) = inverse(least_upper_bound(identity,inverse(inverse(X_216)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,inverse(inverse(X_216)))))]]) ).
cnf(refute_0_973,plain,
( inverse(least_upper_bound(identity,inverse(inverse(X_216)))) != inverse(least_upper_bound(identity,inverse(inverse(X_216))))
| least_upper_bound(identity,inverse(inverse(X_216))) != least_upper_bound(identity,X_216)
| inverse(least_upper_bound(identity,inverse(inverse(X_216)))) = inverse(least_upper_bound(identity,X_216)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(inverse(X_216)))),inverse(least_upper_bound(identity,inverse(inverse(X_216))))) ),[1,0],$fot(least_upper_bound(identity,X_216))]]) ).
cnf(refute_0_974,plain,
( least_upper_bound(identity,inverse(inverse(X_216))) != least_upper_bound(identity,X_216)
| inverse(least_upper_bound(identity,inverse(inverse(X_216)))) = inverse(least_upper_bound(identity,X_216)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(inverse(X_216)))),inverse(least_upper_bound(identity,inverse(inverse(X_216))))) )],[refute_0_972,refute_0_973]) ).
cnf(refute_0_975,plain,
inverse(least_upper_bound(identity,inverse(inverse(X_216)))) = inverse(least_upper_bound(identity,X_216)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_216))),least_upper_bound(identity,X_216)) )],[refute_0_971,refute_0_974]) ).
cnf(refute_0_976,plain,
inverse(least_upper_bound(identity,inverse(X_198))) = multiply(inverse(least_upper_bound(identity,X_198)),multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198))))),
inference(subst,[],[refute_0_19:[bind(X_28,$fot(least_upper_bound(identity,X_198))),bind(X_29,$fot(inverse(least_upper_bound(identity,inverse(X_198)))))]]) ).
cnf(refute_0_977,plain,
multiply(least_upper_bound(identity,X_53),inverse(multiply(inverse(X_53),least_upper_bound(identity,X_53)))) = inverse(inverse(X_53)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(inverse(X_53))),bind(X_38,$fot(least_upper_bound(identity,X_53)))]]) ).
cnf(refute_0_978,plain,
( multiply(inverse(X_53),least_upper_bound(identity,X_53)) != least_upper_bound(identity,inverse(X_53))
| multiply(least_upper_bound(identity,X_53),inverse(multiply(inverse(X_53),least_upper_bound(identity,X_53)))) != inverse(inverse(X_53))
| multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) = inverse(inverse(X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_53),inverse(multiply(inverse(X_53),least_upper_bound(identity,X_53)))),inverse(inverse(X_53))) ),[0,1,0],$fot(least_upper_bound(identity,inverse(X_53)))]]) ).
cnf(refute_0_979,plain,
( multiply(least_upper_bound(identity,X_53),inverse(multiply(inverse(X_53),least_upper_bound(identity,X_53)))) != inverse(inverse(X_53))
| multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) = inverse(inverse(X_53)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_53),least_upper_bound(identity,X_53)),least_upper_bound(identity,inverse(X_53))) )],[refute_0_421,refute_0_978]) ).
cnf(refute_0_980,plain,
multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) = inverse(inverse(X_53)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_53),inverse(multiply(inverse(X_53),least_upper_bound(identity,X_53)))),inverse(inverse(X_53))) )],[refute_0_977,refute_0_979]) ).
cnf(refute_0_981,plain,
inverse(inverse(X_53)) = X_53,
inference(subst,[],[refute_0_119:[bind(X_33,$fot(X_53))]]) ).
cnf(refute_0_982,plain,
( multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) != inverse(inverse(X_53))
| inverse(inverse(X_53)) != X_53
| multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) = X_53 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))),X_53) ),[0],$fot(inverse(inverse(X_53)))]]) ).
cnf(refute_0_983,plain,
( multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) != inverse(inverse(X_53))
| multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) = X_53 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_53)),X_53) )],[refute_0_981,refute_0_982]) ).
cnf(refute_0_984,plain,
multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))) = X_53,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_53),inverse(least_upper_bound(identity,inverse(X_53)))),inverse(inverse(X_53))) )],[refute_0_980,refute_0_983]) ).
cnf(refute_0_985,plain,
multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198)))) = X_198,
inference(subst,[],[refute_0_984:[bind(X_53,$fot(X_198))]]) ).
cnf(refute_0_986,plain,
( multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198)))) != X_198
| inverse(least_upper_bound(identity,inverse(X_198))) != multiply(inverse(least_upper_bound(identity,X_198)),multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198)))))
| inverse(least_upper_bound(identity,inverse(X_198))) = multiply(inverse(least_upper_bound(identity,X_198)),X_198) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_198))),multiply(inverse(least_upper_bound(identity,X_198)),multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198)))))) ),[1,1],$fot(X_198)]]) ).
cnf(refute_0_987,plain,
( inverse(least_upper_bound(identity,inverse(X_198))) != multiply(inverse(least_upper_bound(identity,X_198)),multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198)))))
| inverse(least_upper_bound(identity,inverse(X_198))) = multiply(inverse(least_upper_bound(identity,X_198)),X_198) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198)))),X_198) )],[refute_0_985,refute_0_986]) ).
cnf(refute_0_988,plain,
inverse(least_upper_bound(identity,inverse(X_198))) = multiply(inverse(least_upper_bound(identity,X_198)),X_198),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_198))),multiply(inverse(least_upper_bound(identity,X_198)),multiply(least_upper_bound(identity,X_198),inverse(least_upper_bound(identity,inverse(X_198)))))) )],[refute_0_976,refute_0_987]) ).
cnf(refute_0_989,plain,
( inverse(least_upper_bound(identity,inverse(X_198))) != multiply(inverse(least_upper_bound(identity,X_198)),X_198)
| multiply(inverse(least_upper_bound(identity,X_198)),X_198) = inverse(least_upper_bound(identity,inverse(X_198))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_198))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_198)),X_198)))]]) ).
cnf(refute_0_990,plain,
multiply(inverse(least_upper_bound(identity,X_198)),X_198) = inverse(least_upper_bound(identity,inverse(X_198))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_198))),multiply(inverse(least_upper_bound(identity,X_198)),X_198)) )],[refute_0_988,refute_0_989]) ).
cnf(refute_0_991,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)) = inverse(least_upper_bound(identity,inverse(inverse(X_216)))),
inference(subst,[],[refute_0_990:[bind(X_198,$fot(inverse(X_216)))]]) ).
cnf(refute_0_992,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)) != inverse(least_upper_bound(identity,inverse(inverse(X_216))))
| inverse(least_upper_bound(identity,inverse(inverse(X_216)))) != inverse(least_upper_bound(identity,X_216))
| multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)) = inverse(least_upper_bound(identity,X_216)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)))),bind(Y0,$fot(inverse(least_upper_bound(identity,inverse(inverse(X_216)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_216))))]]) ).
cnf(refute_0_993,plain,
( inverse(least_upper_bound(identity,inverse(inverse(X_216)))) != inverse(least_upper_bound(identity,X_216))
| multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)) = inverse(least_upper_bound(identity,X_216)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)),inverse(least_upper_bound(identity,inverse(inverse(X_216))))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)) = inverse(least_upper_bound(identity,X_216)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(inverse(X_216)))),inverse(least_upper_bound(identity,X_216))) )],[refute_0_975,refute_0_993]) ).
cnf(refute_0_995,plain,
least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))) = least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))))]]) ).
cnf(refute_0_996,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)) != inverse(least_upper_bound(identity,X_216))
| least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))) != least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)))
| least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))),least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_216)))]]) ).
cnf(refute_0_997,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)) != inverse(least_upper_bound(identity,X_216))
| least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))),least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)))) )],[refute_0_995,refute_0_996]) ).
cnf(refute_0_998,plain,
least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)),inverse(least_upper_bound(identity,X_216))) )],[refute_0_994,refute_0_997]) ).
cnf(refute_0_999,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = least_upper_bound(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(least_upper_bound(identity,inverse(X_139))))),bind(Y,$fot(least_upper_bound(identity,X_139)))]]) ).
cnf(refute_0_1000,plain,
X_137 = multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,multiply(identity,X_137))),
inference(subst,[],[refute_0_521:[bind(X_29,$fot(X_137)),bind(X_63,$fot(identity))]]) ).
cnf(refute_0_1001,plain,
multiply(identity,X_137) = X_137,
inference(subst,[],[left_identity:[bind(X,$fot(X_137))]]) ).
cnf(refute_0_1002,plain,
( X_137 != multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,multiply(identity,X_137)))
| multiply(identity,X_137) != X_137
| X_137 = multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,X_137)) ),
introduced(tautology,[equality,[$cnf( $equal(X_137,multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,multiply(identity,X_137)))) ),[1,1,1],$fot(X_137)]]) ).
cnf(refute_0_1003,plain,
( X_137 != multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,multiply(identity,X_137)))
| X_137 = multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,X_137)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_137),X_137) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
X_137 = multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,X_137)),
inference(resolve,[$cnf( $equal(X_137,multiply(inverse(least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,multiply(identity,X_137)))) )],[refute_0_1000,refute_0_1003]) ).
cnf(refute_0_1005,plain,
X_139 = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)),
inference(subst,[],[refute_0_1004:[bind(X_137,$fot(X_139))]]) ).
cnf(refute_0_1006,plain,
( X_139 != multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)) = X_139 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_139)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139))))]]) ).
cnf(refute_0_1007,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)) = X_139,
inference(resolve,[$cnf( $equal(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)) != X_139
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) != least_upper_bound(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),least_upper_bound(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))) ),[1,0],$fot(X_139)]]) ).
cnf(refute_0_1009,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) != least_upper_bound(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)),X_139) )],[refute_0_1007,refute_0_1008]) ).
cnf(refute_0_1010,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),least_upper_bound(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,X_139)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))) )],[refute_0_999,refute_0_1009]) ).
cnf(refute_0_1011,plain,
least_upper_bound(least_upper_bound(identity,X_139),Z) = least_upper_bound(identity,least_upper_bound(X_139,Z)),
inference(subst,[],[refute_0_283:[bind(X,$fot(identity)),bind(Y,$fot(X_139))]]) ).
cnf(refute_0_1012,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)))]]) ).
cnf(refute_0_1013,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) != multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z))
| least_upper_bound(least_upper_bound(identity,X_139),Z) != least_upper_bound(identity,least_upper_bound(X_139,Z))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_139,Z)))]]) ).
cnf(refute_0_1014,plain,
( least_upper_bound(least_upper_bound(identity,X_139),Z) != least_upper_bound(identity,least_upper_bound(X_139,Z))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) = multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_139),Z),least_upper_bound(identity,least_upper_bound(X_139,Z))) )],[refute_0_1011,refute_0_1014]) ).
cnf(refute_0_1016,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) != multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z)))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) != least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z))) = least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))) ),[0],$fot(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z))))]]) ).
cnf(refute_0_1017,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)) != least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))
| multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z))) = least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z)))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(identity,least_upper_bound(X_139,Z))) = least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_139))),least_upper_bound(least_upper_bound(identity,X_139),Z)),least_upper_bound(X_139,multiply(inverse(least_upper_bound(identity,inverse(X_139))),Z))) )],[refute_0_1010,refute_0_1017]) ).
cnf(refute_0_1019,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) = least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))),
inference(subst,[],[refute_0_1018:[bind(Z,$fot(inverse(X_216))),bind(X_139,$fot(X_216))]]) ).
cnf(refute_0_1020,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) != least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)))
| least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))) != least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))
| multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))),bind(Y0,$fot(least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))))),bind(Z0,$fot(least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))))]]) ).
cnf(refute_0_1021,plain,
( least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))) != least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))
| multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))),least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216)))) )],[refute_0_1019,refute_0_1020]) ).
cnf(refute_0_1022,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_216,multiply(inverse(least_upper_bound(identity,inverse(X_216))),inverse(X_216))),least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))) )],[refute_0_998,refute_0_1021]) ).
cnf(refute_0_1023,plain,
least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) = least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))),
inference(subst,[],[refute_0_345:[bind(X_16,$fot(least_upper_bound(X_216,inverse(X_216)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1024,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))))]]) ).
cnf(refute_0_1025,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) != multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))
| least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) != least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))
| multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))]]) ).
cnf(refute_0_1026,plain,
( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) != least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))
| multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))) )],[refute_0_1024,refute_0_1025]) ).
cnf(refute_0_1027,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) )],[refute_0_1023,refute_0_1026]) ).
cnf(refute_0_1028,plain,
multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_61),inverse(X_61))),
inference(subst,[],[refute_0_331:[bind(X_60,$fot(least_upper_bound(identity,X_61)))]]) ).
cnf(refute_0_1029,plain,
least_upper_bound(identity,inverse(X_61)) = multiply(least_upper_bound(identity,X_61),inverse(X_61)),
inference(subst,[],[refute_0_397:[bind(X_65,$fot(X_61))]]) ).
cnf(refute_0_1030,plain,
( least_upper_bound(identity,inverse(X_61)) != multiply(least_upper_bound(identity,X_61),inverse(X_61))
| multiply(least_upper_bound(identity,X_61),inverse(X_61)) = least_upper_bound(identity,inverse(X_61)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,inverse(X_61)))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_61),inverse(X_61))))]]) ).
cnf(refute_0_1031,plain,
multiply(least_upper_bound(identity,X_61),inverse(X_61)) = least_upper_bound(identity,inverse(X_61)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_61)),multiply(least_upper_bound(identity,X_61),inverse(X_61))) )],[refute_0_1029,refute_0_1030]) ).
cnf(refute_0_1032,plain,
( multiply(least_upper_bound(identity,X_61),inverse(X_61)) != least_upper_bound(identity,inverse(X_61))
| multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_61),inverse(X_61)))
| multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)),least_upper_bound(identity,multiply(least_upper_bound(identity,X_61),inverse(X_61)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_61)))]]) ).
cnf(refute_0_1033,plain,
( multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_61),inverse(X_61)))
| multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_61),inverse(X_61)),least_upper_bound(identity,inverse(X_61))) )],[refute_0_1031,refute_0_1032]) ).
cnf(refute_0_1034,plain,
multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)),least_upper_bound(identity,multiply(least_upper_bound(identity,X_61),inverse(X_61)))) )],[refute_0_1028,refute_0_1033]) ).
cnf(refute_0_1035,plain,
least_upper_bound(X_61,least_upper_bound(identity,X_61)) = least_upper_bound(X_61,identity),
inference(subst,[],[refute_0_287:[bind(Y,$fot(identity)),bind(X_15,$fot(X_61))]]) ).
cnf(refute_0_1036,plain,
multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)) = multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)))]]) ).
cnf(refute_0_1037,plain,
( multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)) != multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61))
| least_upper_bound(X_61,least_upper_bound(identity,X_61)) != least_upper_bound(X_61,identity)
| multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)) = multiply(least_upper_bound(X_61,identity),inverse(X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)),multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61))) ),[1,0],$fot(least_upper_bound(X_61,identity))]]) ).
cnf(refute_0_1038,plain,
( least_upper_bound(X_61,least_upper_bound(identity,X_61)) != least_upper_bound(X_61,identity)
| multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)) = multiply(least_upper_bound(X_61,identity),inverse(X_61)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)),multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61))) )],[refute_0_1036,refute_0_1037]) ).
cnf(refute_0_1039,plain,
multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)) = multiply(least_upper_bound(X_61,identity),inverse(X_61)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_61,least_upper_bound(identity,X_61)),least_upper_bound(X_61,identity)) )],[refute_0_1035,refute_0_1038]) ).
cnf(refute_0_1040,plain,
multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)),
inference(subst,[],[refute_0_880:[bind(X_59,$fot(inverse(X_61))),bind(X_60,$fot(least_upper_bound(identity,X_61)))]]) ).
cnf(refute_0_1041,plain,
( multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)) != multiply(least_upper_bound(X_61,identity),inverse(X_61))
| multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) != multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61))
| multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = multiply(least_upper_bound(X_61,identity),inverse(X_61)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)))),bind(Y0,$fot(multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)))),bind(Z0,$fot(multiply(least_upper_bound(X_61,identity),inverse(X_61))))]]) ).
cnf(refute_0_1042,plain,
( multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)) != multiply(least_upper_bound(X_61,identity),inverse(X_61))
| multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = multiply(least_upper_bound(X_61,identity),inverse(X_61)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)),multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61))) )],[refute_0_1040,refute_0_1041]) ).
cnf(refute_0_1043,plain,
multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) = multiply(least_upper_bound(X_61,identity),inverse(X_61)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_61,least_upper_bound(identity,X_61)),inverse(X_61)),multiply(least_upper_bound(X_61,identity),inverse(X_61))) )],[refute_0_1039,refute_0_1042]) ).
cnf(refute_0_1044,plain,
( multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) != multiply(least_upper_bound(X_61,identity),inverse(X_61))
| multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))
| multiply(least_upper_bound(X_61,identity),inverse(X_61)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))) ),[0],$fot(multiply(least_upper_bound(X_61,identity),inverse(X_61)))]]) ).
cnf(refute_0_1045,plain,
( multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))
| multiply(least_upper_bound(X_61,identity),inverse(X_61)) = least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)),multiply(least_upper_bound(X_61,identity),inverse(X_61))) )],[refute_0_1043,refute_0_1044]) ).
cnf(refute_0_1046,plain,
least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))) = least_upper_bound(identity,inverse(X_61)),
inference(subst,[],[refute_0_345:[bind(X_16,$fot(inverse(X_61))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1047,plain,
( multiply(least_upper_bound(X_61,identity),inverse(X_61)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))
| least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))) != least_upper_bound(identity,inverse(X_61))
| multiply(least_upper_bound(X_61,identity),inverse(X_61)) = least_upper_bound(identity,inverse(X_61)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_61,identity),inverse(X_61)),least_upper_bound(identity,inverse(X_61))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))))]]) ).
cnf(refute_0_1048,plain,
( multiply(least_upper_bound(X_61,identity),inverse(X_61)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))
| multiply(least_upper_bound(X_61,identity),inverse(X_61)) = least_upper_bound(identity,inverse(X_61)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,inverse(X_61))),least_upper_bound(identity,inverse(X_61))) )],[refute_0_1046,refute_0_1047]) ).
cnf(refute_0_1049,plain,
( multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)) != least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))
| multiply(least_upper_bound(X_61,identity),inverse(X_61)) = least_upper_bound(identity,inverse(X_61)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_61,identity),inverse(X_61)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))) )],[refute_0_1045,refute_0_1048]) ).
cnf(refute_0_1050,plain,
multiply(least_upper_bound(X_61,identity),inverse(X_61)) = least_upper_bound(identity,inverse(X_61)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(identity,X_61),X_61),inverse(X_61)),least_upper_bound(identity,least_upper_bound(identity,inverse(X_61)))) )],[refute_0_1034,refute_0_1049]) ).
cnf(refute_0_1051,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),
inference(subst,[],[refute_0_1050:[bind(X_61,$fot(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))]]) ).
cnf(refute_0_1052,plain,
X_137 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137))),
inference(subst,[],[refute_0_521:[bind(X_29,$fot(X_137)),bind(X_63,$fot(inverse(least_upper_bound(X_137,X_16))))]]) ).
cnf(refute_0_1053,plain,
multiply(inverse(X_33),least_upper_bound(X_48,inverse(inverse(X_33)))) = least_upper_bound(identity,multiply(inverse(X_33),X_48)),
inference(subst,[],[refute_0_40:[bind(X_44,$fot(inverse(X_33))),bind(X_45,$fot(X_48))]]) ).
cnf(refute_0_1054,plain,
( multiply(inverse(X_33),least_upper_bound(X_48,inverse(inverse(X_33)))) != least_upper_bound(identity,multiply(inverse(X_33),X_48))
| inverse(inverse(X_33)) != X_33
| multiply(inverse(X_33),least_upper_bound(X_48,X_33)) = least_upper_bound(identity,multiply(inverse(X_33),X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_33),least_upper_bound(X_48,inverse(inverse(X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) ),[0,1,1],$fot(X_33)]]) ).
cnf(refute_0_1055,plain,
( multiply(inverse(X_33),least_upper_bound(X_48,inverse(inverse(X_33)))) != least_upper_bound(identity,multiply(inverse(X_33),X_48))
| multiply(inverse(X_33),least_upper_bound(X_48,X_33)) = least_upper_bound(identity,multiply(inverse(X_33),X_48)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_33)),X_33) )],[refute_0_119,refute_0_1054]) ).
cnf(refute_0_1056,plain,
multiply(inverse(X_33),least_upper_bound(X_48,X_33)) = least_upper_bound(identity,multiply(inverse(X_33),X_48)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),least_upper_bound(X_48,inverse(inverse(X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) )],[refute_0_1053,refute_0_1055]) ).
cnf(refute_0_1057,plain,
multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,least_upper_bound(X_71,X_16))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71)),
inference(subst,[],[refute_0_1056:[bind(X_33,$fot(least_upper_bound(X_71,X_16))),bind(X_48,$fot(X_71))]]) ).
cnf(refute_0_1058,plain,
least_upper_bound(X_71,least_upper_bound(X_71,X_16)) = least_upper_bound(X_71,X_16),
inference(subst,[],[refute_0_345:[bind(X_17,$fot(X_71))]]) ).
cnf(refute_0_1059,plain,
( multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,least_upper_bound(X_71,X_16))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))
| least_upper_bound(X_71,least_upper_bound(X_71,X_16)) != least_upper_bound(X_71,X_16)
| multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,least_upper_bound(X_71,X_16))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))) ),[0,1],$fot(least_upper_bound(X_71,X_16))]]) ).
cnf(refute_0_1060,plain,
( multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,least_upper_bound(X_71,X_16))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))
| multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_71,least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) )],[refute_0_1058,refute_0_1059]) ).
cnf(refute_0_1061,plain,
multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,least_upper_bound(X_71,X_16))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))) )],[refute_0_1057,refute_0_1060]) ).
cnf(refute_0_1062,plain,
multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_71,X_16)))]]) ).
cnf(refute_0_1063,plain,
( multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) != identity
| multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1064,plain,
( multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)),identity) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_71,X_16)),least_upper_bound(X_71,X_16)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_71,X_16)),X_71))) )],[refute_0_1061,refute_0_1064]) ).
cnf(refute_0_1066,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)),
inference(subst,[],[refute_0_1065:[bind(X_71,$fot(X_137))]]) ).
cnf(refute_0_1067,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137))))]]) ).
cnf(refute_0_1068,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137))) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
( X_137 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)) != identity
| X_137 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_137,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1070,plain,
( X_137 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)))
| X_137 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)),identity) )],[refute_0_1068,refute_0_1069]) ).
cnf(refute_0_1071,plain,
X_137 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity),
inference(resolve,[$cnf( $equal(X_137,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_137,X_16)),X_137)))) )],[refute_0_1052,refute_0_1070]) ).
cnf(refute_0_1072,plain,
least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)) = least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_137))),bind(Y,$fot(inverse(least_upper_bound(X_137,X_16))))]]) ).
cnf(refute_0_1073,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))) = inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))))]]) ).
cnf(refute_0_1074,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))) != inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)))
| least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)) != least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))) = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)))) ),[1,0],$fot(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))]]) ).
cnf(refute_0_1075,plain,
( least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)) != least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))) = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)))) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))) = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)),least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))) )],[refute_0_1072,refute_0_1075]) ).
cnf(refute_0_1077,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) = inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)))))]]) ).
cnf(refute_0_1078,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) != inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)))
| inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))) != inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity))),bind(Y0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))))),bind(Z0,$fot(inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))))]]) ).
cnf(refute_0_1079,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))) != inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity),inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137)))) )],[refute_0_1077,refute_0_1078]) ).
cnf(refute_0_1080,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))) )],[refute_0_1076,refute_0_1079]) ).
cnf(refute_0_1081,plain,
( X_137 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity)
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity) != inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))
| X_137 = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_137,inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity))]]) ).
cnf(refute_0_1082,plain,
( X_137 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity)
| X_137 = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity),inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16))))) )],[refute_0_1080,refute_0_1081]) ).
cnf(refute_0_1083,plain,
X_137 = inverse(least_upper_bound(inverse(X_137),inverse(least_upper_bound(X_137,X_16)))),
inference(resolve,[$cnf( $equal(X_137,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_137,X_16)),inverse(X_137))),identity)) )],[refute_0_1071,refute_0_1082]) ).
cnf(refute_0_1084,plain,
X_185 = inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),
inference(subst,[],[refute_0_1083:[bind(X_137,$fot(X_185)),bind(X_16,$fot(X_186))]]) ).
cnf(refute_0_1085,plain,
( X_185 != inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))
| inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) = X_185 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_185)),bind(Y0,$fot(inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))]]) ).
cnf(refute_0_1086,plain,
inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) = X_185,
inference(resolve,[$cnf( $equal(X_185,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) )],[refute_0_1084,refute_0_1085]) ).
cnf(refute_0_1087,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) != X_185
| multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) = least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),[0,1],$fot(X_185)]]) ).
cnf(refute_0_1088,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) = least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) )],[refute_0_1086,refute_0_1087]) ).
cnf(refute_0_1089,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) = least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) )],[refute_0_1051,refute_0_1088]) ).
cnf(refute_0_1090,plain,
multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = least_upper_bound(multiply(least_upper_bound(X_63,inverse(X)),X),multiply(Z,X)),
inference(subst,[],[monotony_lub2:[bind(Y,$fot(least_upper_bound(X_63,inverse(X))))]]) ).
cnf(refute_0_1091,plain,
( multiply(least_upper_bound(X_63,inverse(X)),X) != least_upper_bound(identity,multiply(X_63,X))
| multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_63,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_63,inverse(X)),X),multiply(Z,X))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_63,X)))]]) ).
cnf(refute_0_1092,plain,
( multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_63,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_63,inverse(X)),X),least_upper_bound(identity,multiply(X_63,X))) )],[refute_0_799,refute_0_1091]) ).
cnf(refute_0_1093,plain,
multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_63,inverse(X)),X),multiply(Z,X))) )],[refute_0_1090,refute_0_1092]) ).
cnf(refute_0_1094,plain,
least_upper_bound(least_upper_bound(X_63,inverse(X)),Z) = least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_283:[bind(X,$fot(X_63)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_1095,plain,
multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X))]]) ).
cnf(refute_0_1096,plain,
( multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) != multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X)
| least_upper_bound(least_upper_bound(X_63,inverse(X)),Z) != least_upper_bound(X_63,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X)) ),[1,0],$fot(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_1097,plain,
( least_upper_bound(least_upper_bound(X_63,inverse(X)),Z) != least_upper_bound(X_63,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X)) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) = multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),least_upper_bound(X_63,least_upper_bound(inverse(X),Z))) )],[refute_0_1094,refute_0_1097]) ).
cnf(refute_0_1099,plain,
( multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) != multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X)
| multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))
| multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))) ),[0],$fot(multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X))]]) ).
cnf(refute_0_1100,plain,
( multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))
| multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X)) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
least_upper_bound(multiply(X_63,X),multiply(Z,X)) = multiply(least_upper_bound(X_63,Z),X),
inference(subst,[],[refute_0_242:[bind(Y,$fot(X_63))]]) ).
cnf(refute_0_1102,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))) = least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))))]]) ).
cnf(refute_0_1103,plain,
( least_upper_bound(multiply(X_63,X),multiply(Z,X)) != multiply(least_upper_bound(X_63,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))) != least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X)))
| least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X)))) ),[1,1],$fot(multiply(least_upper_bound(X_63,Z),X))]]) ).
cnf(refute_0_1104,plain,
( least_upper_bound(multiply(X_63,X),multiply(Z,X)) != multiply(least_upper_bound(X_63,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X)))) )],[refute_0_1102,refute_0_1103]) ).
cnf(refute_0_1105,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_63,X),multiply(Z,X)),multiply(least_upper_bound(X_63,Z),X)) )],[refute_0_1101,refute_0_1104]) ).
cnf(refute_0_1106,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) = least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))),
inference(subst,[],[refute_0_283:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_63,X))),bind(Z,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_1107,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) != least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X)))
| least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X))))]]) ).
cnf(refute_0_1108,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)),least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X)))) )],[refute_0_1106,refute_0_1107]) ).
cnf(refute_0_1109,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_63,X),multiply(Z,X))),least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X))) )],[refute_0_1105,refute_0_1108]) ).
cnf(refute_0_1110,plain,
( multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))
| least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)) != least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X))
| multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X),least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)))]]) ).
cnf(refute_0_1111,plain,
( multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))
| multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X)),least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X))) )],[refute_0_1109,refute_0_1110]) ).
cnf(refute_0_1112,plain,
( multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))
| multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X),least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))) )],[refute_0_1100,refute_0_1111]) ).
cnf(refute_0_1113,plain,
multiply(least_upper_bound(X_63,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_63,Z),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_63,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_63,X)),multiply(Z,X))) )],[refute_0_1093,refute_0_1112]) ).
cnf(refute_0_1114,plain,
multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) = least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),
inference(subst,[],[refute_0_1113:[bind(X,$fot(X_185)),bind(Z,$fot(inverse(least_upper_bound(X_185,X_186)))),bind(X_63,$fot(identity))]]) ).
cnf(refute_0_1115,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) = multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185),
inference(subst,[],[refute_0_647:[bind(X,$fot(X_185)),bind(Y,$fot(identity)),bind(Z,$fot(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))]]) ).
cnf(refute_0_1116,plain,
( multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) != least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185))
| multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) != multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185)
| multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) = least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185))))]]) ).
cnf(refute_0_1117,plain,
( multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) != least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185))
| multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) = least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185),multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185)) )],[refute_0_1115,refute_0_1116]) ).
cnf(refute_0_1118,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) = least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185))) )],[refute_0_1114,refute_0_1117]) ).
cnf(refute_0_1119,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) != least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185))
| multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185),least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)))]]) ).
cnf(refute_0_1120,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185))) )],[refute_0_1118,refute_0_1119]) ).
cnf(refute_0_1121,plain,
least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))]]) ).
cnf(refute_0_1122,plain,
( inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) != X_185
| least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = least_upper_bound(identity,X_185) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),[1,1],$fot(X_185)]]) ).
cnf(refute_0_1123,plain,
( inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) != X_185
| least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = least_upper_bound(identity,X_185) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) )],[refute_0_1121,refute_0_1122]) ).
cnf(refute_0_1124,plain,
least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = least_upper_bound(identity,X_185),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) )],[refute_0_1086,refute_0_1123]) ).
cnf(refute_0_1125,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != least_upper_bound(identity,X_185)
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,X_185) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(identity,X_185)) ),[0],$fot(least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))]]) ).
cnf(refute_0_1126,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,X_185) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),least_upper_bound(identity,X_185)) )],[refute_0_1124,refute_0_1125]) ).
cnf(refute_0_1127,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185) != least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,X_185) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) )],[refute_0_1120,refute_0_1126]) ).
cnf(refute_0_1128,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,X_185),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))),identity),X_185),least_upper_bound(identity,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) )],[refute_0_1089,refute_0_1127]) ).
cnf(refute_0_1129,plain,
multiply(identity,least_upper_bound(X_185,identity)) = least_upper_bound(X_185,identity),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_185,identity)))]]) ).
cnf(refute_0_1130,plain,
least_upper_bound(identity,multiply(identity,X_185)) = multiply(identity,least_upper_bound(X_185,identity)),
inference(subst,[],[refute_0_375:[bind(X_44,$fot(identity)),bind(X_45,$fot(X_185))]]) ).
cnf(refute_0_1131,plain,
( multiply(identity,least_upper_bound(X_185,identity)) != least_upper_bound(X_185,identity)
| least_upper_bound(identity,multiply(identity,X_185)) != multiply(identity,least_upper_bound(X_185,identity))
| least_upper_bound(identity,multiply(identity,X_185)) = least_upper_bound(X_185,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,X_185)))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_185,identity)))),bind(Z0,$fot(least_upper_bound(X_185,identity)))]]) ).
cnf(refute_0_1132,plain,
( multiply(identity,least_upper_bound(X_185,identity)) != least_upper_bound(X_185,identity)
| least_upper_bound(identity,multiply(identity,X_185)) = least_upper_bound(X_185,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_185)),multiply(identity,least_upper_bound(X_185,identity))) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
least_upper_bound(identity,multiply(identity,X_185)) = least_upper_bound(X_185,identity),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_185,identity)),least_upper_bound(X_185,identity)) )],[refute_0_1129,refute_0_1132]) ).
cnf(refute_0_1134,plain,
multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))),
inference(subst,[],[refute_0_331:[bind(X_61,$fot(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))]]) ).
cnf(refute_0_1135,plain,
( multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) != X_185
| multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) = least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) ),[0,1],$fot(X_185)]]) ).
cnf(refute_0_1136,plain,
( multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) = least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) )],[refute_0_1086,refute_0_1135]) ).
cnf(refute_0_1137,plain,
multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) = least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) )],[refute_0_1134,refute_0_1136]) ).
cnf(refute_0_1138,plain,
multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) = least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)),
inference(subst,[],[refute_0_1113:[bind(X,$fot(X_185)),bind(Z,$fot(inverse(least_upper_bound(X_185,X_186)))),bind(X_63,$fot(X_60))]]) ).
cnf(refute_0_1139,plain,
( multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) != least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185))
| least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)))]]) ).
cnf(refute_0_1140,plain,
( multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185),least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185))) )],[refute_0_1138,refute_0_1139]) ).
cnf(refute_0_1141,plain,
multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),
introduced(tautology,[refl,[$fot(multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))]]) ).
cnf(refute_0_1142,plain,
( multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))
| inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) != X_185
| multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = multiply(X_60,X_185) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) ),[1,1],$fot(X_185)]]) ).
cnf(refute_0_1143,plain,
( inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))) != X_185
| multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = multiply(X_60,X_185) ),
inference(resolve,[$cnf( $equal(multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) )],[refute_0_1141,refute_0_1142]) ).
cnf(refute_0_1144,plain,
multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) = multiply(X_60,X_185),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) )],[refute_0_1086,refute_0_1143]) ).
cnf(refute_0_1145,plain,
least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) = least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))))]]) ).
cnf(refute_0_1146,plain,
( multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != multiply(X_60,X_185)
| least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) = least_upper_bound(identity,multiply(X_60,X_185)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) ),[1,1],$fot(multiply(X_60,X_185))]]) ).
cnf(refute_0_1147,plain,
( multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))) != multiply(X_60,X_185)
| least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) = least_upper_bound(identity,multiply(X_60,X_185)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) )],[refute_0_1145,refute_0_1146]) ).
cnf(refute_0_1148,plain,
least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) = least_upper_bound(identity,multiply(X_60,X_185)),
inference(resolve,[$cnf( $equal(multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))),multiply(X_60,X_185)) )],[refute_0_1144,refute_0_1147]) ).
cnf(refute_0_1149,plain,
( least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))) != least_upper_bound(identity,multiply(X_60,X_185))
| least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,multiply(X_60,X_185)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) ),[1],$fot(least_upper_bound(identity,multiply(X_60,X_185)))]]) ).
cnf(refute_0_1150,plain,
( least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,multiply(X_60,X_185)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))))),least_upper_bound(identity,multiply(X_60,X_185))) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
( multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185) != least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))
| least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,multiply(X_60,X_185)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) )],[refute_0_1140,refute_0_1150]) ).
cnf(refute_0_1152,plain,
least_upper_bound(identity,multiply(least_upper_bound(X_60,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,multiply(X_60,X_185)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186)))),X_185),least_upper_bound(identity,multiply(X_60,inverse(least_upper_bound(inverse(X_185),inverse(least_upper_bound(X_185,X_186))))))) )],[refute_0_1137,refute_0_1151]) ).
cnf(refute_0_1153,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(identity,multiply(identity,X_185)),
inference(subst,[],[refute_0_1152:[bind(X_60,$fot(identity))]]) ).
cnf(refute_0_1154,plain,
( least_upper_bound(identity,multiply(identity,X_185)) != least_upper_bound(X_185,identity)
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(identity,multiply(identity,X_185))
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(X_185,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,X_185)))),bind(Z0,$fot(least_upper_bound(X_185,identity)))]]) ).
cnf(refute_0_1155,plain,
( least_upper_bound(identity,multiply(identity,X_185)) != least_upper_bound(X_185,identity)
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(X_185,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(identity,multiply(identity,X_185))) )],[refute_0_1153,refute_0_1154]) ).
cnf(refute_0_1156,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) = least_upper_bound(X_185,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_185)),least_upper_bound(X_185,identity)) )],[refute_0_1133,refute_0_1155]) ).
cnf(refute_0_1157,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(X_185,identity)
| least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(identity,X_185)
| least_upper_bound(X_185,identity) = least_upper_bound(identity,X_185) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(identity,X_185)) ),[0],$fot(least_upper_bound(X_185,identity))]]) ).
cnf(refute_0_1158,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)) != least_upper_bound(identity,X_185)
| least_upper_bound(X_185,identity) = least_upper_bound(identity,X_185) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(X_185,identity)) )],[refute_0_1156,refute_0_1157]) ).
cnf(refute_0_1159,plain,
least_upper_bound(X_185,identity) = least_upper_bound(identity,X_185),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(least_upper_bound(X_185,X_186))),X_185)),least_upper_bound(identity,X_185)) )],[refute_0_1128,refute_0_1158]) ).
cnf(refute_0_1160,plain,
least_upper_bound(inverse(X_216),identity) = least_upper_bound(identity,inverse(X_216)),
inference(subst,[],[refute_0_1159:[bind(X_185,$fot(inverse(X_216)))]]) ).
cnf(refute_0_1161,plain,
least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(X_45,identity)))),
inference(subst,[],[refute_0_829:[bind(X,$fot(inverse(least_upper_bound(X_45,identity)))),bind(X_18,$fot(X_110)),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_1162,plain,
( least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))) != identity
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1163,plain,
( least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))),identity) )],[refute_0_451,refute_0_1162]) ).
cnf(refute_0_1164,plain,
least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(X_45,identity))))) )],[refute_0_1161,refute_0_1163]) ).
cnf(refute_0_1165,plain,
least_upper_bound(X_109,least_upper_bound(X_110,least_upper_bound(Y,X_110))) = least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)),
inference(subst,[],[refute_0_829:[bind(X,$fot(X_109)),bind(X_18,$fot(X_110)),bind(X_19,$fot(least_upper_bound(Y,X_110)))]]) ).
cnf(refute_0_1166,plain,
least_upper_bound(X_110,least_upper_bound(Y,X_110)) = least_upper_bound(X_110,Y),
inference(subst,[],[refute_0_287:[bind(X_15,$fot(X_110))]]) ).
cnf(refute_0_1167,plain,
( least_upper_bound(X_109,least_upper_bound(X_110,least_upper_bound(Y,X_110))) != least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))
| least_upper_bound(X_110,least_upper_bound(Y,X_110)) != least_upper_bound(X_110,Y)
| least_upper_bound(X_109,least_upper_bound(X_110,Y)) = least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(X_110,least_upper_bound(Y,X_110))),least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))) ),[0,1],$fot(least_upper_bound(X_110,Y))]]) ).
cnf(refute_0_1168,plain,
( least_upper_bound(X_109,least_upper_bound(X_110,least_upper_bound(Y,X_110))) != least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))
| least_upper_bound(X_109,least_upper_bound(X_110,Y)) = least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(Y,X_110)),least_upper_bound(X_110,Y)) )],[refute_0_1166,refute_0_1167]) ).
cnf(refute_0_1169,plain,
least_upper_bound(X_109,least_upper_bound(X_110,Y)) = least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(X_110,least_upper_bound(Y,X_110))),least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))) )],[refute_0_1165,refute_0_1168]) ).
cnf(refute_0_1170,plain,
least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))) = least_upper_bound(Y,least_upper_bound(X_110,X_109)),
inference(subst,[],[refute_0_840:[bind(Y,$fot(X_109)),bind(X_18,$fot(Y)),bind(X_19,$fot(X_110))]]) ).
cnf(refute_0_1171,plain,
least_upper_bound(least_upper_bound(Y,X_110),X_109) = least_upper_bound(Y,least_upper_bound(X_110,X_109)),
inference(subst,[],[refute_0_283:[bind(X,$fot(Y)),bind(Y,$fot(X_110)),bind(Z,$fot(X_109))]]) ).
cnf(refute_0_1172,plain,
least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) = least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)))]]) ).
cnf(refute_0_1173,plain,
( least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) != least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))
| least_upper_bound(least_upper_bound(Y,X_110),X_109) != least_upper_bound(Y,least_upper_bound(X_110,X_109))
| least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) = least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)),least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_110,X_109)))]]) ).
cnf(refute_0_1174,plain,
( least_upper_bound(least_upper_bound(Y,X_110),X_109) != least_upper_bound(Y,least_upper_bound(X_110,X_109))
| least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) = least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)),least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))) )],[refute_0_1172,refute_0_1173]) ).
cnf(refute_0_1175,plain,
least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) = least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_110),X_109),least_upper_bound(Y,least_upper_bound(X_110,X_109))) )],[refute_0_1171,refute_0_1174]) ).
cnf(refute_0_1176,plain,
( least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))) != least_upper_bound(Y,least_upper_bound(X_110,X_109))
| least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) != least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109)))
| least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) = least_upper_bound(Y,least_upper_bound(X_110,X_109)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)))),bind(Y0,$fot(least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_110,X_109))))]]) ).
cnf(refute_0_1177,plain,
( least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))) != least_upper_bound(Y,least_upper_bound(X_110,X_109))
| least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) = least_upper_bound(Y,least_upper_bound(X_110,X_109)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)),least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109)))) )],[refute_0_1175,refute_0_1176]) ).
cnf(refute_0_1178,plain,
least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) = least_upper_bound(Y,least_upper_bound(X_110,X_109)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(Y,least_upper_bound(X_110,X_109))),least_upper_bound(Y,least_upper_bound(X_110,X_109))) )],[refute_0_1170,refute_0_1177]) ).
cnf(refute_0_1179,plain,
( least_upper_bound(X_109,least_upper_bound(X_110,Y)) != least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))
| least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)) != least_upper_bound(Y,least_upper_bound(X_110,X_109))
| least_upper_bound(X_109,least_upper_bound(X_110,Y)) = least_upper_bound(Y,least_upper_bound(X_110,X_109)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_109,least_upper_bound(X_110,Y)),least_upper_bound(Y,least_upper_bound(X_110,X_109))) ),[0],$fot(least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)))]]) ).
cnf(refute_0_1180,plain,
( least_upper_bound(X_109,least_upper_bound(X_110,Y)) != least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))
| least_upper_bound(X_109,least_upper_bound(X_110,Y)) = least_upper_bound(Y,least_upper_bound(X_110,X_109)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109)),least_upper_bound(Y,least_upper_bound(X_110,X_109))) )],[refute_0_1178,refute_0_1179]) ).
cnf(refute_0_1181,plain,
least_upper_bound(X_109,least_upper_bound(X_110,Y)) = least_upper_bound(Y,least_upper_bound(X_110,X_109)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(X_110,Y)),least_upper_bound(X_110,least_upper_bound(least_upper_bound(Y,X_110),X_109))) )],[refute_0_1169,refute_0_1180]) ).
cnf(refute_0_1182,plain,
( least_upper_bound(X_109,least_upper_bound(X_110,Y)) != least_upper_bound(Y,least_upper_bound(X_110,X_109))
| least_upper_bound(Y,least_upper_bound(X_110,X_109)) = least_upper_bound(X_109,least_upper_bound(X_110,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_109,least_upper_bound(X_110,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_110,X_109))))]]) ).
cnf(refute_0_1183,plain,
least_upper_bound(Y,least_upper_bound(X_110,X_109)) = least_upper_bound(X_109,least_upper_bound(X_110,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(X_110,Y)),least_upper_bound(Y,least_upper_bound(X_110,X_109))) )],[refute_0_1181,refute_0_1182]) ).
cnf(refute_0_1184,plain,
least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) = least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))),
inference(subst,[],[refute_0_1183:[bind(Y,$fot(inverse(least_upper_bound(X_45,identity)))),bind(X_109,$fot(identity))]]) ).
cnf(refute_0_1185,plain,
( least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,identity)
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) != least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(X_110,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,identity)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))))]]) ).
cnf(refute_0_1186,plain,
( least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,identity)
| least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(X_110,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)),least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))) )],[refute_0_1184,refute_0_1185]) ).
cnf(refute_0_1187,plain,
least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(X_110,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,identity)) )],[refute_0_1164,refute_0_1186]) ).
cnf(refute_0_1188,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))) = least_upper_bound(inverse(X_216),identity),
inference(subst,[],[refute_0_1187:[bind(X_110,$fot(inverse(X_216))),bind(X_45,$fot(X_216))]]) ).
cnf(refute_0_1189,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))) != least_upper_bound(inverse(X_216),identity)
| least_upper_bound(inverse(X_216),identity) != least_upper_bound(identity,inverse(X_216))
| least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))) = least_upper_bound(identity,inverse(X_216)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))),bind(Y0,$fot(least_upper_bound(inverse(X_216),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_216))))]]) ).
cnf(refute_0_1190,plain,
( least_upper_bound(inverse(X_216),identity) != least_upper_bound(identity,inverse(X_216))
| least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))) = least_upper_bound(identity,inverse(X_216)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(inverse(X_216),identity)) )],[refute_0_1188,refute_0_1189]) ).
cnf(refute_0_1191,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))) = least_upper_bound(identity,inverse(X_216)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_216),identity),least_upper_bound(identity,inverse(X_216))) )],[refute_0_1160,refute_0_1190]) ).
cnf(refute_0_1192,plain,
inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))))]]) ).
cnf(refute_0_1193,plain,
( inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))
| least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))) != least_upper_bound(identity,inverse(X_216))
| inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) = inverse(least_upper_bound(identity,inverse(X_216))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))),inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_216)))]]) ).
cnf(refute_0_1194,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))) != least_upper_bound(identity,inverse(X_216))
| inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) = inverse(least_upper_bound(identity,inverse(X_216))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))),inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))) )],[refute_0_1192,refute_0_1193]) ).
cnf(refute_0_1195,plain,
inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) = inverse(least_upper_bound(identity,inverse(X_216))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,inverse(X_216))) )],[refute_0_1191,refute_0_1194]) ).
cnf(refute_0_1196,plain,
inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) = inverse(least_upper_bound(identity,least_upper_bound(X_19,X))),
inference(subst,[],[refute_0_465:[bind(X_69,$fot(least_upper_bound(X_19,X)))]]) ).
cnf(refute_0_1197,plain,
least_upper_bound(X,least_upper_bound(identity,X_19)) = least_upper_bound(identity,least_upper_bound(X_19,X)),
inference(subst,[],[refute_0_829:[bind(X_18,$fot(identity))]]) ).
cnf(refute_0_1198,plain,
( least_upper_bound(X,least_upper_bound(identity,X_19)) != least_upper_bound(identity,least_upper_bound(X_19,X))
| least_upper_bound(identity,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(identity,X_19)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(identity,X_19)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_19,X))))]]) ).
cnf(refute_0_1199,plain,
least_upper_bound(identity,least_upper_bound(X_19,X)) = least_upper_bound(X,least_upper_bound(identity,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,X_19)),least_upper_bound(identity,least_upper_bound(X_19,X))) )],[refute_0_1197,refute_0_1198]) ).
cnf(refute_0_1200,plain,
( inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) != inverse(least_upper_bound(identity,least_upper_bound(X_19,X)))
| least_upper_bound(identity,least_upper_bound(X_19,X)) != least_upper_bound(X,least_upper_bound(identity,X_19))
| inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) = inverse(least_upper_bound(X,least_upper_bound(identity,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_19,X),identity)),inverse(least_upper_bound(identity,least_upper_bound(X_19,X)))) ),[1,0],$fot(least_upper_bound(X,least_upper_bound(identity,X_19)))]]) ).
cnf(refute_0_1201,plain,
( inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) != inverse(least_upper_bound(identity,least_upper_bound(X_19,X)))
| inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) = inverse(least_upper_bound(X,least_upper_bound(identity,X_19))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_19,X)),least_upper_bound(X,least_upper_bound(identity,X_19))) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) = inverse(least_upper_bound(X,least_upper_bound(identity,X_19))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_19,X),identity)),inverse(least_upper_bound(identity,least_upper_bound(X_19,X)))) )],[refute_0_1196,refute_0_1201]) ).
cnf(refute_0_1203,plain,
( inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) != inverse(least_upper_bound(X,least_upper_bound(identity,X_19)))
| inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) != inverse(least_upper_bound(identity,least_upper_bound(X_19,X)))
| inverse(least_upper_bound(identity,least_upper_bound(X_19,X))) = inverse(least_upper_bound(X,least_upper_bound(identity,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_19,X),identity)),inverse(least_upper_bound(X,least_upper_bound(identity,X_19)))) ),[0],$fot(inverse(least_upper_bound(identity,least_upper_bound(X_19,X))))]]) ).
cnf(refute_0_1204,plain,
( inverse(least_upper_bound(least_upper_bound(X_19,X),identity)) != inverse(least_upper_bound(X,least_upper_bound(identity,X_19)))
| inverse(least_upper_bound(identity,least_upper_bound(X_19,X))) = inverse(least_upper_bound(X,least_upper_bound(identity,X_19))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_19,X),identity)),inverse(least_upper_bound(identity,least_upper_bound(X_19,X)))) )],[refute_0_1196,refute_0_1203]) ).
cnf(refute_0_1205,plain,
inverse(least_upper_bound(identity,least_upper_bound(X_19,X))) = inverse(least_upper_bound(X,least_upper_bound(identity,X_19))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_19,X),identity)),inverse(least_upper_bound(X,least_upper_bound(identity,X_19)))) )],[refute_0_1202,refute_0_1204]) ).
cnf(refute_0_1206,plain,
( inverse(least_upper_bound(identity,least_upper_bound(X_19,X))) != inverse(least_upper_bound(X,least_upper_bound(identity,X_19)))
| inverse(least_upper_bound(X,least_upper_bound(identity,X_19))) = inverse(least_upper_bound(identity,least_upper_bound(X_19,X))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,least_upper_bound(X_19,X))))),bind(Y0,$fot(inverse(least_upper_bound(X,least_upper_bound(identity,X_19)))))]]) ).
cnf(refute_0_1207,plain,
inverse(least_upper_bound(X,least_upper_bound(identity,X_19))) = inverse(least_upper_bound(identity,least_upper_bound(X_19,X))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_19,X))),inverse(least_upper_bound(X,least_upper_bound(identity,X_19)))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))),
inference(subst,[],[refute_0_1207:[bind(X,$fot(inverse(least_upper_bound(X_216,identity)))),bind(X_19,$fot(inverse(X_216)))]]) ).
cnf(refute_0_1209,plain,
multiply(inverse(X_61),inverse(multiply(least_upper_bound(X_60,X_61),inverse(X_61)))) = inverse(least_upper_bound(X_60,X_61)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(least_upper_bound(X_60,X_61))),bind(X_38,$fot(inverse(X_61)))]]) ).
cnf(refute_0_1210,plain,
( multiply(inverse(X_61),inverse(multiply(least_upper_bound(X_60,X_61),inverse(X_61)))) != inverse(least_upper_bound(X_60,X_61))
| multiply(least_upper_bound(X_60,X_61),inverse(X_61)) != least_upper_bound(identity,multiply(X_60,inverse(X_61)))
| multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) = inverse(least_upper_bound(X_60,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_61),inverse(multiply(least_upper_bound(X_60,X_61),inverse(X_61)))),inverse(least_upper_bound(X_60,X_61))) ),[0,1,0],$fot(least_upper_bound(identity,multiply(X_60,inverse(X_61))))]]) ).
cnf(refute_0_1211,plain,
( multiply(inverse(X_61),inverse(multiply(least_upper_bound(X_60,X_61),inverse(X_61)))) != inverse(least_upper_bound(X_60,X_61))
| multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) = inverse(least_upper_bound(X_60,X_61)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_60,X_61),inverse(X_61)),least_upper_bound(identity,multiply(X_60,inverse(X_61)))) )],[refute_0_331,refute_0_1210]) ).
cnf(refute_0_1212,plain,
multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) = inverse(least_upper_bound(X_60,X_61)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),inverse(multiply(least_upper_bound(X_60,X_61),inverse(X_61)))),inverse(least_upper_bound(X_60,X_61))) )],[refute_0_1209,refute_0_1211]) ).
cnf(refute_0_1213,plain,
inverse(inverse(X_61)) = X_61,
inference(subst,[],[refute_0_119:[bind(X_33,$fot(X_61))]]) ).
cnf(refute_0_1214,plain,
least_upper_bound(inverse(inverse(X_61)),X_60) = least_upper_bound(inverse(inverse(X_61)),X_60),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(X_61)),X_60))]]) ).
cnf(refute_0_1215,plain,
( inverse(inverse(X_61)) != X_61
| least_upper_bound(inverse(inverse(X_61)),X_60) != least_upper_bound(inverse(inverse(X_61)),X_60)
| least_upper_bound(inverse(inverse(X_61)),X_60) = least_upper_bound(X_61,X_60) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_61)),X_60),least_upper_bound(inverse(inverse(X_61)),X_60)) ),[1,0],$fot(X_61)]]) ).
cnf(refute_0_1216,plain,
( inverse(inverse(X_61)) != X_61
| least_upper_bound(inverse(inverse(X_61)),X_60) = least_upper_bound(X_61,X_60) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_61)),X_60),least_upper_bound(inverse(inverse(X_61)),X_60)) )],[refute_0_1214,refute_0_1215]) ).
cnf(refute_0_1217,plain,
least_upper_bound(inverse(inverse(X_61)),X_60) = least_upper_bound(X_61,X_60),
inference(resolve,[$cnf( $equal(inverse(inverse(X_61)),X_61) )],[refute_0_1213,refute_0_1216]) ).
cnf(refute_0_1218,plain,
inverse(least_upper_bound(inverse(inverse(X_61)),X_60)) = inverse(least_upper_bound(inverse(inverse(X_61)),X_60)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(inverse(X_61)),X_60)))]]) ).
cnf(refute_0_1219,plain,
( inverse(least_upper_bound(inverse(inverse(X_61)),X_60)) != inverse(least_upper_bound(inverse(inverse(X_61)),X_60))
| least_upper_bound(inverse(inverse(X_61)),X_60) != least_upper_bound(X_61,X_60)
| inverse(least_upper_bound(inverse(inverse(X_61)),X_60)) = inverse(least_upper_bound(X_61,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X_61)),X_60)),inverse(least_upper_bound(inverse(inverse(X_61)),X_60))) ),[1,0],$fot(least_upper_bound(X_61,X_60))]]) ).
cnf(refute_0_1220,plain,
( least_upper_bound(inverse(inverse(X_61)),X_60) != least_upper_bound(X_61,X_60)
| inverse(least_upper_bound(inverse(inverse(X_61)),X_60)) = inverse(least_upper_bound(X_61,X_60)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X_61)),X_60)),inverse(least_upper_bound(inverse(inverse(X_61)),X_60))) )],[refute_0_1218,refute_0_1219]) ).
cnf(refute_0_1221,plain,
inverse(least_upper_bound(inverse(inverse(X_61)),X_60)) = inverse(least_upper_bound(X_61,X_60)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_61)),X_60),least_upper_bound(X_61,X_60)) )],[refute_0_1217,refute_0_1220]) ).
cnf(refute_0_1222,plain,
multiply(X_197,inverse(multiply(least_upper_bound(inverse(X_197),X_61),X_197))) = inverse(least_upper_bound(inverse(X_197),X_61)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(least_upper_bound(inverse(X_197),X_61))),bind(X_38,$fot(X_197))]]) ).
cnf(refute_0_1223,plain,
multiply(least_upper_bound(inverse(X_59),X_61),X_59) = least_upper_bound(multiply(inverse(X_59),X_59),multiply(X_61,X_59)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_59)),bind(Y,$fot(inverse(X_59))),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_1224,plain,
( multiply(inverse(X_59),X_59) != identity
| multiply(least_upper_bound(inverse(X_59),X_61),X_59) != least_upper_bound(multiply(inverse(X_59),X_59),multiply(X_61,X_59))
| multiply(least_upper_bound(inverse(X_59),X_61),X_59) = least_upper_bound(identity,multiply(X_61,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_59),X_61),X_59),least_upper_bound(multiply(inverse(X_59),X_59),multiply(X_61,X_59))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1225,plain,
( multiply(least_upper_bound(inverse(X_59),X_61),X_59) != least_upper_bound(multiply(inverse(X_59),X_59),multiply(X_61,X_59))
| multiply(least_upper_bound(inverse(X_59),X_61),X_59) = least_upper_bound(identity,multiply(X_61,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),X_59),identity) )],[refute_0_510,refute_0_1224]) ).
cnf(refute_0_1226,plain,
multiply(least_upper_bound(inverse(X_59),X_61),X_59) = least_upper_bound(identity,multiply(X_61,X_59)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_59),X_61),X_59),least_upper_bound(multiply(inverse(X_59),X_59),multiply(X_61,X_59))) )],[refute_0_1223,refute_0_1225]) ).
cnf(refute_0_1227,plain,
multiply(least_upper_bound(inverse(X_197),X_61),X_197) = least_upper_bound(identity,multiply(X_61,X_197)),
inference(subst,[],[refute_0_1226:[bind(X_59,$fot(X_197))]]) ).
cnf(refute_0_1228,plain,
( multiply(X_197,inverse(multiply(least_upper_bound(inverse(X_197),X_61),X_197))) != inverse(least_upper_bound(inverse(X_197),X_61))
| multiply(least_upper_bound(inverse(X_197),X_61),X_197) != least_upper_bound(identity,multiply(X_61,X_197))
| multiply(X_197,inverse(least_upper_bound(identity,multiply(X_61,X_197)))) = inverse(least_upper_bound(inverse(X_197),X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_197,inverse(multiply(least_upper_bound(inverse(X_197),X_61),X_197))),inverse(least_upper_bound(inverse(X_197),X_61))) ),[0,1,0],$fot(least_upper_bound(identity,multiply(X_61,X_197)))]]) ).
cnf(refute_0_1229,plain,
( multiply(X_197,inverse(multiply(least_upper_bound(inverse(X_197),X_61),X_197))) != inverse(least_upper_bound(inverse(X_197),X_61))
| multiply(X_197,inverse(least_upper_bound(identity,multiply(X_61,X_197)))) = inverse(least_upper_bound(inverse(X_197),X_61)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_197),X_61),X_197),least_upper_bound(identity,multiply(X_61,X_197))) )],[refute_0_1227,refute_0_1228]) ).
cnf(refute_0_1230,plain,
multiply(X_197,inverse(least_upper_bound(identity,multiply(X_61,X_197)))) = inverse(least_upper_bound(inverse(X_197),X_61)),
inference(resolve,[$cnf( $equal(multiply(X_197,inverse(multiply(least_upper_bound(inverse(X_197),X_61),X_197))),inverse(least_upper_bound(inverse(X_197),X_61))) )],[refute_0_1222,refute_0_1229]) ).
cnf(refute_0_1231,plain,
multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) = inverse(least_upper_bound(inverse(inverse(X_61)),X_60)),
inference(subst,[],[refute_0_1230:[bind(X_197,$fot(inverse(X_61))),bind(X_61,$fot(X_60))]]) ).
cnf(refute_0_1232,plain,
( multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) != inverse(least_upper_bound(inverse(inverse(X_61)),X_60))
| inverse(least_upper_bound(inverse(inverse(X_61)),X_60)) != inverse(least_upper_bound(X_61,X_60))
| multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) = inverse(least_upper_bound(X_61,X_60)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))))),bind(Y0,$fot(inverse(least_upper_bound(inverse(inverse(X_61)),X_60)))),bind(Z0,$fot(inverse(least_upper_bound(X_61,X_60))))]]) ).
cnf(refute_0_1233,plain,
( inverse(least_upper_bound(inverse(inverse(X_61)),X_60)) != inverse(least_upper_bound(X_61,X_60))
| multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) = inverse(least_upper_bound(X_61,X_60)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))),inverse(least_upper_bound(inverse(inverse(X_61)),X_60))) )],[refute_0_1231,refute_0_1232]) ).
cnf(refute_0_1234,plain,
multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) = inverse(least_upper_bound(X_61,X_60)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(inverse(X_61)),X_60)),inverse(least_upper_bound(X_61,X_60))) )],[refute_0_1221,refute_0_1233]) ).
cnf(refute_0_1235,plain,
( multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) != inverse(least_upper_bound(X_60,X_61))
| multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) != inverse(least_upper_bound(X_61,X_60))
| inverse(least_upper_bound(X_61,X_60)) = inverse(least_upper_bound(X_60,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))),inverse(least_upper_bound(X_60,X_61))) ),[0],$fot(inverse(least_upper_bound(X_61,X_60)))]]) ).
cnf(refute_0_1236,plain,
( multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))) != inverse(least_upper_bound(X_60,X_61))
| inverse(least_upper_bound(X_61,X_60)) = inverse(least_upper_bound(X_60,X_61)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))),inverse(least_upper_bound(X_61,X_60))) )],[refute_0_1234,refute_0_1235]) ).
cnf(refute_0_1237,plain,
inverse(least_upper_bound(X_61,X_60)) = inverse(least_upper_bound(X_60,X_61)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),inverse(least_upper_bound(identity,multiply(X_60,inverse(X_61))))),inverse(least_upper_bound(X_60,X_61))) )],[refute_0_1212,refute_0_1236]) ).
cnf(refute_0_1238,plain,
( inverse(least_upper_bound(X_61,X_60)) != inverse(least_upper_bound(X_60,X_61))
| inverse(least_upper_bound(X_60,X_61)) = inverse(least_upper_bound(X_61,X_60)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_61,X_60)))),bind(Y0,$fot(inverse(least_upper_bound(X_60,X_61))))]]) ).
cnf(refute_0_1239,plain,
inverse(least_upper_bound(X_60,X_61)) = inverse(least_upper_bound(X_61,X_60)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_61,X_60)),inverse(least_upper_bound(X_60,X_61))) )],[refute_0_1237,refute_0_1238]) ).
cnf(refute_0_1240,plain,
inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) = inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216)))),
inference(subst,[],[refute_0_1239:[bind(X_60,$fot(least_upper_bound(identity,inverse(X_216)))),bind(X_61,$fot(inverse(least_upper_bound(X_216,identity))))]]) ).
cnf(refute_0_1241,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) != inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216))))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))))),bind(Y0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))))]]) ).
cnf(refute_0_1242,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216))))) )],[refute_0_1240,refute_0_1241]) ).
cnf(refute_0_1243,plain,
inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_216,identity)),least_upper_bound(identity,inverse(X_216)))),inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))) )],[refute_0_1208,refute_0_1242]) ).
cnf(refute_0_1244,plain,
( inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) != inverse(least_upper_bound(identity,inverse(X_216)))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) = inverse(least_upper_bound(identity,inverse(X_216))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))))),bind(Y0,$fot(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_216)))))]]) ).
cnf(refute_0_1245,plain,
( inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))) != inverse(least_upper_bound(identity,inverse(X_216)))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) = inverse(least_upper_bound(identity,inverse(X_216))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity)))))) )],[refute_0_1243,refute_0_1244]) ).
cnf(refute_0_1246,plain,
inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) = inverse(least_upper_bound(identity,inverse(X_216))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_216),inverse(least_upper_bound(X_216,identity))))),inverse(least_upper_bound(identity,inverse(X_216)))) )],[refute_0_1195,refute_0_1245]) ).
cnf(refute_0_1247,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))))]]) ).
cnf(refute_0_1248,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) != inverse(least_upper_bound(identity,inverse(X_216)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))) ),[1,0],$fot(inverse(least_upper_bound(identity,inverse(X_216))))]]) ).
cnf(refute_0_1249,plain,
( inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))) != inverse(least_upper_bound(identity,inverse(X_216)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),inverse(least_upper_bound(identity,inverse(X_216)))) )],[refute_0_1246,refute_0_1249]) ).
cnf(refute_0_1251,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) != multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) != multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))))]]) ).
cnf(refute_0_1252,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) != multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))) )],[refute_0_1250,refute_0_1251]) ).
cnf(refute_0_1253,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) )],[refute_0_1027,refute_0_1252]) ).
cnf(refute_0_1254,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) != least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) != multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))),bind(Z0,$fot(least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))))]]) ).
cnf(refute_0_1255,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))) != least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) )],[refute_0_1253,refute_0_1254]) ).
cnf(refute_0_1256,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_216))),least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))),least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))) )],[refute_0_1022,refute_0_1255]) ).
cnf(refute_0_1257,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))) != least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))
| least_upper_bound(X_216,identity) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))
| least_upper_bound(X_216,identity) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_216,identity),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))) ),[1],$fot(least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))))]]) ).
cnf(refute_0_1258,plain,
( least_upper_bound(X_216,identity) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))
| least_upper_bound(X_216,identity) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216))))),least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216)))) )],[refute_0_1256,refute_0_1257]) ).
cnf(refute_0_1259,plain,
least_upper_bound(X_216,identity) = least_upper_bound(X_216,inverse(least_upper_bound(identity,X_216))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_216,identity),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_216)),inverse(least_upper_bound(X_216,identity)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_216,inverse(X_216)))))) )],[refute_0_966,refute_0_1258]) ).
cnf(refute_0_1260,plain,
least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))))),
inference(subst,[],[refute_0_1259:[bind(X_216,$fot(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))))]]) ).
cnf(refute_0_1261,plain,
( least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) != least_upper_bound(X_110,identity)
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) != least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))))
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity),least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))))) ),[1,1,0],$fot(least_upper_bound(X_110,identity))]]) ).
cnf(refute_0_1262,plain,
( least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) != least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))))
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))),least_upper_bound(X_110,identity)) )],[refute_0_1187,refute_0_1261]) ).
cnf(refute_0_1263,plain,
least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity),least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))))) )],[refute_0_1260,refute_0_1262]) ).
cnf(refute_0_1264,plain,
least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))),
inference(subst,[],[refute_0_1159:[bind(X_185,$fot(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))))]]) ).
cnf(refute_0_1265,plain,
( least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) != least_upper_bound(X_110,identity)
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) != least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(X_110,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))))),bind(Z0,$fot(least_upper_bound(X_110,identity)))]]) ).
cnf(refute_0_1266,plain,
( least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) != least_upper_bound(X_110,identity)
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(X_110,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity),least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))) )],[refute_0_1264,refute_0_1265]) ).
cnf(refute_0_1267,plain,
least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) = least_upper_bound(X_110,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))),least_upper_bound(X_110,identity)) )],[refute_0_1187,refute_0_1266]) ).
cnf(refute_0_1268,plain,
( least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) != least_upper_bound(X_110,identity)
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) != least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))
| least_upper_bound(X_110,identity) = least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity),least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))) ),[0],$fot(least_upper_bound(X_110,identity))]]) ).
cnf(refute_0_1269,plain,
( least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) != least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))
| least_upper_bound(X_110,identity) = least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity),least_upper_bound(X_110,identity)) )],[refute_0_1267,refute_0_1268]) ).
cnf(refute_0_1270,plain,
least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,least_upper_bound(X_111,least_upper_bound(Y,X_111))),
inference(subst,[],[refute_0_829:[bind(X,$fot(least_upper_bound(Y,X_111))),bind(X_18,$fot(X_110)),bind(X_19,$fot(X_111))]]) ).
cnf(refute_0_1271,plain,
least_upper_bound(X_111,least_upper_bound(Y,X_111)) = least_upper_bound(X_111,Y),
inference(subst,[],[refute_0_287:[bind(X_15,$fot(X_111))]]) ).
cnf(refute_0_1272,plain,
( least_upper_bound(X_111,least_upper_bound(Y,X_111)) != least_upper_bound(X_111,Y)
| least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,least_upper_bound(X_111,least_upper_bound(Y,X_111)))
| least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,least_upper_bound(X_111,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,least_upper_bound(X_111,least_upper_bound(Y,X_111)))) ),[1,1],$fot(least_upper_bound(X_111,Y))]]) ).
cnf(refute_0_1273,plain,
( least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,least_upper_bound(X_111,least_upper_bound(Y,X_111)))
| least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,least_upper_bound(X_111,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_111,least_upper_bound(Y,X_111)),least_upper_bound(X_111,Y)) )],[refute_0_1271,refute_0_1272]) ).
cnf(refute_0_1274,plain,
least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,least_upper_bound(X_111,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,least_upper_bound(X_111,least_upper_bound(Y,X_111)))) )],[refute_0_1270,refute_0_1273]) ).
cnf(refute_0_1275,plain,
least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111))) = least_upper_bound(X_111,least_upper_bound(X_110,Y)),
inference(subst,[],[refute_0_946:[bind(X_15,$fot(X_111)),bind(X_18,$fot(X_110)),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_1276,plain,
least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111))),
inference(subst,[],[refute_0_1183:[bind(Y,$fot(least_upper_bound(Y,X_111))),bind(X_109,$fot(X_111))]]) ).
cnf(refute_0_1277,plain,
( least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111))) != least_upper_bound(X_111,least_upper_bound(X_110,Y))
| least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) != least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111)))
| least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_111,least_upper_bound(X_110,Y)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)))),bind(Y0,$fot(least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111))))),bind(Z0,$fot(least_upper_bound(X_111,least_upper_bound(X_110,Y))))]]) ).
cnf(refute_0_1278,plain,
( least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111))) != least_upper_bound(X_111,least_upper_bound(X_110,Y))
| least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_111,least_upper_bound(X_110,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)),least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111)))) )],[refute_0_1276,refute_0_1277]) ).
cnf(refute_0_1279,plain,
least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) = least_upper_bound(X_111,least_upper_bound(X_110,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_111,least_upper_bound(X_110,least_upper_bound(Y,X_111))),least_upper_bound(X_111,least_upper_bound(X_110,Y))) )],[refute_0_1275,refute_0_1278]) ).
cnf(refute_0_1280,plain,
( least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,least_upper_bound(X_111,Y))
| least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) != least_upper_bound(X_111,least_upper_bound(X_110,Y))
| least_upper_bound(X_111,least_upper_bound(X_110,Y)) = least_upper_bound(X_110,least_upper_bound(X_111,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,least_upper_bound(X_111,Y))) ),[0],$fot(least_upper_bound(X_111,least_upper_bound(X_110,Y)))]]) ).
cnf(refute_0_1281,plain,
( least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,least_upper_bound(X_111,Y))
| least_upper_bound(X_111,least_upper_bound(X_110,Y)) = least_upper_bound(X_110,least_upper_bound(X_111,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)),least_upper_bound(X_111,least_upper_bound(X_110,Y))) )],[refute_0_1279,refute_0_1280]) ).
cnf(refute_0_1282,plain,
least_upper_bound(X_111,least_upper_bound(X_110,Y)) = least_upper_bound(X_110,least_upper_bound(X_111,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_111),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,least_upper_bound(X_111,Y))) )],[refute_0_1274,refute_0_1281]) ).
cnf(refute_0_1283,plain,
( least_upper_bound(X_111,least_upper_bound(X_110,Y)) != least_upper_bound(X_110,least_upper_bound(X_111,Y))
| least_upper_bound(X_110,least_upper_bound(X_111,Y)) = least_upper_bound(X_111,least_upper_bound(X_110,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_111,least_upper_bound(X_110,Y)))),bind(Y0,$fot(least_upper_bound(X_110,least_upper_bound(X_111,Y))))]]) ).
cnf(refute_0_1284,plain,
least_upper_bound(X_110,least_upper_bound(X_111,Y)) = least_upper_bound(X_111,least_upper_bound(X_110,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_111,least_upper_bound(X_110,Y)),least_upper_bound(X_110,least_upper_bound(X_111,Y))) )],[refute_0_1282,refute_0_1283]) ).
cnf(refute_0_1285,plain,
least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))),
inference(subst,[],[refute_0_1284:[bind(Y,$fot(inverse(least_upper_bound(X_45,identity)))),bind(X_110,$fot(inverse(least_upper_bound(X_110,identity)))),bind(X_111,$fot(X_110))]]) ).
cnf(refute_0_1286,plain,
least_upper_bound(X_48,X_33) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),least_upper_bound(X_48,X_33)))),
inference(subst,[],[refute_0_521:[bind(X_29,$fot(least_upper_bound(X_48,X_33))),bind(X_63,$fot(inverse(X_33)))]]) ).
cnf(refute_0_1287,plain,
( multiply(inverse(X_33),least_upper_bound(X_48,X_33)) != least_upper_bound(identity,multiply(inverse(X_33),X_48))
| least_upper_bound(X_48,X_33) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),least_upper_bound(X_48,X_33))))
| least_upper_bound(X_48,X_33) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_48,X_33),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),least_upper_bound(X_48,X_33))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(inverse(X_33),X_48)))]]) ).
cnf(refute_0_1288,plain,
( least_upper_bound(X_48,X_33) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),least_upper_bound(X_48,X_33))))
| least_upper_bound(X_48,X_33) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),least_upper_bound(X_48,X_33)),least_upper_bound(identity,multiply(inverse(X_33),X_48))) )],[refute_0_1056,refute_0_1287]) ).
cnf(refute_0_1289,plain,
least_upper_bound(X_48,X_33) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_48,X_33),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),least_upper_bound(X_48,X_33))))) )],[refute_0_1286,refute_0_1288]) ).
cnf(refute_0_1290,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(identity,multiply(inverse(X_33),X_48)),
inference(subst,[],[refute_0_345:[bind(X_16,$fot(multiply(inverse(X_33),X_48))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1291,plain,
multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))))]]) ).
cnf(refute_0_1292,plain,
( multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))) != least_upper_bound(identity,multiply(inverse(X_33),X_48))
| multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_33),X_48)))]]) ).
cnf(refute_0_1293,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))) != least_upper_bound(identity,multiply(inverse(X_33),X_48))
| multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))))) )],[refute_0_1291,refute_0_1292]) ).
cnf(refute_0_1294,plain,
multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) )],[refute_0_1290,refute_0_1293]) ).
cnf(refute_0_1295,plain,
( multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))
| least_upper_bound(X_48,X_33) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))))
| least_upper_bound(X_48,X_33) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_48,X_33),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))))) ),[1],$fot(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))))]]) ).
cnf(refute_0_1296,plain,
( least_upper_bound(X_48,X_33) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))))
| least_upper_bound(X_48,X_33) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48)))),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))) )],[refute_0_1294,refute_0_1295]) ).
cnf(refute_0_1297,plain,
least_upper_bound(X_48,X_33) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_48,X_33),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_33),X_48))))) )],[refute_0_1289,refute_0_1296]) ).
cnf(refute_0_1298,plain,
least_upper_bound(multiply(X_33,identity),X_48) = least_upper_bound(multiply(X_33,identity),X_48),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_33,identity),X_48))]]) ).
cnf(refute_0_1299,plain,
( multiply(X_33,identity) != X_33
| least_upper_bound(multiply(X_33,identity),X_48) != least_upper_bound(multiply(X_33,identity),X_48)
| least_upper_bound(multiply(X_33,identity),X_48) = least_upper_bound(X_33,X_48) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_33,identity),X_48),least_upper_bound(multiply(X_33,identity),X_48)) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_1300,plain,
( multiply(X_33,identity) != X_33
| least_upper_bound(multiply(X_33,identity),X_48) = least_upper_bound(X_33,X_48) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_33,identity),X_48),least_upper_bound(multiply(X_33,identity),X_48)) )],[refute_0_1298,refute_0_1299]) ).
cnf(refute_0_1301,plain,
least_upper_bound(multiply(X_33,identity),X_48) = least_upper_bound(X_33,X_48),
inference(resolve,[$cnf( $equal(multiply(X_33,identity),X_33) )],[refute_0_116,refute_0_1300]) ).
cnf(refute_0_1302,plain,
multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))) = least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_67))),
inference(subst,[],[monotony_lub1:[bind(Z,$fot(multiply(inverse(X),X_67)))]]) ).
cnf(refute_0_1303,plain,
X_67 = multiply(X,multiply(inverse(X),X_67)),
inference(subst,[],[refute_0_487:[bind(X_29,$fot(X_67)),bind(X_33,$fot(X))]]) ).
cnf(refute_0_1304,plain,
( X_67 != multiply(X,multiply(inverse(X),X_67))
| multiply(X,multiply(inverse(X),X_67)) = X_67 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_67)),bind(Y0,$fot(multiply(X,multiply(inverse(X),X_67))))]]) ).
cnf(refute_0_1305,plain,
multiply(X,multiply(inverse(X),X_67)) = X_67,
inference(resolve,[$cnf( $equal(X_67,multiply(X,multiply(inverse(X),X_67))) )],[refute_0_1303,refute_0_1304]) ).
cnf(refute_0_1306,plain,
( multiply(X,multiply(inverse(X),X_67)) != X_67
| multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))) != least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_67)))
| multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))) = least_upper_bound(multiply(X,Y),X_67) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))),least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_67)))) ),[1,1],$fot(X_67)]]) ).
cnf(refute_0_1307,plain,
( multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))) != least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_67)))
| multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))) = least_upper_bound(multiply(X,Y),X_67) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(inverse(X),X_67)),X_67) )],[refute_0_1305,refute_0_1306]) ).
cnf(refute_0_1308,plain,
multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))) = least_upper_bound(multiply(X,Y),X_67),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,multiply(inverse(X),X_67))),least_upper_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_67)))) )],[refute_0_1302,refute_0_1307]) ).
cnf(refute_0_1309,plain,
multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(multiply(X_33,identity),X_48),
inference(subst,[],[refute_0_1308:[bind(X,$fot(X_33)),bind(Y,$fot(identity)),bind(X_67,$fot(X_48))]]) ).
cnf(refute_0_1310,plain,
( multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) != least_upper_bound(multiply(X_33,identity),X_48)
| least_upper_bound(multiply(X_33,identity),X_48) != least_upper_bound(X_33,X_48)
| multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(X_33,X_48) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))))),bind(Y0,$fot(least_upper_bound(multiply(X_33,identity),X_48))),bind(Z0,$fot(least_upper_bound(X_33,X_48)))]]) ).
cnf(refute_0_1311,plain,
( least_upper_bound(multiply(X_33,identity),X_48) != least_upper_bound(X_33,X_48)
| multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(X_33,X_48) ),
inference(resolve,[$cnf( $equal(multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))),least_upper_bound(multiply(X_33,identity),X_48)) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(X_33,X_48),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_33,identity),X_48),least_upper_bound(X_33,X_48)) )],[refute_0_1301,refute_0_1311]) ).
cnf(refute_0_1313,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137)))),
inference(subst,[],[refute_0_321:[bind(X_44,$fot(inverse(least_upper_bound(X_138,inverse(X_137))))),bind(X_45,$fot(least_upper_bound(identity,multiply(X_138,X_137))))]]) ).
cnf(refute_0_1314,plain,
X_137 = multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))),
inference(subst,[],[refute_0_521:[bind(X_29,$fot(X_137)),bind(X_63,$fot(X_138))]]) ).
cnf(refute_0_1315,plain,
( X_137 != multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137)))
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))) = X_137 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_137)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137)))))]]) ).
cnf(refute_0_1316,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))) = X_137,
inference(resolve,[$cnf( $equal(X_137,multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137)))) )],[refute_0_1314,refute_0_1315]) ).
cnf(refute_0_1317,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))) != X_137
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) != least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))))
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)),least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))))) ),[1,1],$fot(X_137)]]) ).
cnf(refute_0_1318,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) != least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))))
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))),X_137) )],[refute_0_1316,refute_0_1317]) ).
cnf(refute_0_1319,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)),least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))))) )],[refute_0_1313,refute_0_1318]) ).
cnf(refute_0_1320,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))) = least_upper_bound(identity,multiply(X_138,X_137)),
inference(subst,[],[refute_0_345:[bind(X_16,$fot(multiply(X_138,X_137))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1321,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) = multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))))]]) ).
cnf(refute_0_1322,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) != multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))) != least_upper_bound(identity,multiply(X_138,X_137))
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) = multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_138,X_137)))]]) ).
cnf(refute_0_1323,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))) != least_upper_bound(identity,multiply(X_138,X_137))
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) = multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))))) )],[refute_0_1321,refute_0_1322]) ).
cnf(refute_0_1324,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) = multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))),least_upper_bound(identity,multiply(X_138,X_137))) )],[refute_0_1320,refute_0_1323]) ).
cnf(refute_0_1325,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))) != X_137
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) != multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137)))
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) = X_137 ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))))),bind(Z0,$fot(X_137))]]) ).
cnf(refute_0_1326,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))) != X_137
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) = X_137 ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137)))) )],[refute_0_1324,refute_0_1325]) ).
cnf(refute_0_1327,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) = X_137,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,multiply(X_138,X_137))),X_137) )],[refute_0_1316,refute_0_1326]) ).
cnf(refute_0_1328,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))),
inference(subst,[],[refute_0_745:[bind(X,$fot(inverse(least_upper_bound(X_138,inverse(X_137))))),bind(Y,$fot(identity)),bind(Z,$fot(least_upper_bound(identity,multiply(X_138,X_137))))]]) ).
cnf(refute_0_1329,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) != X_137
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) != multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))))
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = X_137 ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))))),bind(Z0,$fot(X_137))]]) ).
cnf(refute_0_1330,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))) != X_137
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = X_137 ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)),multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137))))) )],[refute_0_1328,refute_0_1329]) ).
cnf(refute_0_1331,plain,
multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) = X_137,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_138,X_137)))),X_137) )],[refute_0_1327,refute_0_1330]) ).
cnf(refute_0_1332,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) != X_137
| multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) != least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)
| X_137 = least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)),least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)) ),[0],$fot(X_137)]]) ).
cnf(refute_0_1333,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) != least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)
| X_137 = least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)),X_137) )],[refute_0_1331,refute_0_1332]) ).
cnf(refute_0_1334,plain,
least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137) = least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137)))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_137)),bind(Y,$fot(inverse(least_upper_bound(X_138,inverse(X_137)))))]]) ).
cnf(refute_0_1335,plain,
( X_137 != least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)
| least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137) != least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137))))
| X_137 = least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_137,least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137))))) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137))]]) ).
cnf(refute_0_1336,plain,
( X_137 != least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)
| X_137 = least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137),least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137))))) )],[refute_0_1334,refute_0_1335]) ).
cnf(refute_0_1337,plain,
( multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)) != least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)
| X_137 = least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137)))) ),
inference(resolve,[$cnf( $equal(X_137,least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)) )],[refute_0_1333,refute_0_1336]) ).
cnf(refute_0_1338,plain,
X_137 = least_upper_bound(X_137,inverse(least_upper_bound(X_138,inverse(X_137)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,inverse(X_137))),least_upper_bound(least_upper_bound(identity,multiply(X_138,X_137)),identity)),least_upper_bound(inverse(least_upper_bound(X_138,inverse(X_137))),X_137)) )],[refute_0_1319,refute_0_1337]) ).
cnf(refute_0_1339,plain,
inverse(X_33) = least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,inverse(inverse(X_33))))),
inference(subst,[],[refute_0_1338:[bind(X_137,$fot(inverse(X_33))),bind(X_138,$fot(X_144))]]) ).
cnf(refute_0_1340,plain,
( inverse(X_33) != least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,inverse(inverse(X_33)))))
| inverse(inverse(X_33)) != X_33
| inverse(X_33) = least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_33),least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,inverse(inverse(X_33)))))) ),[1,1,0,1],$fot(X_33)]]) ).
cnf(refute_0_1341,plain,
( inverse(X_33) != least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,inverse(inverse(X_33)))))
| inverse(X_33) = least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_33)),X_33) )],[refute_0_119,refute_0_1340]) ).
cnf(refute_0_1342,plain,
inverse(X_33) = least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33))),
inference(resolve,[$cnf( $equal(inverse(X_33),least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,inverse(inverse(X_33)))))) )],[refute_0_1339,refute_0_1341]) ).
cnf(refute_0_1343,plain,
( inverse(X_33) != least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33)))
| least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33))) = inverse(X_33) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_33))),bind(Y0,$fot(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33)))))]]) ).
cnf(refute_0_1344,plain,
least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33))) = inverse(X_33),
inference(resolve,[$cnf( $equal(inverse(X_33),least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_144,X_33)))) )],[refute_0_1342,refute_0_1343]) ).
cnf(refute_0_1345,plain,
least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33))) = inverse(X_33),
inference(subst,[],[refute_0_1344:[bind(X_144,$fot(X_48))]]) ).
cnf(refute_0_1346,plain,
inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) = inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))))]]) ).
cnf(refute_0_1347,plain,
( inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) != inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33))))
| least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33))) != inverse(X_33)
| inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) = inverse(inverse(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33))))) ),[1,0],$fot(inverse(X_33))]]) ).
cnf(refute_0_1348,plain,
( least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33))) != inverse(X_33)
| inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) = inverse(inverse(X_33)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33))))) )],[refute_0_1346,refute_0_1347]) ).
cnf(refute_0_1349,plain,
inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) = inverse(inverse(X_33)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33))),inverse(X_33)) )],[refute_0_1345,refute_0_1348]) ).
cnf(refute_0_1350,plain,
( inverse(inverse(X_33)) != X_33
| inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) != inverse(inverse(X_33))
| inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) = X_33 ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))))),bind(Y0,$fot(inverse(inverse(X_33)))),bind(Z0,$fot(X_33))]]) ).
cnf(refute_0_1351,plain,
( inverse(inverse(X_33)) != X_33
| inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) = X_33 ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),inverse(inverse(X_33))) )],[refute_0_1349,refute_0_1350]) ).
cnf(refute_0_1352,plain,
inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) = X_33,
inference(resolve,[$cnf( $equal(inverse(inverse(X_33)),X_33) )],[refute_0_119,refute_0_1351]) ).
cnf(refute_0_1353,plain,
multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) = multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))))]]) ).
cnf(refute_0_1354,plain,
( multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))
| inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) != X_33
| multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) = multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_1355,plain,
( inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))) != X_33
| multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) = multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) = multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),X_33) )],[refute_0_1352,refute_0_1355]) ).
cnf(refute_0_1357,plain,
( multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) != least_upper_bound(X_33,X_48)
| multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) != multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48)))
| multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(X_33,X_48) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))))),bind(Y0,$fot(multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))))),bind(Z0,$fot(least_upper_bound(X_33,X_48)))]]) ).
cnf(refute_0_1358,plain,
( multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))) != least_upper_bound(X_33,X_48)
| multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(X_33,X_48) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))),multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48)))) )],[refute_0_1356,refute_0_1357]) ).
cnf(refute_0_1359,plain,
multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) = least_upper_bound(X_33,X_48),
inference(resolve,[$cnf( $equal(multiply(X_33,least_upper_bound(identity,multiply(inverse(X_33),X_48))),least_upper_bound(X_33,X_48)) )],[refute_0_1312,refute_0_1358]) ).
cnf(refute_0_1360,plain,
( multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))) != least_upper_bound(X_33,X_48)
| least_upper_bound(X_48,X_33) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))
| least_upper_bound(X_48,X_33) = least_upper_bound(X_33,X_48) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_48,X_33),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))) ),[1],$fot(least_upper_bound(X_33,X_48))]]) ).
cnf(refute_0_1361,plain,
( least_upper_bound(X_48,X_33) != multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))
| least_upper_bound(X_48,X_33) = least_upper_bound(X_33,X_48) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48))),least_upper_bound(X_33,X_48)) )],[refute_0_1359,refute_0_1360]) ).
cnf(refute_0_1362,plain,
least_upper_bound(X_48,X_33) = least_upper_bound(X_33,X_48),
inference(resolve,[$cnf( $equal(least_upper_bound(X_48,X_33),multiply(inverse(least_upper_bound(inverse(X_33),inverse(least_upper_bound(X_48,X_33)))),least_upper_bound(identity,multiply(inverse(X_33),X_48)))) )],[refute_0_1297,refute_0_1361]) ).
cnf(refute_0_1363,plain,
( least_upper_bound(X_48,X_33) != least_upper_bound(X_33,X_48)
| least_upper_bound(X_33,X_48) = least_upper_bound(X_48,X_33) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_48,X_33))),bind(Y0,$fot(least_upper_bound(X_33,X_48)))]]) ).
cnf(refute_0_1364,plain,
least_upper_bound(X_33,X_48) = least_upper_bound(X_48,X_33),
inference(resolve,[$cnf( $equal(least_upper_bound(X_48,X_33),least_upper_bound(X_33,X_48)) )],[refute_0_1362,refute_0_1363]) ).
cnf(refute_0_1365,plain,
least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) = least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))),
inference(subst,[],[refute_0_1364:[bind(X_33,$fot(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))),bind(X_48,$fot(inverse(least_upper_bound(X_110,identity))))]]) ).
cnf(refute_0_1366,plain,
( least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) != least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) != least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))))),bind(Z0,$fot(least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))))]]) ).
cnf(refute_0_1367,plain,
( least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))) != least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))),least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))))) )],[refute_0_1365,refute_0_1366]) ).
cnf(refute_0_1368,plain,
least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_110,identity)),least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity)))),least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))) )],[refute_0_1285,refute_0_1367]) ).
cnf(refute_0_1369,plain,
( least_upper_bound(X_110,identity) != least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))
| least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))) != least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(X_110,identity) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_110,identity),least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))) ),[0],$fot(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))))]]) ).
cnf(refute_0_1370,plain,
( least_upper_bound(X_110,identity) != least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))
| least_upper_bound(X_110,identity) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity))),least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))) )],[refute_0_1368,refute_0_1369]) ).
cnf(refute_0_1371,plain,
( least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity) != least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))
| least_upper_bound(X_110,identity) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,identity),least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))) )],[refute_0_1269,refute_0_1370]) ).
cnf(refute_0_1372,plain,
least_upper_bound(X_110,identity) = least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),identity),least_upper_bound(least_upper_bound(X_110,inverse(least_upper_bound(X_45,identity))),inverse(least_upper_bound(X_110,identity)))) )],[refute_0_1263,refute_0_1371]) ).
cnf(refute_0_1373,plain,
least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)) = least_upper_bound(least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))),Z),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(inverse(least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_1374,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))),
inference(subst,[],[refute_0_449:[bind(X_45,$fot(X_58))]]) ).
cnf(refute_0_1375,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(X_58,identity)))
| least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(X_58,identity)))))]]) ).
cnf(refute_0_1376,plain,
least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(X_58,identity)))) )],[refute_0_1374,refute_0_1375]) ).
cnf(refute_0_1377,plain,
( least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))) != identity
| least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)) != least_upper_bound(least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))),Z)
| least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)) = least_upper_bound(identity,Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)),least_upper_bound(least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))),Z)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1378,plain,
( least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)) != least_upper_bound(least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))),Z)
| least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)) = least_upper_bound(identity,Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))),identity) )],[refute_0_1376,refute_0_1377]) ).
cnf(refute_0_1379,plain,
least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)) = least_upper_bound(identity,Z),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_58,identity)),Z)),least_upper_bound(least_upper_bound(identity,inverse(least_upper_bound(X_58,identity))),Z)) )],[refute_0_1373,refute_0_1378]) ).
cnf(refute_0_1380,plain,
least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110)) = least_upper_bound(identity,X_110),
inference(subst,[],[refute_0_1379:[bind(Z,$fot(X_110)),bind(X_58,$fot(X_45))]]) ).
cnf(refute_0_1381,plain,
least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)) = least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110)),
inference(subst,[],[refute_0_1284:[bind(Y,$fot(X_110)),bind(X_110,$fot(inverse(least_upper_bound(X_45,identity)))),bind(X_111,$fot(identity))]]) ).
cnf(refute_0_1382,plain,
( least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110)) != least_upper_bound(identity,X_110)
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)) != least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110))
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)) = least_upper_bound(identity,X_110) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110)))),bind(Z0,$fot(least_upper_bound(identity,X_110)))]]) ).
cnf(refute_0_1383,plain,
( least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110)) != least_upper_bound(identity,X_110)
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)) = least_upper_bound(identity,X_110) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)),least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110))) )],[refute_0_1381,refute_0_1382]) ).
cnf(refute_0_1384,plain,
least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)) = least_upper_bound(identity,X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(X_45,identity)),X_110)),least_upper_bound(identity,X_110)) )],[refute_0_1380,refute_0_1383]) ).
cnf(refute_0_1385,plain,
least_upper_bound(X,least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))) = least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X)),
inference(subst,[],[refute_0_829:[bind(X_19,$fot(inverse(least_upper_bound(X_18,identity))))]]) ).
cnf(refute_0_1386,plain,
least_upper_bound(identity,X_165) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165)))),
inference(subst,[],[refute_0_521:[bind(X_29,$fot(least_upper_bound(identity,X_165))),bind(X_63,$fot(least_upper_bound(identity,inverse(X_165))))]]) ).
cnf(refute_0_1387,plain,
multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) = least_upper_bound(least_upper_bound(identity,X_53),multiply(inverse(X_53),least_upper_bound(identity,X_53))),
inference(subst,[],[refute_0_607:[bind(X_59,$fot(least_upper_bound(identity,X_53))),bind(X_60,$fot(inverse(X_53)))]]) ).
cnf(refute_0_1388,plain,
( multiply(inverse(X_53),least_upper_bound(identity,X_53)) != least_upper_bound(identity,inverse(X_53))
| multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) != least_upper_bound(least_upper_bound(identity,X_53),multiply(inverse(X_53),least_upper_bound(identity,X_53)))
| multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) = least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)),least_upper_bound(least_upper_bound(identity,X_53),multiply(inverse(X_53),least_upper_bound(identity,X_53)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_53)))]]) ).
cnf(refute_0_1389,plain,
( multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) != least_upper_bound(least_upper_bound(identity,X_53),multiply(inverse(X_53),least_upper_bound(identity,X_53)))
| multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) = least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_53),least_upper_bound(identity,X_53)),least_upper_bound(identity,inverse(X_53))) )],[refute_0_421,refute_0_1388]) ).
cnf(refute_0_1390,plain,
multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) = least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)),least_upper_bound(least_upper_bound(identity,X_53),multiply(inverse(X_53),least_upper_bound(identity,X_53)))) )],[refute_0_1387,refute_0_1389]) ).
cnf(refute_0_1391,plain,
multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) = multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)),
inference(subst,[],[refute_0_898:[bind(X_17,$fot(least_upper_bound(identity,X_53))),bind(X_82,$fot(inverse(X_53)))]]) ).
cnf(refute_0_1392,plain,
( multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) != multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53))
| multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) != least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))
| multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) = least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)),least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)))]]) ).
cnf(refute_0_1393,plain,
( multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) != least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))
| multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) = least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)),multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53))) )],[refute_0_1391,refute_0_1392]) ).
cnf(refute_0_1394,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))),
inference(subst,[],[refute_0_938:[bind(X_18,$fot(identity)),bind(X_19,$fot(inverse(X_53))),bind(X_20,$fot(X_53))]]) ).
cnf(refute_0_1395,plain,
least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53)),
inference(subst,[],[refute_0_858:[bind(Y,$fot(identity)),bind(X_18,$fot(inverse(X_53))),bind(X_20,$fot(X_53))]]) ).
cnf(refute_0_1396,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53)) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)) != least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53))
| least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))))]]) ).
cnf(refute_0_1397,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53)) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)),least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53))) )],[refute_0_1395,refute_0_1396]) ).
cnf(refute_0_1398,plain,
least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_53),X_53)),least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))) )],[refute_0_1394,refute_0_1397]) ).
cnf(refute_0_1399,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) = least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)),
inference(subst,[],[refute_0_840:[bind(Y,$fot(X_53)),bind(X_18,$fot(inverse(X_53))),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_1400,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) != least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))
| least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))))),bind(Y0,$fot(least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))))]]) ).
cnf(refute_0_1401,plain,
( least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))),least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)),least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))) )],[refute_0_1398,refute_0_1401]) ).
cnf(refute_0_1403,plain,
least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))) = least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))),
inference(subst,[],[refute_0_938:[bind(X_18,$fot(identity)),bind(X_19,$fot(least_upper_bound(identity,X_53))),bind(X_20,$fot(inverse(X_53)))]]) ).
cnf(refute_0_1404,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))) != least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))))]]) ).
cnf(refute_0_1405,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))),least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53)))) )],[refute_0_1403,refute_0_1404]) ).
cnf(refute_0_1406,plain,
least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_53),least_upper_bound(identity,X_53))),least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))) )],[refute_0_1402,refute_0_1405]) ).
cnf(refute_0_1407,plain,
least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))),
inference(subst,[],[refute_0_858:[bind(Y,$fot(identity)),bind(X_18,$fot(least_upper_bound(identity,X_53))),bind(X_20,$fot(inverse(X_53)))]]) ).
cnf(refute_0_1408,plain,
( least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53)))
| least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))))]]) ).
cnf(refute_0_1409,plain,
( least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))),least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53)))) )],[refute_0_1407,refute_0_1408]) ).
cnf(refute_0_1410,plain,
least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(identity,X_53),inverse(X_53))),least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))) )],[refute_0_1406,refute_0_1409]) ).
cnf(refute_0_1411,plain,
( multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) != least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))
| least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))) != least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))
| multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)),least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))))]]) ).
cnf(refute_0_1412,plain,
( multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) != least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))
| multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53))),least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53)))) )],[refute_0_1410,refute_0_1411]) ).
cnf(refute_0_1413,plain,
( multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)) != least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))
| multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)),least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))) )],[refute_0_1393,refute_0_1412]) ).
cnf(refute_0_1414,plain,
multiply(least_upper_bound(identity,inverse(X_53)),least_upper_bound(identity,X_53)) = least_upper_bound(identity,least_upper_bound(X_53,inverse(X_53))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_53),identity),least_upper_bound(identity,X_53)),least_upper_bound(least_upper_bound(identity,X_53),least_upper_bound(identity,inverse(X_53)))) )],[refute_0_1390,refute_0_1413]) ).
cnf(refute_0_1415,plain,
multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))),
inference(subst,[],[refute_0_1414:[bind(X_53,$fot(X_165))]]) ).
cnf(refute_0_1416,plain,
( multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))
| least_upper_bound(identity,X_165) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165))))
| least_upper_bound(identity,X_165) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_165),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165))))) ),[1,1,1],$fot(least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))]]) ).
cnf(refute_0_1417,plain,
( least_upper_bound(identity,X_165) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165))))
| least_upper_bound(identity,X_165) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165)),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
least_upper_bound(identity,X_165) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_165),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_165)),least_upper_bound(identity,X_165))))) )],[refute_0_1386,refute_0_1417]) ).
cnf(refute_0_1419,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))),
inference(subst,[],[refute_0_1018:[bind(Z,$fot(inverse(X_165))),bind(X_139,$fot(X_165))]]) ).
cnf(refute_0_1420,plain,
least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))),
inference(subst,[],[refute_0_345:[bind(X_16,$fot(least_upper_bound(X_165,inverse(X_165)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1421,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))))]]) ).
cnf(refute_0_1422,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) != multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))
| least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) != least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))
| multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))]]) ).
cnf(refute_0_1423,plain,
( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) != least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))
| multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))) )],[refute_0_1421,refute_0_1422]) ).
cnf(refute_0_1424,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) )],[refute_0_1420,refute_0_1423]) ).
cnf(refute_0_1425,plain,
least_upper_bound(inverse(X_165),identity) = least_upper_bound(identity,inverse(X_165)),
inference(subst,[],[refute_0_1364:[bind(X_33,$fot(inverse(X_165))),bind(X_48,$fot(identity))]]) ).
cnf(refute_0_1426,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))),
inference(subst,[],[refute_0_829:[bind(X,$fot(inverse(least_upper_bound(identity,X_16)))),bind(X_18,$fot(X_110)),bind(X_19,$fot(identity))]]) ).
cnf(refute_0_1427,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))))]]) ).
cnf(refute_0_1428,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) )],[refute_0_430,refute_0_1427]) ).
cnf(refute_0_1429,plain,
( least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) != identity
| least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))))
| least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1430,plain,
( least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))))
| least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))),identity) )],[refute_0_1428,refute_0_1429]) ).
cnf(refute_0_1431,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) = least_upper_bound(X_110,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))))) )],[refute_0_1426,refute_0_1430]) ).
cnf(refute_0_1432,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) = least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(identity,X_16)))),
inference(subst,[],[refute_0_1183:[bind(Y,$fot(inverse(least_upper_bound(identity,X_16)))),bind(X_109,$fot(identity))]]) ).
cnf(refute_0_1433,plain,
( least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,identity)
| least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) != least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(identity,X_16))))
| least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(identity,X_16)))) = least_upper_bound(X_110,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,identity)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(identity,X_16)))))]]) ).
cnf(refute_0_1434,plain,
( least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)) != least_upper_bound(X_110,identity)
| least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(identity,X_16)))) = least_upper_bound(X_110,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)),least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(identity,X_16))))) )],[refute_0_1432,refute_0_1433]) ).
cnf(refute_0_1435,plain,
least_upper_bound(identity,least_upper_bound(X_110,inverse(least_upper_bound(identity,X_16)))) = least_upper_bound(X_110,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_16)),least_upper_bound(X_110,identity)),least_upper_bound(X_110,identity)) )],[refute_0_1431,refute_0_1434]) ).
cnf(refute_0_1436,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(inverse(X_165),identity),
inference(subst,[],[refute_0_1435:[bind(X_110,$fot(inverse(X_165))),bind(X_16,$fot(X_165))]]) ).
cnf(refute_0_1437,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))) != least_upper_bound(inverse(X_165),identity)
| least_upper_bound(inverse(X_165),identity) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(identity,inverse(X_165)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))))),bind(Y0,$fot(least_upper_bound(inverse(X_165),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_165))))]]) ).
cnf(refute_0_1438,plain,
( least_upper_bound(inverse(X_165),identity) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(identity,inverse(X_165)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(inverse(X_165),identity)) )],[refute_0_1436,refute_0_1437]) ).
cnf(refute_0_1439,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(identity,inverse(X_165)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_165),identity),least_upper_bound(identity,inverse(X_165))) )],[refute_0_1425,refute_0_1438]) ).
cnf(refute_0_1440,plain,
least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))),
inference(subst,[],[refute_0_1284:[bind(Y,$fot(inverse(least_upper_bound(identity,X_165)))),bind(X_110,$fot(inverse(X_165))),bind(X_111,$fot(identity))]]) ).
cnf(refute_0_1441,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))) != least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165))))
| least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(identity,inverse(X_165)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_165))))]]) ).
cnf(refute_0_1442,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(identity,inverse(X_165)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165))))) )],[refute_0_1440,refute_0_1441]) ).
cnf(refute_0_1443,plain,
least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))) = least_upper_bound(identity,inverse(X_165)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_165),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,inverse(X_165))) )],[refute_0_1439,refute_0_1442]) ).
cnf(refute_0_1444,plain,
least_upper_bound(X_18,least_upper_bound(X_19,X)) = least_upper_bound(X_19,least_upper_bound(X_18,X)),
inference(subst,[],[refute_0_856:[bind(Y,$fot(X_18)),bind(X_18,$fot(X_19)),bind(X_20,$fot(X))]]) ).
cnf(refute_0_1445,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_19,least_upper_bound(X_18,X))
| least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,least_upper_bound(X_18,X))) ),[0],$fot(least_upper_bound(X_18,least_upper_bound(X_19,X)))]]) ).
cnf(refute_0_1446,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,least_upper_bound(X_18,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,least_upper_bound(X_19,X)),least_upper_bound(X_19,least_upper_bound(X_18,X))) )],[refute_0_1444,refute_0_1445]) ).
cnf(refute_0_1447,plain,
least_upper_bound(X,least_upper_bound(X_18,X_19)) = least_upper_bound(X_19,least_upper_bound(X_18,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_18,least_upper_bound(X_19,X))) )],[refute_0_829,refute_0_1446]) ).
cnf(refute_0_1448,plain,
( least_upper_bound(X,least_upper_bound(X_18,X_19)) != least_upper_bound(X_19,least_upper_bound(X_18,X))
| least_upper_bound(X_19,least_upper_bound(X_18,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_18,X_19)))),bind(Y0,$fot(least_upper_bound(X_19,least_upper_bound(X_18,X))))]]) ).
cnf(refute_0_1449,plain,
least_upper_bound(X_19,least_upper_bound(X_18,X)) = least_upper_bound(X,least_upper_bound(X_18,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,X_19)),least_upper_bound(X_19,least_upper_bound(X_18,X))) )],[refute_0_1447,refute_0_1448]) ).
cnf(refute_0_1450,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))) = least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))),
inference(subst,[],[refute_0_1449:[bind(X,$fot(inverse(X_165))),bind(X_18,$fot(identity)),bind(X_19,$fot(inverse(least_upper_bound(identity,X_165))))]]) ).
cnf(refute_0_1451,plain,
( least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))) != least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165))))
| least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))) = least_upper_bound(identity,inverse(X_165)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))))),bind(Y0,$fot(least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_165))))]]) ).
cnf(refute_0_1452,plain,
( least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))) = least_upper_bound(identity,inverse(X_165)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))),least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165))))) )],[refute_0_1450,refute_0_1451]) ).
cnf(refute_0_1453,plain,
least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))) = least_upper_bound(identity,inverse(X_165)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_165),least_upper_bound(identity,inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,inverse(X_165))) )],[refute_0_1443,refute_0_1452]) ).
cnf(refute_0_1454,plain,
least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))) = least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))),
inference(subst,[],[refute_0_1364:[bind(X_33,$fot(least_upper_bound(identity,inverse(X_165)))),bind(X_48,$fot(inverse(least_upper_bound(identity,X_165))))]]) ).
cnf(refute_0_1455,plain,
( least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))) != least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165)))
| least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))) = least_upper_bound(identity,inverse(X_165)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_165))))]]) ).
cnf(refute_0_1456,plain,
( least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))) != least_upper_bound(identity,inverse(X_165))
| least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))) = least_upper_bound(identity,inverse(X_165)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))),least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165)))) )],[refute_0_1454,refute_0_1455]) ).
cnf(refute_0_1457,plain,
least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))) = least_upper_bound(identity,inverse(X_165)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_165)),least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,inverse(X_165))) )],[refute_0_1453,refute_0_1456]) ).
cnf(refute_0_1458,plain,
inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))) = inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))))]]) ).
cnf(refute_0_1459,plain,
( inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))) != inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))))
| least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))) != least_upper_bound(identity,inverse(X_165))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))) = inverse(least_upper_bound(identity,inverse(X_165))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_165)))]]) ).
cnf(refute_0_1460,plain,
( least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))) != least_upper_bound(identity,inverse(X_165))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))) = inverse(least_upper_bound(identity,inverse(X_165))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))))) )],[refute_0_1458,refute_0_1459]) ).
cnf(refute_0_1461,plain,
inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))) = inverse(least_upper_bound(identity,inverse(X_165))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165))),least_upper_bound(identity,inverse(X_165))) )],[refute_0_1457,refute_0_1460]) ).
cnf(refute_0_1462,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))))]]) ).
cnf(refute_0_1463,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))
| inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))) != inverse(least_upper_bound(identity,inverse(X_165)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))) ),[1,0],$fot(inverse(least_upper_bound(identity,inverse(X_165))))]]) ).
cnf(refute_0_1464,plain,
( inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))) != inverse(least_upper_bound(identity,inverse(X_165)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))) )],[refute_0_1462,refute_0_1463]) ).
cnf(refute_0_1465,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),inverse(least_upper_bound(identity,inverse(X_165)))) )],[refute_0_1461,refute_0_1464]) ).
cnf(refute_0_1466,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) != multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) != multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))))]]) ).
cnf(refute_0_1467,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) != multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))) )],[refute_0_1465,refute_0_1466]) ).
cnf(refute_0_1468,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) )],[refute_0_1424,refute_0_1467]) ).
cnf(refute_0_1469,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) != least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) != multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))),bind(Z0,$fot(least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))))]]) ).
cnf(refute_0_1470,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) != least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))
| multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) )],[refute_0_1468,refute_0_1469]) ).
cnf(refute_0_1471,plain,
multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))),least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))) )],[refute_0_1419,refute_0_1470]) ).
cnf(refute_0_1472,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))) != least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))
| least_upper_bound(identity,X_165) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))
| least_upper_bound(identity,X_165) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_165),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))) ),[1],$fot(least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))))]]) ).
cnf(refute_0_1473,plain,
( least_upper_bound(identity,X_165) != multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))
| least_upper_bound(identity,X_165) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))))),least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))) )],[refute_0_1471,refute_0_1472]) ).
cnf(refute_0_1474,plain,
least_upper_bound(identity,X_165) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_165),multiply(inverse(least_upper_bound(least_upper_bound(identity,inverse(X_165)),inverse(least_upper_bound(identity,X_165)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))) )],[refute_0_1418,refute_0_1473]) ).
cnf(refute_0_1475,plain,
multiply(least_upper_bound(X_165,identity),identity) = least_upper_bound(X_165,identity),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(least_upper_bound(X_165,identity)))]]) ).
cnf(refute_0_1476,plain,
least_upper_bound(identity,multiply(X_165,identity)) = multiply(least_upper_bound(X_165,identity),identity),
inference(subst,[],[refute_0_883:[bind(X_59,$fot(identity)),bind(X_60,$fot(X_165))]]) ).
cnf(refute_0_1477,plain,
( multiply(least_upper_bound(X_165,identity),identity) != least_upper_bound(X_165,identity)
| least_upper_bound(identity,multiply(X_165,identity)) != multiply(least_upper_bound(X_165,identity),identity)
| least_upper_bound(identity,multiply(X_165,identity)) = least_upper_bound(X_165,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,multiply(X_165,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_165,identity),identity))),bind(Z0,$fot(least_upper_bound(X_165,identity)))]]) ).
cnf(refute_0_1478,plain,
( multiply(least_upper_bound(X_165,identity),identity) != least_upper_bound(X_165,identity)
| least_upper_bound(identity,multiply(X_165,identity)) = least_upper_bound(X_165,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_165,identity)),multiply(least_upper_bound(X_165,identity),identity)) )],[refute_0_1476,refute_0_1477]) ).
cnf(refute_0_1479,plain,
least_upper_bound(identity,multiply(X_165,identity)) = least_upper_bound(X_165,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_165,identity),identity),least_upper_bound(X_165,identity)) )],[refute_0_1475,refute_0_1478]) ).
cnf(refute_0_1480,plain,
multiply(X_165,least_upper_bound(identity,inverse(X_165))) = least_upper_bound(identity,multiply(X_165,identity)),
inference(subst,[],[refute_0_40:[bind(X_44,$fot(X_165)),bind(X_45,$fot(identity))]]) ).
cnf(refute_0_1481,plain,
( multiply(X_165,least_upper_bound(identity,inverse(X_165))) != least_upper_bound(identity,multiply(X_165,identity))
| least_upper_bound(identity,multiply(X_165,identity)) != least_upper_bound(X_165,identity)
| multiply(X_165,least_upper_bound(identity,inverse(X_165))) = least_upper_bound(X_165,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(X_165,least_upper_bound(identity,inverse(X_165))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_165,identity)))),bind(Z0,$fot(least_upper_bound(X_165,identity)))]]) ).
cnf(refute_0_1482,plain,
( least_upper_bound(identity,multiply(X_165,identity)) != least_upper_bound(X_165,identity)
| multiply(X_165,least_upper_bound(identity,inverse(X_165))) = least_upper_bound(X_165,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_165,least_upper_bound(identity,inverse(X_165))),least_upper_bound(identity,multiply(X_165,identity))) )],[refute_0_1480,refute_0_1481]) ).
cnf(refute_0_1483,plain,
multiply(X_165,least_upper_bound(identity,inverse(X_165))) = least_upper_bound(X_165,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_165,identity)),least_upper_bound(X_165,identity)) )],[refute_0_1479,refute_0_1482]) ).
cnf(refute_0_1484,plain,
inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))) = inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))))]]) ).
cnf(refute_0_1485,plain,
( multiply(X_165,least_upper_bound(identity,inverse(X_165))) != least_upper_bound(X_165,identity)
| inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))) != inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165))))
| inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))) = inverse(least_upper_bound(X_165,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))),inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165))))) ),[1,0],$fot(least_upper_bound(X_165,identity))]]) ).
cnf(refute_0_1486,plain,
( multiply(X_165,least_upper_bound(identity,inverse(X_165))) != least_upper_bound(X_165,identity)
| inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))) = inverse(least_upper_bound(X_165,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))),inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165))))) )],[refute_0_1484,refute_0_1485]) ).
cnf(refute_0_1487,plain,
inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))) = inverse(least_upper_bound(X_165,identity)),
inference(resolve,[$cnf( $equal(multiply(X_165,least_upper_bound(identity,inverse(X_165))),least_upper_bound(X_165,identity)) )],[refute_0_1483,refute_0_1486]) ).
cnf(refute_0_1488,plain,
inverse(multiply(X_196,X_28)) = multiply(inverse(X_28),multiply(X_28,inverse(multiply(X_196,X_28)))),
inference(subst,[],[refute_0_19:[bind(X_29,$fot(inverse(multiply(X_196,X_28))))]]) ).
cnf(refute_0_1489,plain,
multiply(X_28,inverse(multiply(X_196,X_28))) = inverse(X_196),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(X_196)),bind(X_38,$fot(X_28))]]) ).
cnf(refute_0_1490,plain,
( multiply(X_28,inverse(multiply(X_196,X_28))) != inverse(X_196)
| inverse(multiply(X_196,X_28)) != multiply(inverse(X_28),multiply(X_28,inverse(multiply(X_196,X_28))))
| inverse(multiply(X_196,X_28)) = multiply(inverse(X_28),inverse(X_196)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_196,X_28)),multiply(inverse(X_28),multiply(X_28,inverse(multiply(X_196,X_28))))) ),[1,1],$fot(inverse(X_196))]]) ).
cnf(refute_0_1491,plain,
( inverse(multiply(X_196,X_28)) != multiply(inverse(X_28),multiply(X_28,inverse(multiply(X_196,X_28))))
| inverse(multiply(X_196,X_28)) = multiply(inverse(X_28),inverse(X_196)) ),
inference(resolve,[$cnf( $equal(multiply(X_28,inverse(multiply(X_196,X_28))),inverse(X_196)) )],[refute_0_1489,refute_0_1490]) ).
cnf(refute_0_1492,plain,
inverse(multiply(X_196,X_28)) = multiply(inverse(X_28),inverse(X_196)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_196,X_28)),multiply(inverse(X_28),multiply(X_28,inverse(multiply(X_196,X_28))))) )],[refute_0_1488,refute_0_1491]) ).
cnf(refute_0_1493,plain,
( inverse(multiply(X_196,X_28)) != multiply(inverse(X_28),inverse(X_196))
| multiply(inverse(X_28),inverse(X_196)) = inverse(multiply(X_196,X_28)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X_196,X_28)))),bind(Y0,$fot(multiply(inverse(X_28),inverse(X_196))))]]) ).
cnf(refute_0_1494,plain,
multiply(inverse(X_28),inverse(X_196)) = inverse(multiply(X_196,X_28)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_196,X_28)),multiply(inverse(X_28),inverse(X_196))) )],[refute_0_1492,refute_0_1493]) ).
cnf(refute_0_1495,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)) = inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))),
inference(subst,[],[refute_0_1494:[bind(X_196,$fot(X_165)),bind(X_28,$fot(least_upper_bound(identity,inverse(X_165))))]]) ).
cnf(refute_0_1496,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)) != inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165))))
| inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))) != inverse(least_upper_bound(X_165,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)) = inverse(least_upper_bound(X_165,identity)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))),bind(Y0,$fot(inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))))),bind(Z0,$fot(inverse(least_upper_bound(X_165,identity))))]]) ).
cnf(refute_0_1497,plain,
( inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))) != inverse(least_upper_bound(X_165,identity))
| multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)) = inverse(least_upper_bound(X_165,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)),inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165))))) )],[refute_0_1495,refute_0_1496]) ).
cnf(refute_0_1498,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)) = inverse(least_upper_bound(X_165,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_165,least_upper_bound(identity,inverse(X_165)))),inverse(least_upper_bound(X_165,identity))) )],[refute_0_1487,refute_0_1497]) ).
cnf(refute_0_1499,plain,
least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) = least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))))]]) ).
cnf(refute_0_1500,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)) != inverse(least_upper_bound(X_165,identity))
| least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) != least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))
| least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) = least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))),least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))) ),[1,1],$fot(inverse(least_upper_bound(X_165,identity)))]]) ).
cnf(refute_0_1501,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)) != inverse(least_upper_bound(X_165,identity))
| least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) = least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))),least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))) )],[refute_0_1499,refute_0_1500]) ).
cnf(refute_0_1502,plain,
least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) = least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)),inverse(least_upper_bound(X_165,identity))) )],[refute_0_1498,refute_0_1501]) ).
cnf(refute_0_1503,plain,
( least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))) != least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity)))
| least_upper_bound(identity,X_165) != least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))
| least_upper_bound(identity,X_165) = least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_165),least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))) ),[1],$fot(least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity))))]]) ).
cnf(refute_0_1504,plain,
( least_upper_bound(identity,X_165) != least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))
| least_upper_bound(identity,X_165) = least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165))),least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity)))) )],[refute_0_1502,refute_0_1503]) ).
cnf(refute_0_1505,plain,
least_upper_bound(identity,X_165) = least_upper_bound(X_165,inverse(least_upper_bound(X_165,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_165),least_upper_bound(X_165,multiply(inverse(least_upper_bound(identity,inverse(X_165))),inverse(X_165)))) )],[refute_0_1474,refute_0_1504]) ).
cnf(refute_0_1506,plain,
least_upper_bound(identity,X_18) = least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity))),
inference(subst,[],[refute_0_1505:[bind(X_165,$fot(X_18))]]) ).
cnf(refute_0_1507,plain,
( least_upper_bound(identity,X_18) != least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))
| least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity))) = least_upper_bound(identity,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,X_18))),bind(Y0,$fot(least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))))]]) ).
cnf(refute_0_1508,plain,
least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity))) = least_upper_bound(identity,X_18),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_18),least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))) )],[refute_0_1506,refute_0_1507]) ).
cnf(refute_0_1509,plain,
( least_upper_bound(X,least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))) != least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X))
| least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity))) != least_upper_bound(identity,X_18)
| least_upper_bound(X,least_upper_bound(identity,X_18)) = least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))),least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X))) ),[0,1],$fot(least_upper_bound(identity,X_18))]]) ).
cnf(refute_0_1510,plain,
( least_upper_bound(X,least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))) != least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X))
| least_upper_bound(X,least_upper_bound(identity,X_18)) = least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity))),least_upper_bound(identity,X_18)) )],[refute_0_1508,refute_0_1509]) ).
cnf(refute_0_1511,plain,
least_upper_bound(X,least_upper_bound(identity,X_18)) = least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_18,inverse(least_upper_bound(X_18,identity)))),least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X))) )],[refute_0_1385,refute_0_1510]) ).
cnf(refute_0_1512,plain,
( least_upper_bound(X,least_upper_bound(identity,X_18)) != least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X))
| least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X)) = least_upper_bound(X,least_upper_bound(identity,X_18)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(identity,X_18)))),bind(Y0,$fot(least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X))))]]) ).
cnf(refute_0_1513,plain,
least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X)) = least_upper_bound(X,least_upper_bound(identity,X_18)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,X_18)),least_upper_bound(X_18,least_upper_bound(inverse(least_upper_bound(X_18,identity)),X))) )],[refute_0_1511,refute_0_1512]) ).
cnf(refute_0_1514,plain,
least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)),
inference(subst,[],[refute_0_1513:[bind(X,$fot(inverse(least_upper_bound(X_45,identity)))),bind(X_18,$fot(X_110))]]) ).
cnf(refute_0_1515,plain,
( least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) != least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110))
| least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)) != least_upper_bound(identity,X_110)
| least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(identity,X_110) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)))),bind(Z0,$fot(least_upper_bound(identity,X_110)))]]) ).
cnf(refute_0_1516,plain,
( least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)) != least_upper_bound(identity,X_110)
| least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(identity,X_110) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))),least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110))) )],[refute_0_1514,refute_0_1515]) ).
cnf(refute_0_1517,plain,
least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) = least_upper_bound(identity,X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(identity,X_110)),least_upper_bound(identity,X_110)) )],[refute_0_1384,refute_0_1516]) ).
cnf(refute_0_1518,plain,
( least_upper_bound(X_110,identity) != least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))) != least_upper_bound(identity,X_110)
| least_upper_bound(X_110,identity) = least_upper_bound(identity,X_110) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_110,identity),least_upper_bound(identity,X_110)) ),[0],$fot(least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))))]]) ).
cnf(refute_0_1519,plain,
( least_upper_bound(X_110,identity) != least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))
| least_upper_bound(X_110,identity) = least_upper_bound(identity,X_110) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity)))),least_upper_bound(identity,X_110)) )],[refute_0_1517,refute_0_1518]) ).
cnf(refute_0_1520,plain,
least_upper_bound(X_110,identity) = least_upper_bound(identity,X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(X_110,identity),least_upper_bound(X_110,least_upper_bound(inverse(least_upper_bound(X_110,identity)),inverse(least_upper_bound(X_45,identity))))) )],[refute_0_1372,refute_0_1519]) ).
cnf(refute_0_1521,plain,
least_upper_bound(greatest_lower_bound(X_87,identity),identity) = least_upper_bound(identity,greatest_lower_bound(X_87,identity)),
inference(subst,[],[refute_0_1520:[bind(X_110,$fot(greatest_lower_bound(X_87,identity)))]]) ).
cnf(refute_0_1522,plain,
( least_upper_bound(greatest_lower_bound(X_87,identity),identity) != least_upper_bound(identity,greatest_lower_bound(X_87,identity))
| least_upper_bound(identity,greatest_lower_bound(X_87,identity)) != identity
| least_upper_bound(greatest_lower_bound(X_87,identity),identity) = identity ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_87,identity),identity))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(X_87,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1523,plain,
( least_upper_bound(identity,greatest_lower_bound(X_87,identity)) != identity
| least_upper_bound(greatest_lower_bound(X_87,identity),identity) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_87,identity),identity),least_upper_bound(identity,greatest_lower_bound(X_87,identity))) )],[refute_0_1521,refute_0_1522]) ).
cnf(refute_0_1524,plain,
least_upper_bound(greatest_lower_bound(X_87,identity),identity) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_87,identity)),identity) )],[refute_0_917,refute_0_1523]) ).
cnf(refute_0_1525,plain,
least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,least_upper_bound(X_111,greatest_lower_bound(X_111,Y))),
inference(subst,[],[refute_0_829:[bind(X,$fot(greatest_lower_bound(X_111,Y))),bind(X_18,$fot(X_110)),bind(X_19,$fot(X_111))]]) ).
cnf(refute_0_1526,plain,
least_upper_bound(X_111,greatest_lower_bound(X_111,Y)) = X_111,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_111))]]) ).
cnf(refute_0_1527,plain,
( least_upper_bound(X_111,greatest_lower_bound(X_111,Y)) != X_111
| least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,least_upper_bound(X_111,greatest_lower_bound(X_111,Y)))
| least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,X_111) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,least_upper_bound(X_111,greatest_lower_bound(X_111,Y)))) ),[1,1],$fot(X_111)]]) ).
cnf(refute_0_1528,plain,
( least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,least_upper_bound(X_111,greatest_lower_bound(X_111,Y)))
| least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,X_111) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_111,greatest_lower_bound(X_111,Y)),X_111) )],[refute_0_1526,refute_0_1527]) ).
cnf(refute_0_1529,plain,
least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) = least_upper_bound(X_110,X_111),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,least_upper_bound(X_111,greatest_lower_bound(X_111,Y)))) )],[refute_0_1525,refute_0_1528]) ).
cnf(refute_0_1530,plain,
least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) = least_upper_bound(X_111,least_upper_bound(X_110,greatest_lower_bound(X_111,Y))),
inference(subst,[],[refute_0_1183:[bind(Y,$fot(greatest_lower_bound(X_111,Y))),bind(X_109,$fot(X_111))]]) ).
cnf(refute_0_1531,plain,
( least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,X_111)
| least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) != least_upper_bound(X_111,least_upper_bound(X_110,greatest_lower_bound(X_111,Y)))
| least_upper_bound(X_111,least_upper_bound(X_110,greatest_lower_bound(X_111,Y))) = least_upper_bound(X_110,X_111) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,X_111)) ),[0],$fot(least_upper_bound(X_111,least_upper_bound(X_110,greatest_lower_bound(X_111,Y))))]]) ).
cnf(refute_0_1532,plain,
( least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)) != least_upper_bound(X_110,X_111)
| least_upper_bound(X_111,least_upper_bound(X_110,greatest_lower_bound(X_111,Y))) = least_upper_bound(X_110,X_111) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)),least_upper_bound(X_111,least_upper_bound(X_110,greatest_lower_bound(X_111,Y)))) )],[refute_0_1530,refute_0_1531]) ).
cnf(refute_0_1533,plain,
least_upper_bound(X_111,least_upper_bound(X_110,greatest_lower_bound(X_111,Y))) = least_upper_bound(X_110,X_111),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_111,Y),least_upper_bound(X_110,X_111)),least_upper_bound(X_110,X_111)) )],[refute_0_1529,refute_0_1532]) ).
cnf(refute_0_1534,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))) = least_upper_bound(greatest_lower_bound(X_87,identity),identity),
inference(subst,[],[refute_0_1533:[bind(Y,$fot(inverse(X_87))),bind(X_110,$fot(greatest_lower_bound(X_87,identity))),bind(X_111,$fot(identity))]]) ).
cnf(refute_0_1535,plain,
( least_upper_bound(greatest_lower_bound(X_87,identity),identity) != identity
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))) != least_upper_bound(greatest_lower_bound(X_87,identity),identity)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))) = identity ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_87,identity),identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1536,plain,
( least_upper_bound(greatest_lower_bound(X_87,identity),identity) != identity
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))),least_upper_bound(greatest_lower_bound(X_87,identity),identity)) )],[refute_0_1534,refute_0_1535]) ).
cnf(refute_0_1537,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_87,identity),identity),identity) )],[refute_0_1524,refute_0_1536]) ).
cnf(refute_0_1538,plain,
least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))),
inference(subst,[],[refute_0_1284:[bind(Y,$fot(greatest_lower_bound(identity,inverse(X_87)))),bind(X_110,$fot(greatest_lower_bound(X_87,identity))),bind(X_111,$fot(identity))]]) ).
cnf(refute_0_1539,plain,
( least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87))))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))) != identity
| least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) = identity ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1540,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))) != identity
| least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87))))) )],[refute_0_1538,refute_0_1539]) ).
cnf(refute_0_1541,plain,
least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_87,identity),greatest_lower_bound(identity,inverse(X_87)))),identity) )],[refute_0_1537,refute_0_1540]) ).
cnf(refute_0_1542,plain,
( least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) != least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))),least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))) ),[1],$fot(identity)]]) ).
cnf(refute_0_1543,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) != least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87)))),identity) )],[refute_0_1541,refute_0_1542]) ).
cnf(refute_0_1544,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))) != least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))),least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))) )],[refute_0_916,refute_0_1543]) ).
cnf(refute_0_1545,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_87,identity),least_upper_bound(identity,inverse(X_87)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X_87)),greatest_lower_bound(X_87,identity))),least_upper_bound(greatest_lower_bound(X_87,identity),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_87))))) )],[refute_0_909,refute_0_1544]) ).
cnf(refute_0_1546,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) = identity,
inference(subst,[],[refute_0_1545:[bind(X_87,$fot(X_276))]]) ).
cnf(refute_0_1547,plain,
( greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))) != multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) != identity
| greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))),multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_1548,plain,
( greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))) != multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))
| greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))),identity) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),least_upper_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))),multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) )],[refute_0_792,refute_0_1548]) ).
cnf(refute_0_1550,plain,
greatest_lower_bound(identity,least_upper_bound(X_276,identity)) = identity,
inference(subst,[],[refute_0_142:[bind(X_8,$fot(identity)),bind(X_9,$fot(X_276))]]) ).
cnf(refute_0_1551,plain,
multiply(least_upper_bound(X_276,identity),identity) = least_upper_bound(X_276,identity),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(least_upper_bound(X_276,identity)))]]) ).
cnf(refute_0_1552,plain,
least_upper_bound(identity,multiply(X_276,identity)) = multiply(least_upper_bound(X_276,identity),identity),
inference(subst,[],[refute_0_883:[bind(X_59,$fot(identity)),bind(X_60,$fot(X_276))]]) ).
cnf(refute_0_1553,plain,
( multiply(least_upper_bound(X_276,identity),identity) != least_upper_bound(X_276,identity)
| least_upper_bound(identity,multiply(X_276,identity)) != multiply(least_upper_bound(X_276,identity),identity)
| least_upper_bound(identity,multiply(X_276,identity)) = least_upper_bound(X_276,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(least_upper_bound(identity,multiply(X_276,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_276,identity),identity))),bind(Z0,$fot(least_upper_bound(X_276,identity)))]]) ).
cnf(refute_0_1554,plain,
( multiply(least_upper_bound(X_276,identity),identity) != least_upper_bound(X_276,identity)
| least_upper_bound(identity,multiply(X_276,identity)) = least_upper_bound(X_276,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_276,identity)),multiply(least_upper_bound(X_276,identity),identity)) )],[refute_0_1552,refute_0_1553]) ).
cnf(refute_0_1555,plain,
least_upper_bound(identity,multiply(X_276,identity)) = least_upper_bound(X_276,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_276,identity),identity),least_upper_bound(X_276,identity)) )],[refute_0_1551,refute_0_1554]) ).
cnf(refute_0_1556,plain,
multiply(X_276,least_upper_bound(identity,inverse(X_276))) = least_upper_bound(identity,multiply(X_276,identity)),
inference(subst,[],[refute_0_40:[bind(X_44,$fot(X_276)),bind(X_45,$fot(identity))]]) ).
cnf(refute_0_1557,plain,
( multiply(X_276,least_upper_bound(identity,inverse(X_276))) != least_upper_bound(identity,multiply(X_276,identity))
| least_upper_bound(identity,multiply(X_276,identity)) != least_upper_bound(X_276,identity)
| multiply(X_276,least_upper_bound(identity,inverse(X_276))) = least_upper_bound(X_276,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(X_276,least_upper_bound(identity,inverse(X_276))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_276,identity)))),bind(Z0,$fot(least_upper_bound(X_276,identity)))]]) ).
cnf(refute_0_1558,plain,
( least_upper_bound(identity,multiply(X_276,identity)) != least_upper_bound(X_276,identity)
| multiply(X_276,least_upper_bound(identity,inverse(X_276))) = least_upper_bound(X_276,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_276,least_upper_bound(identity,inverse(X_276))),least_upper_bound(identity,multiply(X_276,identity))) )],[refute_0_1556,refute_0_1557]) ).
cnf(refute_0_1559,plain,
multiply(X_276,least_upper_bound(identity,inverse(X_276))) = least_upper_bound(X_276,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_276,identity)),least_upper_bound(X_276,identity)) )],[refute_0_1555,refute_0_1558]) ).
cnf(refute_0_1560,plain,
greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) = greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))))]]) ).
cnf(refute_0_1561,plain,
( multiply(X_276,least_upper_bound(identity,inverse(X_276))) != least_upper_bound(X_276,identity)
| greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) != greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))
| greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) = greatest_lower_bound(identity,least_upper_bound(X_276,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))),greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))) ),[1,1],$fot(least_upper_bound(X_276,identity))]]) ).
cnf(refute_0_1562,plain,
( multiply(X_276,least_upper_bound(identity,inverse(X_276))) != least_upper_bound(X_276,identity)
| greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) = greatest_lower_bound(identity,least_upper_bound(X_276,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))),greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))) )],[refute_0_1560,refute_0_1561]) ).
cnf(refute_0_1563,plain,
greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) = greatest_lower_bound(identity,least_upper_bound(X_276,identity)),
inference(resolve,[$cnf( $equal(multiply(X_276,least_upper_bound(identity,inverse(X_276))),least_upper_bound(X_276,identity)) )],[refute_0_1559,refute_0_1562]) ).
cnf(refute_0_1564,plain,
( greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) != greatest_lower_bound(identity,least_upper_bound(X_276,identity))
| greatest_lower_bound(identity,least_upper_bound(X_276,identity)) != identity
| greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) = identity ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_276,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1565,plain,
( greatest_lower_bound(identity,least_upper_bound(X_276,identity)) != identity
| greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))),greatest_lower_bound(identity,least_upper_bound(X_276,identity))) )],[refute_0_1563,refute_0_1564]) ).
cnf(refute_0_1566,plain,
greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_276,identity)),identity) )],[refute_0_1550,refute_0_1565]) ).
cnf(refute_0_1567,plain,
greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)) = greatest_lower_bound(greatest_lower_bound(X_39,least_upper_bound(X_39,Y)),X_41),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_39)),bind(Y,$fot(least_upper_bound(X_39,Y))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_1568,plain,
greatest_lower_bound(X_39,least_upper_bound(X_39,Y)) = X_39,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_1569,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)) != greatest_lower_bound(greatest_lower_bound(X_39,least_upper_bound(X_39,Y)),X_41)
| greatest_lower_bound(X_39,least_upper_bound(X_39,Y)) != X_39
| greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)) = greatest_lower_bound(X_39,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)),greatest_lower_bound(greatest_lower_bound(X_39,least_upper_bound(X_39,Y)),X_41)) ),[1,0],$fot(X_39)]]) ).
cnf(refute_0_1570,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)) != greatest_lower_bound(greatest_lower_bound(X_39,least_upper_bound(X_39,Y)),X_41)
| greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)) = greatest_lower_bound(X_39,X_41) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,least_upper_bound(X_39,Y)),X_39) )],[refute_0_1568,refute_0_1569]) ).
cnf(refute_0_1571,plain,
greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)) = greatest_lower_bound(X_39,X_41),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),X_41)),greatest_lower_bound(greatest_lower_bound(X_39,least_upper_bound(X_39,Y)),X_41)) )],[refute_0_1567,refute_0_1570]) ).
cnf(refute_0_1572,plain,
greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))) = greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y))),
inference(subst,[],[refute_0_1571:[bind(X_41,$fot(multiply(X_152,least_upper_bound(X_39,Y))))]]) ).
cnf(refute_0_1573,plain,
multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_97)),bind(Y,$fot(X_98)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_1574,plain,
multiply(identity,X_97) = X_97,
inference(subst,[],[left_identity:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_1575,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))
| multiply(identity,X_97) != X_97
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),X_97) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))) ),[1,1],$fot(X_97)]]) ).
cnf(refute_0_1576,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),X_97) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_97),X_97) )],[refute_0_1574,refute_0_1575]) ).
cnf(refute_0_1577,plain,
multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(multiply(X_98,X_97),X_97),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(multiply(X_98,X_97),multiply(identity,X_97))) )],[refute_0_1573,refute_0_1576]) ).
cnf(refute_0_1578,plain,
greatest_lower_bound(multiply(X_98,X_97),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_97)),bind(Y,$fot(multiply(X_98,X_97)))]]) ).
cnf(refute_0_1579,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),X_97)
| greatest_lower_bound(multiply(X_98,X_97),X_97) != greatest_lower_bound(X_97,multiply(X_98,X_97))
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(X_97,multiply(X_98,X_97))) ),[0],$fot(greatest_lower_bound(multiply(X_98,X_97),X_97))]]) ).
cnf(refute_0_1580,plain,
( multiply(greatest_lower_bound(X_98,identity),X_97) != greatest_lower_bound(multiply(X_98,X_97),X_97)
| multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_98,X_97),X_97),greatest_lower_bound(X_97,multiply(X_98,X_97))) )],[refute_0_1578,refute_0_1579]) ).
cnf(refute_0_1581,plain,
multiply(greatest_lower_bound(X_98,identity),X_97) = greatest_lower_bound(X_97,multiply(X_98,X_97)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_98,identity),X_97),greatest_lower_bound(multiply(X_98,X_97),X_97)) )],[refute_0_1577,refute_0_1580]) ).
cnf(refute_0_1582,plain,
multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y)) = greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y))),
inference(subst,[],[refute_0_1581:[bind(X_97,$fot(least_upper_bound(X_39,Y))),bind(X_98,$fot(X_152))]]) ).
cnf(refute_0_1583,plain,
( multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y)) != greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))
| greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y))) = multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))))]]) ).
cnf(refute_0_1584,plain,
greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y))) = multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y)),greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))) )],[refute_0_1582,refute_0_1583]) ).
cnf(refute_0_1585,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))) != greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y)))
| greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y))) != multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y))
| greatest_lower_bound(X_39,multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y))) = greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))),greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y)))) ),[0,1],$fot(multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y)))]]) ).
cnf(refute_0_1586,plain,
( greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))) != greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y)))
| greatest_lower_bound(X_39,multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y))) = greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y))),multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y))) )],[refute_0_1584,refute_0_1585]) ).
cnf(refute_0_1587,plain,
greatest_lower_bound(X_39,multiply(greatest_lower_bound(X_152,identity),least_upper_bound(X_39,Y))) = greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(X_39,Y),multiply(X_152,least_upper_bound(X_39,Y)))),greatest_lower_bound(X_39,multiply(X_152,least_upper_bound(X_39,Y)))) )],[refute_0_1572,refute_0_1586]) ).
cnf(refute_0_1588,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) = greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))),
inference(subst,[],[refute_0_1587:[bind(Y,$fot(inverse(X_276))),bind(X_152,$fot(X_276)),bind(X_39,$fot(identity))]]) ).
cnf(refute_0_1589,plain,
multiply(least_upper_bound(X_48,X_33),inverse(multiply(inverse(X_33),least_upper_bound(X_48,X_33)))) = inverse(inverse(X_33)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(inverse(X_33))),bind(X_38,$fot(least_upper_bound(X_48,X_33)))]]) ).
cnf(refute_0_1590,plain,
( multiply(inverse(X_33),least_upper_bound(X_48,X_33)) != least_upper_bound(identity,multiply(inverse(X_33),X_48))
| multiply(least_upper_bound(X_48,X_33),inverse(multiply(inverse(X_33),least_upper_bound(X_48,X_33)))) != inverse(inverse(X_33))
| multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = inverse(inverse(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_48,X_33),inverse(multiply(inverse(X_33),least_upper_bound(X_48,X_33)))),inverse(inverse(X_33))) ),[0,1,0],$fot(least_upper_bound(identity,multiply(inverse(X_33),X_48)))]]) ).
cnf(refute_0_1591,plain,
( multiply(least_upper_bound(X_48,X_33),inverse(multiply(inverse(X_33),least_upper_bound(X_48,X_33)))) != inverse(inverse(X_33))
| multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = inverse(inverse(X_33)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),least_upper_bound(X_48,X_33)),least_upper_bound(identity,multiply(inverse(X_33),X_48))) )],[refute_0_1056,refute_0_1590]) ).
cnf(refute_0_1592,plain,
multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = inverse(inverse(X_33)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_48,X_33),inverse(multiply(inverse(X_33),least_upper_bound(X_48,X_33)))),inverse(inverse(X_33))) )],[refute_0_1589,refute_0_1591]) ).
cnf(refute_0_1593,plain,
( multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) != inverse(inverse(X_33))
| inverse(inverse(X_33)) != X_33
| multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = X_33 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))),X_33) ),[0],$fot(inverse(inverse(X_33)))]]) ).
cnf(refute_0_1594,plain,
( multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) != inverse(inverse(X_33))
| multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = X_33 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_33)),X_33) )],[refute_0_119,refute_0_1593]) ).
cnf(refute_0_1595,plain,
multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))) = X_33,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_48,X_33),inverse(least_upper_bound(identity,multiply(inverse(X_33),X_48)))),inverse(inverse(X_33))) )],[refute_0_1592,refute_0_1594]) ).
cnf(refute_0_1596,plain,
multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_105,identity)),X_265)))) = greatest_lower_bound(X_105,identity),
inference(subst,[],[refute_0_1595:[bind(X_33,$fot(greatest_lower_bound(X_105,identity))),bind(X_48,$fot(X_265))]]) ).
cnf(refute_0_1597,plain,
multiply(inverse(X_105),inverse(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)))) = inverse(greatest_lower_bound(identity,X_105)),
inference(subst,[],[refute_0_88:[bind(X_28,$fot(greatest_lower_bound(identity,X_105))),bind(X_38,$fot(inverse(X_105)))]]) ).
cnf(refute_0_1598,plain,
( multiply(greatest_lower_bound(identity,X_105),inverse(X_105)) != greatest_lower_bound(identity,inverse(X_105))
| multiply(inverse(X_105),inverse(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)))) != inverse(greatest_lower_bound(identity,X_105))
| multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(greatest_lower_bound(identity,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_105),inverse(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)))),inverse(greatest_lower_bound(identity,X_105))) ),[0,1,0],$fot(greatest_lower_bound(identity,inverse(X_105)))]]) ).
cnf(refute_0_1599,plain,
( multiply(inverse(X_105),inverse(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)))) != inverse(greatest_lower_bound(identity,X_105))
| multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(greatest_lower_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)),greatest_lower_bound(identity,inverse(X_105))) )],[refute_0_503,refute_0_1598]) ).
cnf(refute_0_1600,plain,
multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(greatest_lower_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),inverse(multiply(greatest_lower_bound(identity,X_105),inverse(X_105)))),inverse(greatest_lower_bound(identity,X_105))) )],[refute_0_1597,refute_0_1599]) ).
cnf(refute_0_1601,plain,
multiply(identity,greatest_lower_bound(X_105,identity)) = greatest_lower_bound(X_105,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_1602,plain,
multiply(X_85,greatest_lower_bound(X_86,identity)) = greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_85)),bind(Y,$fot(X_86)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_1603,plain,
X_85 = multiply(X_85,identity),
inference(subst,[],[refute_0_82:[bind(X_31,$fot(X_85))]]) ).
cnf(refute_0_1604,plain,
( X_85 != multiply(X_85,identity)
| multiply(X_85,identity) = X_85 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_85)),bind(Y0,$fot(multiply(X_85,identity)))]]) ).
cnf(refute_0_1605,plain,
multiply(X_85,identity) = X_85,
inference(resolve,[$cnf( $equal(X_85,multiply(X_85,identity)) )],[refute_0_1603,refute_0_1604]) ).
cnf(refute_0_1606,plain,
( multiply(X_85,greatest_lower_bound(X_86,identity)) != greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,identity))
| multiply(X_85,identity) != X_85
| multiply(X_85,greatest_lower_bound(X_86,identity)) = greatest_lower_bound(multiply(X_85,X_86),X_85) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,identity)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,identity))) ),[1,1],$fot(X_85)]]) ).
cnf(refute_0_1607,plain,
( multiply(X_85,greatest_lower_bound(X_86,identity)) != greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,identity))
| multiply(X_85,greatest_lower_bound(X_86,identity)) = greatest_lower_bound(multiply(X_85,X_86),X_85) ),
inference(resolve,[$cnf( $equal(multiply(X_85,identity),X_85) )],[refute_0_1605,refute_0_1606]) ).
cnf(refute_0_1608,plain,
multiply(X_85,greatest_lower_bound(X_86,identity)) = greatest_lower_bound(multiply(X_85,X_86),X_85),
inference(resolve,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,identity)),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,identity))) )],[refute_0_1602,refute_0_1607]) ).
cnf(refute_0_1609,plain,
greatest_lower_bound(multiply(X_85,X_86),X_85) = greatest_lower_bound(X_85,multiply(X_85,X_86)),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_85)),bind(Y,$fot(multiply(X_85,X_86)))]]) ).
cnf(refute_0_1610,plain,
( multiply(X_85,greatest_lower_bound(X_86,identity)) != greatest_lower_bound(multiply(X_85,X_86),X_85)
| greatest_lower_bound(multiply(X_85,X_86),X_85) != greatest_lower_bound(X_85,multiply(X_85,X_86))
| multiply(X_85,greatest_lower_bound(X_86,identity)) = greatest_lower_bound(X_85,multiply(X_85,X_86)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_85,greatest_lower_bound(X_86,identity)),greatest_lower_bound(X_85,multiply(X_85,X_86))) ),[0],$fot(greatest_lower_bound(multiply(X_85,X_86),X_85))]]) ).
cnf(refute_0_1611,plain,
( multiply(X_85,greatest_lower_bound(X_86,identity)) != greatest_lower_bound(multiply(X_85,X_86),X_85)
| multiply(X_85,greatest_lower_bound(X_86,identity)) = greatest_lower_bound(X_85,multiply(X_85,X_86)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_85,X_86),X_85),greatest_lower_bound(X_85,multiply(X_85,X_86))) )],[refute_0_1609,refute_0_1610]) ).
cnf(refute_0_1612,plain,
multiply(X_85,greatest_lower_bound(X_86,identity)) = greatest_lower_bound(X_85,multiply(X_85,X_86)),
inference(resolve,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,identity)),greatest_lower_bound(multiply(X_85,X_86),X_85)) )],[refute_0_1608,refute_0_1611]) ).
cnf(refute_0_1613,plain,
( multiply(X_85,greatest_lower_bound(X_86,identity)) != greatest_lower_bound(X_85,multiply(X_85,X_86))
| greatest_lower_bound(X_85,multiply(X_85,X_86)) = multiply(X_85,greatest_lower_bound(X_86,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_85,greatest_lower_bound(X_86,identity)))),bind(Y0,$fot(greatest_lower_bound(X_85,multiply(X_85,X_86))))]]) ).
cnf(refute_0_1614,plain,
greatest_lower_bound(X_85,multiply(X_85,X_86)) = multiply(X_85,greatest_lower_bound(X_86,identity)),
inference(resolve,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,identity)),greatest_lower_bound(X_85,multiply(X_85,X_86))) )],[refute_0_1612,refute_0_1613]) ).
cnf(refute_0_1615,plain,
greatest_lower_bound(identity,multiply(identity,X_105)) = multiply(identity,greatest_lower_bound(X_105,identity)),
inference(subst,[],[refute_0_1614:[bind(X_85,$fot(identity)),bind(X_86,$fot(X_105))]]) ).
cnf(refute_0_1616,plain,
( multiply(identity,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(X_105,identity)
| greatest_lower_bound(identity,multiply(identity,X_105)) != multiply(identity,greatest_lower_bound(X_105,identity))
| greatest_lower_bound(identity,multiply(identity,X_105)) = greatest_lower_bound(X_105,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,X_105)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_105,identity)))),bind(Z0,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_1617,plain,
( multiply(identity,greatest_lower_bound(X_105,identity)) != greatest_lower_bound(X_105,identity)
| greatest_lower_bound(identity,multiply(identity,X_105)) = greatest_lower_bound(X_105,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_105)),multiply(identity,greatest_lower_bound(X_105,identity))) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
greatest_lower_bound(identity,multiply(identity,X_105)) = greatest_lower_bound(X_105,identity),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_105,identity)),greatest_lower_bound(X_105,identity)) )],[refute_0_1601,refute_0_1617]) ).
cnf(refute_0_1619,plain,
multiply(greatest_lower_bound(identity,inverse(X_105)),X_105) = greatest_lower_bound(identity,multiply(identity,X_105)),
inference(subst,[],[refute_0_53:[bind(X_97,$fot(X_105)),bind(X_98,$fot(identity))]]) ).
cnf(refute_0_1620,plain,
( multiply(greatest_lower_bound(identity,inverse(X_105)),X_105) != greatest_lower_bound(identity,multiply(identity,X_105))
| greatest_lower_bound(identity,multiply(identity,X_105)) != greatest_lower_bound(X_105,identity)
| multiply(greatest_lower_bound(identity,inverse(X_105)),X_105) = greatest_lower_bound(X_105,identity) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(identity,X_105)))),bind(Z0,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_1621,plain,
( greatest_lower_bound(identity,multiply(identity,X_105)) != greatest_lower_bound(X_105,identity)
| multiply(greatest_lower_bound(identity,inverse(X_105)),X_105) = greatest_lower_bound(X_105,identity) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105),greatest_lower_bound(identity,multiply(identity,X_105))) )],[refute_0_1619,refute_0_1620]) ).
cnf(refute_0_1622,plain,
multiply(greatest_lower_bound(identity,inverse(X_105)),X_105) = greatest_lower_bound(X_105,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_105)),greatest_lower_bound(X_105,identity)) )],[refute_0_1618,refute_0_1621]) ).
cnf(refute_0_1623,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)) = inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)))]]) ).
cnf(refute_0_1624,plain,
( multiply(greatest_lower_bound(identity,inverse(X_105)),X_105) != greatest_lower_bound(X_105,identity)
| inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)) != inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)) = inverse(greatest_lower_bound(X_105,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)),inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105))) ),[1,0],$fot(greatest_lower_bound(X_105,identity))]]) ).
cnf(refute_0_1625,plain,
( multiply(greatest_lower_bound(identity,inverse(X_105)),X_105) != greatest_lower_bound(X_105,identity)
| inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)) = inverse(greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)),inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105))) )],[refute_0_1623,refute_0_1624]) ).
cnf(refute_0_1626,plain,
inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)) = inverse(greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105),greatest_lower_bound(X_105,identity)) )],[refute_0_1622,refute_0_1625]) ).
cnf(refute_0_1627,plain,
multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)),
inference(subst,[],[refute_0_1494:[bind(X_196,$fot(greatest_lower_bound(identity,inverse(X_105)))),bind(X_28,$fot(X_105))]]) ).
cnf(refute_0_1628,plain,
( multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) != inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105))
| inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)) != inverse(greatest_lower_bound(X_105,identity))
| multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(greatest_lower_bound(X_105,identity)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_105,identity))))]]) ).
cnf(refute_0_1629,plain,
( inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)) != inverse(greatest_lower_bound(X_105,identity))
| multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(greatest_lower_bound(X_105,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))),inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105))) )],[refute_0_1627,refute_0_1628]) ).
cnf(refute_0_1630,plain,
multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) = inverse(greatest_lower_bound(X_105,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,inverse(X_105)),X_105)),inverse(greatest_lower_bound(X_105,identity))) )],[refute_0_1626,refute_0_1629]) ).
cnf(refute_0_1631,plain,
( multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) != inverse(greatest_lower_bound(X_105,identity))
| multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) != inverse(greatest_lower_bound(identity,X_105))
| inverse(greatest_lower_bound(X_105,identity)) = inverse(greatest_lower_bound(identity,X_105)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))),inverse(greatest_lower_bound(identity,X_105))) ),[0],$fot(inverse(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_1632,plain,
( multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))) != inverse(greatest_lower_bound(identity,X_105))
| inverse(greatest_lower_bound(X_105,identity)) = inverse(greatest_lower_bound(identity,X_105)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))),inverse(greatest_lower_bound(X_105,identity))) )],[refute_0_1630,refute_0_1631]) ).
cnf(refute_0_1633,plain,
inverse(greatest_lower_bound(X_105,identity)) = inverse(greatest_lower_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),inverse(greatest_lower_bound(identity,inverse(X_105)))),inverse(greatest_lower_bound(identity,X_105))) )],[refute_0_1600,refute_0_1632]) ).
cnf(refute_0_1634,plain,
( multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_105,identity)),X_265)))) != greatest_lower_bound(X_105,identity)
| inverse(greatest_lower_bound(X_105,identity)) != inverse(greatest_lower_bound(identity,X_105))
| multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))) = greatest_lower_bound(X_105,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_105,identity)),X_265)))),greatest_lower_bound(X_105,identity)) ),[0,1,0,1,0],$fot(inverse(greatest_lower_bound(identity,X_105)))]]) ).
cnf(refute_0_1635,plain,
( multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_105,identity)),X_265)))) != greatest_lower_bound(X_105,identity)
| multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))) = greatest_lower_bound(X_105,identity) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_105,identity)),inverse(greatest_lower_bound(identity,X_105))) )],[refute_0_1633,refute_0_1634]) ).
cnf(refute_0_1636,plain,
multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))) = greatest_lower_bound(X_105,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_105,identity)),X_265)))),greatest_lower_bound(X_105,identity)) )],[refute_0_1596,refute_0_1635]) ).
cnf(refute_0_1637,plain,
multiply(least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))) = greatest_lower_bound(X_13,X_23),
inference(subst,[],[refute_0_1595:[bind(X_33,$fot(greatest_lower_bound(X_13,X_23))),bind(X_48,$fot(X_265))]]) ).
cnf(refute_0_1638,plain,
least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23))) = least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))),
inference(subst,[],[refute_0_936:[bind(X_18,$fot(X_208)),bind(X_19,$fot(greatest_lower_bound(X_13,X_23))),bind(X_20,$fot(greatest_lower_bound(X_23,X_13)))]]) ).
cnf(refute_0_1639,plain,
( least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23))) != least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))
| least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23)) != greatest_lower_bound(X_23,X_13)
| least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) = least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23))),least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))) ),[0,1],$fot(greatest_lower_bound(X_23,X_13))]]) ).
cnf(refute_0_1640,plain,
( least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23))) != least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))
| least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) = least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23)),greatest_lower_bound(X_23,X_13)) )],[refute_0_538,refute_0_1639]) ).
cnf(refute_0_1641,plain,
least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) = least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_23,X_13),greatest_lower_bound(X_13,X_23))),least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))) )],[refute_0_1638,refute_0_1640]) ).
cnf(refute_0_1642,plain,
least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)) = greatest_lower_bound(X_13,X_23),
inference(subst,[],[refute_0_538:[bind(X_13,$fot(X_23)),bind(X_23,$fot(X_13))]]) ).
cnf(refute_0_1643,plain,
least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) = least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))))]]) ).
cnf(refute_0_1644,plain,
( least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) != least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))
| least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)) != greatest_lower_bound(X_13,X_23)
| least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) = least_upper_bound(X_208,greatest_lower_bound(X_13,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))),least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))) ),[1,1],$fot(greatest_lower_bound(X_13,X_23))]]) ).
cnf(refute_0_1645,plain,
( least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)) != greatest_lower_bound(X_13,X_23)
| least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) = least_upper_bound(X_208,greatest_lower_bound(X_13,X_23)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))),least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))) )],[refute_0_1643,refute_0_1644]) ).
cnf(refute_0_1646,plain,
least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) = least_upper_bound(X_208,greatest_lower_bound(X_13,X_23)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)),greatest_lower_bound(X_13,X_23)) )],[refute_0_1642,refute_0_1645]) ).
cnf(refute_0_1647,plain,
( least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) != least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))
| least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))) != least_upper_bound(X_208,greatest_lower_bound(X_13,X_23))
| least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) = least_upper_bound(X_208,greatest_lower_bound(X_13,X_23)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)),least_upper_bound(X_208,greatest_lower_bound(X_13,X_23))) ),[0],$fot(least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))))]]) ).
cnf(refute_0_1648,plain,
( least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) != least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))
| least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) = least_upper_bound(X_208,greatest_lower_bound(X_13,X_23)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13))),least_upper_bound(X_208,greatest_lower_bound(X_13,X_23))) )],[refute_0_1646,refute_0_1647]) ).
cnf(refute_0_1649,plain,
least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)) = least_upper_bound(X_208,greatest_lower_bound(X_13,X_23)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_208,greatest_lower_bound(X_23,X_13)),least_upper_bound(X_208,least_upper_bound(greatest_lower_bound(X_13,X_23),greatest_lower_bound(X_23,X_13)))) )],[refute_0_1641,refute_0_1648]) ).
cnf(refute_0_1650,plain,
least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)) = least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)),
inference(subst,[],[refute_0_1649:[bind(X_208,$fot(X_265))]]) ).
cnf(refute_0_1651,plain,
( least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)) != least_upper_bound(X_265,greatest_lower_bound(X_13,X_23))
| least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)) = least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)))),bind(Y0,$fot(least_upper_bound(X_265,greatest_lower_bound(X_13,X_23))))]]) ).
cnf(refute_0_1652,plain,
least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)) = least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)),least_upper_bound(X_265,greatest_lower_bound(X_13,X_23))) )],[refute_0_1650,refute_0_1651]) ).
cnf(refute_0_1653,plain,
( multiply(least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))) != greatest_lower_bound(X_13,X_23)
| least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)) != least_upper_bound(X_265,greatest_lower_bound(X_23,X_13))
| multiply(least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))) = greatest_lower_bound(X_13,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))),greatest_lower_bound(X_13,X_23)) ),[0,0],$fot(least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)))]]) ).
cnf(refute_0_1654,plain,
( multiply(least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))) != greatest_lower_bound(X_13,X_23)
| multiply(least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))) = greatest_lower_bound(X_13,X_23) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)),least_upper_bound(X_265,greatest_lower_bound(X_23,X_13))) )],[refute_0_1652,refute_0_1653]) ).
cnf(refute_0_1655,plain,
multiply(least_upper_bound(X_265,greatest_lower_bound(X_23,X_13)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))) = greatest_lower_bound(X_13,X_23),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_265,greatest_lower_bound(X_13,X_23)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_13,X_23)),X_265)))),greatest_lower_bound(X_13,X_23)) )],[refute_0_1637,refute_0_1654]) ).
cnf(refute_0_1656,plain,
multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))) = greatest_lower_bound(identity,X_105),
inference(subst,[],[refute_0_1655:[bind(X_13,$fot(identity)),bind(X_23,$fot(X_105))]]) ).
cnf(refute_0_1657,plain,
( multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))) != greatest_lower_bound(X_105,identity)
| multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))) != greatest_lower_bound(identity,X_105)
| greatest_lower_bound(identity,X_105) = greatest_lower_bound(X_105,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))),greatest_lower_bound(X_105,identity)) ),[0],$fot(greatest_lower_bound(identity,X_105))]]) ).
cnf(refute_0_1658,plain,
( multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))) != greatest_lower_bound(X_105,identity)
| greatest_lower_bound(identity,X_105) = greatest_lower_bound(X_105,identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))),greatest_lower_bound(identity,X_105)) )],[refute_0_1656,refute_0_1657]) ).
cnf(refute_0_1659,plain,
greatest_lower_bound(identity,X_105) = greatest_lower_bound(X_105,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_265,greatest_lower_bound(X_105,identity)),inverse(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_105)),X_265)))),greatest_lower_bound(X_105,identity)) )],[refute_0_1636,refute_0_1658]) ).
cnf(refute_0_1660,plain,
( greatest_lower_bound(identity,X_105) != greatest_lower_bound(X_105,identity)
| greatest_lower_bound(X_105,identity) = greatest_lower_bound(identity,X_105) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(identity,X_105))),bind(Y0,$fot(greatest_lower_bound(X_105,identity)))]]) ).
cnf(refute_0_1661,plain,
greatest_lower_bound(X_105,identity) = greatest_lower_bound(identity,X_105),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_105),greatest_lower_bound(X_105,identity)) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))),
inference(subst,[],[refute_0_1661:[bind(X_105,$fot(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))))]]) ).
cnf(refute_0_1663,plain,
( greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) != greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))
| greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))))]]) ).
cnf(refute_0_1664,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) != greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))
| greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))))) )],[refute_0_1662,refute_0_1663]) ).
cnf(refute_0_1665,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))),greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))) )],[refute_0_1588,refute_0_1664]) ).
cnf(refute_0_1666,plain,
( greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) != greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))
| greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) != identity
| greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = identity ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1667,plain,
( greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))) != identity
| greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity),greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276))))) )],[refute_0_1665,refute_0_1666]) ).
cnf(refute_0_1668,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_276,least_upper_bound(identity,inverse(X_276)))),identity) )],[refute_0_1566,refute_0_1667]) ).
cnf(refute_0_1669,plain,
( greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) != multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))
| greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) != identity
| identity = multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity),multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1670,plain,
( greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity) != multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))
| identity = multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity),identity) )],[refute_0_1668,refute_0_1669]) ).
cnf(refute_0_1671,plain,
identity = multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))),identity),multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) )],[refute_0_1549,refute_0_1670]) ).
cnf(refute_0_1672,plain,
( identity != multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))
| multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))))]]) ).
cnf(refute_0_1673,plain,
multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(greatest_lower_bound(X_276,identity),least_upper_bound(identity,inverse(X_276)))) )],[refute_0_1671,refute_0_1672]) ).
cnf(refute_0_1674,plain,
multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))) = identity,
inference(subst,[],[refute_0_1673:[bind(X_276,$fot(X_232))]]) ).
cnf(refute_0_1675,plain,
inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) = inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))))]]) ).
cnf(refute_0_1676,plain,
( multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))) != identity
| inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) != inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))))
| inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1677,plain,
( multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))) != identity
| inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))))) )],[refute_0_1675,refute_0_1676]) ).
cnf(refute_0_1678,plain,
inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232))),identity) )],[refute_0_1674,refute_0_1677]) ).
cnf(refute_0_1679,plain,
( inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) != inverse(identity)
| inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) = identity ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1680,plain,
( inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),inverse(identity)) )],[refute_0_1678,refute_0_1679]) ).
cnf(refute_0_1681,plain,
inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_791,refute_0_1680]) ).
cnf(refute_0_1682,plain,
multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) = multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)))]]) ).
cnf(refute_0_1683,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) != multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))
| inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) = multiply(identity,least_upper_bound(identity,X_232)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)),multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1684,plain,
( inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) = multiply(identity,least_upper_bound(identity,X_232)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)),multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))) )],[refute_0_1682,refute_0_1683]) ).
cnf(refute_0_1685,plain,
multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) = multiply(identity,least_upper_bound(identity,X_232)),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),identity) )],[refute_0_1681,refute_0_1684]) ).
cnf(refute_0_1686,plain,
( multiply(identity,least_upper_bound(identity,X_232)) != least_upper_bound(identity,X_232)
| multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) != multiply(identity,least_upper_bound(identity,X_232))
| multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) = least_upper_bound(identity,X_232) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,X_232)))),bind(Z0,$fot(least_upper_bound(identity,X_232)))]]) ).
cnf(refute_0_1687,plain,
( multiply(identity,least_upper_bound(identity,X_232)) != least_upper_bound(identity,X_232)
| multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) = least_upper_bound(identity,X_232) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)),multiply(identity,least_upper_bound(identity,X_232))) )],[refute_0_1685,refute_0_1686]) ).
cnf(refute_0_1688,plain,
multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) = least_upper_bound(identity,X_232),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,X_232)),least_upper_bound(identity,X_232)) )],[refute_0_784,refute_0_1687]) ).
cnf(refute_0_1689,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)) != least_upper_bound(identity,X_232)
| inverse(greatest_lower_bound(identity,inverse(X_232))) != multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))
| inverse(greatest_lower_bound(identity,inverse(X_232))) = least_upper_bound(identity,X_232) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_232))),multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))) ),[1],$fot(least_upper_bound(identity,X_232))]]) ).
cnf(refute_0_1690,plain,
( inverse(greatest_lower_bound(identity,inverse(X_232))) != multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))
| inverse(greatest_lower_bound(identity,inverse(X_232))) = least_upper_bound(identity,X_232) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232)),least_upper_bound(identity,X_232)) )],[refute_0_1688,refute_0_1689]) ).
cnf(refute_0_1691,plain,
inverse(greatest_lower_bound(identity,inverse(X_232))) = least_upper_bound(identity,X_232),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_232))),multiply(inverse(multiply(greatest_lower_bound(X_232,identity),least_upper_bound(identity,inverse(X_232)))),least_upper_bound(identity,X_232))) )],[refute_0_783,refute_0_1690]) ).
cnf(refute_0_1692,plain,
inverse(greatest_lower_bound(identity,inverse(X_202))) = least_upper_bound(identity,X_202),
inference(subst,[],[refute_0_1691:[bind(X_232,$fot(X_202))]]) ).
cnf(refute_0_1693,plain,
( inverse(greatest_lower_bound(identity,inverse(X_202))) != multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))
| inverse(greatest_lower_bound(identity,inverse(X_202))) != least_upper_bound(identity,X_202)
| least_upper_bound(identity,X_202) = multiply(X_202,inverse(greatest_lower_bound(identity,X_202))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_202))),multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))) ),[0],$fot(least_upper_bound(identity,X_202))]]) ).
cnf(refute_0_1694,plain,
( inverse(greatest_lower_bound(identity,inverse(X_202))) != multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))
| least_upper_bound(identity,X_202) = multiply(X_202,inverse(greatest_lower_bound(identity,X_202))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_202))),least_upper_bound(identity,X_202)) )],[refute_0_1692,refute_0_1693]) ).
cnf(refute_0_1695,plain,
least_upper_bound(identity,X_202) = multiply(X_202,inverse(greatest_lower_bound(identity,X_202))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_202))),multiply(X_202,inverse(greatest_lower_bound(identity,X_202)))) )],[refute_0_507,refute_0_1694]) ).
cnf(refute_0_1696,plain,
least_upper_bound(identity,X_196) = multiply(X_196,inverse(greatest_lower_bound(identity,X_196))),
inference(subst,[],[refute_0_1695:[bind(X_202,$fot(X_196))]]) ).
cnf(refute_0_1697,plain,
( least_upper_bound(identity,X_196) != multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))
| multiply(X_196,inverse(greatest_lower_bound(identity,X_196))) = least_upper_bound(identity,X_196) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,X_196))),bind(Y0,$fot(multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))))]]) ).
cnf(refute_0_1698,plain,
multiply(X_196,inverse(greatest_lower_bound(identity,X_196))) = least_upper_bound(identity,X_196),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_196),multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))) )],[refute_0_1696,refute_0_1697]) ).
cnf(refute_0_1699,plain,
( multiply(X_196,inverse(greatest_lower_bound(identity,X_196))) != least_upper_bound(identity,X_196)
| inverse(multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))) != multiply(greatest_lower_bound(identity,X_196),inverse(X_196))
| inverse(least_upper_bound(identity,X_196)) = multiply(greatest_lower_bound(identity,X_196),inverse(X_196)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))),multiply(greatest_lower_bound(identity,X_196),inverse(X_196))) ),[0,0],$fot(least_upper_bound(identity,X_196))]]) ).
cnf(refute_0_1700,plain,
( inverse(multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))) != multiply(greatest_lower_bound(identity,X_196),inverse(X_196))
| inverse(least_upper_bound(identity,X_196)) = multiply(greatest_lower_bound(identity,X_196),inverse(X_196)) ),
inference(resolve,[$cnf( $equal(multiply(X_196,inverse(greatest_lower_bound(identity,X_196))),least_upper_bound(identity,X_196)) )],[refute_0_1698,refute_0_1699]) ).
cnf(refute_0_1701,plain,
inverse(least_upper_bound(identity,X_196)) = multiply(greatest_lower_bound(identity,X_196),inverse(X_196)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_196,inverse(greatest_lower_bound(identity,X_196)))),multiply(greatest_lower_bound(identity,X_196),inverse(X_196))) )],[refute_0_497,refute_0_1700]) ).
cnf(refute_0_1702,plain,
multiply(greatest_lower_bound(identity,X_196),inverse(X_196)) = greatest_lower_bound(identity,inverse(X_196)),
inference(subst,[],[refute_0_503:[bind(X_105,$fot(X_196))]]) ).
cnf(refute_0_1703,plain,
( multiply(greatest_lower_bound(identity,X_196),inverse(X_196)) != greatest_lower_bound(identity,inverse(X_196))
| inverse(least_upper_bound(identity,X_196)) != multiply(greatest_lower_bound(identity,X_196),inverse(X_196))
| inverse(least_upper_bound(identity,X_196)) = greatest_lower_bound(identity,inverse(X_196)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_196)),multiply(greatest_lower_bound(identity,X_196),inverse(X_196))) ),[1],$fot(greatest_lower_bound(identity,inverse(X_196)))]]) ).
cnf(refute_0_1704,plain,
( inverse(least_upper_bound(identity,X_196)) != multiply(greatest_lower_bound(identity,X_196),inverse(X_196))
| inverse(least_upper_bound(identity,X_196)) = greatest_lower_bound(identity,inverse(X_196)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_196),inverse(X_196)),greatest_lower_bound(identity,inverse(X_196))) )],[refute_0_1702,refute_0_1703]) ).
cnf(refute_0_1705,plain,
inverse(least_upper_bound(identity,X_196)) = greatest_lower_bound(identity,inverse(X_196)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_196)),multiply(greatest_lower_bound(identity,X_196),inverse(X_196))) )],[refute_0_1701,refute_0_1704]) ).
cnf(refute_0_1706,plain,
inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))) = greatest_lower_bound(identity,inverse(multiply(X_196,inverse(X_33)))),
inference(subst,[],[refute_0_1705:[bind(X_196,$fot(multiply(X_196,inverse(X_33))))]]) ).
cnf(refute_0_1707,plain,
( inverse(multiply(X_196,inverse(X_33))) != multiply(X_33,inverse(X_196))
| inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))) != greatest_lower_bound(identity,inverse(multiply(X_196,inverse(X_33))))
| inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))) = greatest_lower_bound(identity,multiply(X_33,inverse(X_196))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))),greatest_lower_bound(identity,inverse(multiply(X_196,inverse(X_33))))) ),[1,1],$fot(multiply(X_33,inverse(X_196)))]]) ).
cnf(refute_0_1708,plain,
( inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))) != greatest_lower_bound(identity,inverse(multiply(X_196,inverse(X_33))))
| inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))) = greatest_lower_bound(identity,multiply(X_33,inverse(X_196))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_196,inverse(X_33))),multiply(X_33,inverse(X_196))) )],[refute_0_492,refute_0_1707]) ).
cnf(refute_0_1709,plain,
inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))) = greatest_lower_bound(identity,multiply(X_33,inverse(X_196))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_196,inverse(X_33)))),greatest_lower_bound(identity,inverse(multiply(X_196,inverse(X_33))))) )],[refute_0_1706,refute_0_1708]) ).
cnf(refute_0_1710,plain,
inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) = greatest_lower_bound(identity,multiply(X_180,inverse(X_181))),
inference(subst,[],[refute_0_1709:[bind(X_196,$fot(X_181)),bind(X_33,$fot(X_180))]]) ).
cnf(refute_0_1711,plain,
( inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) != multiply(X_180,inverse(least_upper_bound(X_180,X_181)))
| inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) != greatest_lower_bound(identity,multiply(X_180,inverse(X_181)))
| greatest_lower_bound(identity,multiply(X_180,inverse(X_181))) = multiply(X_180,inverse(least_upper_bound(X_180,X_181))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))),multiply(X_180,inverse(least_upper_bound(X_180,X_181)))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_180,inverse(X_181))))]]) ).
cnf(refute_0_1712,plain,
( inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))) != multiply(X_180,inverse(least_upper_bound(X_180,X_181)))
| greatest_lower_bound(identity,multiply(X_180,inverse(X_181))) = multiply(X_180,inverse(least_upper_bound(X_180,X_181))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))),greatest_lower_bound(identity,multiply(X_180,inverse(X_181)))) )],[refute_0_1710,refute_0_1711]) ).
cnf(refute_0_1713,plain,
greatest_lower_bound(identity,multiply(X_180,inverse(X_181))) = multiply(X_180,inverse(least_upper_bound(X_180,X_181))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_181,inverse(X_180)))),multiply(X_180,inverse(least_upper_bound(X_180,X_181)))) )],[refute_0_496,refute_0_1712]) ).
cnf(refute_0_1714,plain,
greatest_lower_bound(identity,multiply(X_101,inverse(X_324))) = multiply(X_101,inverse(least_upper_bound(X_101,X_324))),
inference(subst,[],[refute_0_1713:[bind(X_180,$fot(X_101)),bind(X_181,$fot(X_324))]]) ).
cnf(refute_0_1715,plain,
( greatest_lower_bound(identity,multiply(X_101,inverse(X_324))) != multiply(X_101,inverse(least_upper_bound(X_101,X_324)))
| multiply(X_101,inverse(least_upper_bound(X_101,X_324))) = greatest_lower_bound(identity,multiply(X_101,inverse(X_324))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),bind(Y0,$fot(multiply(X_101,inverse(least_upper_bound(X_101,X_324)))))]]) ).
cnf(refute_0_1716,plain,
multiply(X_101,inverse(least_upper_bound(X_101,X_324))) = greatest_lower_bound(identity,multiply(X_101,inverse(X_324))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_101,inverse(X_324))),multiply(X_101,inverse(least_upper_bound(X_101,X_324)))) )],[refute_0_1714,refute_0_1715]) ).
cnf(refute_0_1717,plain,
( multiply(X_101,inverse(least_upper_bound(X_101,X_324))) != greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))
| inverse(least_upper_bound(X_101,X_324)) != multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,multiply(X_101,inverse(least_upper_bound(X_101,X_324)))))
| inverse(least_upper_bound(X_101,X_324)) = multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_101,X_324)),multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,multiply(X_101,inverse(least_upper_bound(X_101,X_324)))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))]]) ).
cnf(refute_0_1718,plain,
( inverse(least_upper_bound(X_101,X_324)) != multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,multiply(X_101,inverse(least_upper_bound(X_101,X_324)))))
| inverse(least_upper_bound(X_101,X_324)) = multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) ),
inference(resolve,[$cnf( $equal(multiply(X_101,inverse(least_upper_bound(X_101,X_324))),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) )],[refute_0_1716,refute_0_1717]) ).
cnf(refute_0_1719,plain,
inverse(least_upper_bound(X_101,X_324)) = multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_101,X_324)),multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,multiply(X_101,inverse(least_upper_bound(X_101,X_324)))))) )],[refute_0_309,refute_0_1718]) ).
cnf(refute_0_1720,plain,
multiply(inverse(X_101),identity) = inverse(X_101),
inference(subst,[],[refute_0_84:[bind(X_31,$fot(inverse(X_101)))]]) ).
cnf(refute_0_1721,plain,
greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)) = greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)))]]) ).
cnf(refute_0_1722,plain,
( multiply(inverse(X_101),identity) != inverse(X_101)
| greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)) != greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324))
| greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)),greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324))) ),[1,0],$fot(inverse(X_101))]]) ).
cnf(refute_0_1723,plain,
( multiply(inverse(X_101),identity) != inverse(X_101)
| greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)),greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324))) )],[refute_0_1721,refute_0_1722]) ).
cnf(refute_0_1724,plain,
greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)) = greatest_lower_bound(inverse(X_101),inverse(X_324)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),identity),inverse(X_101)) )],[refute_0_1720,refute_0_1723]) ).
cnf(refute_0_1725,plain,
multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))) = greatest_lower_bound(multiply(inverse(X_28),X_86),multiply(inverse(X_28),multiply(X_28,X_29))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_28))),bind(Y,$fot(X_86)),bind(Z,$fot(multiply(X_28,X_29)))]]) ).
cnf(refute_0_1726,plain,
( X_29 != multiply(inverse(X_28),multiply(X_28,X_29))
| multiply(inverse(X_28),multiply(X_28,X_29)) = X_29 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_29)),bind(Y0,$fot(multiply(inverse(X_28),multiply(X_28,X_29))))]]) ).
cnf(refute_0_1727,plain,
multiply(inverse(X_28),multiply(X_28,X_29)) = X_29,
inference(resolve,[$cnf( $equal(X_29,multiply(inverse(X_28),multiply(X_28,X_29))) )],[refute_0_19,refute_0_1726]) ).
cnf(refute_0_1728,plain,
( multiply(inverse(X_28),multiply(X_28,X_29)) != X_29
| multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))) != greatest_lower_bound(multiply(inverse(X_28),X_86),multiply(inverse(X_28),multiply(X_28,X_29)))
| multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))) = greatest_lower_bound(multiply(inverse(X_28),X_86),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))),greatest_lower_bound(multiply(inverse(X_28),X_86),multiply(inverse(X_28),multiply(X_28,X_29)))) ),[1,1],$fot(X_29)]]) ).
cnf(refute_0_1729,plain,
( multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))) != greatest_lower_bound(multiply(inverse(X_28),X_86),multiply(inverse(X_28),multiply(X_28,X_29)))
| multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))) = greatest_lower_bound(multiply(inverse(X_28),X_86),X_29) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),multiply(X_28,X_29)),X_29) )],[refute_0_1727,refute_0_1728]) ).
cnf(refute_0_1730,plain,
multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))) = greatest_lower_bound(multiply(inverse(X_28),X_86),X_29),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),greatest_lower_bound(X_86,multiply(X_28,X_29))),greatest_lower_bound(multiply(inverse(X_28),X_86),multiply(inverse(X_28),multiply(X_28,X_29)))) )],[refute_0_1725,refute_0_1729]) ).
cnf(refute_0_1731,plain,
multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) = greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)),
inference(subst,[],[refute_0_1730:[bind(X_28,$fot(X_101)),bind(X_29,$fot(inverse(X_324))),bind(X_86,$fot(identity))]]) ).
cnf(refute_0_1732,plain,
( multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) != greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324))
| greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)) != greatest_lower_bound(inverse(X_101),inverse(X_324))
| multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)))),bind(Z0,$fot(greatest_lower_bound(inverse(X_101),inverse(X_324))))]]) ).
cnf(refute_0_1733,plain,
( greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)) != greatest_lower_bound(inverse(X_101),inverse(X_324))
| multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))),greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324))) )],[refute_0_1731,refute_0_1732]) ).
cnf(refute_0_1734,plain,
multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) = greatest_lower_bound(inverse(X_101),inverse(X_324)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_101),identity),inverse(X_324)),greatest_lower_bound(inverse(X_101),inverse(X_324))) )],[refute_0_1724,refute_0_1733]) ).
cnf(refute_0_1735,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) = greatest_lower_bound(identity,multiply(X_101,inverse(X_324))),
inference(subst,[],[refute_0_160:[bind(X_23,$fot(multiply(X_101,inverse(X_324)))),bind(X_24,$fot(identity))]]) ).
cnf(refute_0_1736,plain,
multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))))]]) ).
cnf(refute_0_1737,plain,
( multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) != multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))
| greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) != greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))
| multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))]]) ).
cnf(refute_0_1738,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) != greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))
| multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))) )],[refute_0_1736,refute_0_1737]) ).
cnf(refute_0_1739,plain,
multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) )],[refute_0_1735,refute_0_1738]) ).
cnf(refute_0_1740,plain,
greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)) = X_101,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_101)),bind(Y,$fot(X_324))]]) ).
cnf(refute_0_1741,plain,
inverse(inverse(least_upper_bound(X_101,X_324))) = least_upper_bound(X_101,X_324),
inference(subst,[],[refute_0_119:[bind(X_33,$fot(least_upper_bound(X_101,X_324)))]]) ).
cnf(refute_0_1742,plain,
greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) = greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))))]]) ).
cnf(refute_0_1743,plain,
( greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) != greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))
| inverse(inverse(least_upper_bound(X_101,X_324))) != least_upper_bound(X_101,X_324)
| greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) = greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))),greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) ),[1,1],$fot(least_upper_bound(X_101,X_324))]]) ).
cnf(refute_0_1744,plain,
( inverse(inverse(least_upper_bound(X_101,X_324))) != least_upper_bound(X_101,X_324)
| greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) = greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))),greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) )],[refute_0_1742,refute_0_1743]) ).
cnf(refute_0_1745,plain,
greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) = greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_101,X_324))),least_upper_bound(X_101,X_324)) )],[refute_0_1741,refute_0_1744]) ).
cnf(refute_0_1746,plain,
( greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) != greatest_lower_bound(X_101,least_upper_bound(X_101,X_324))
| greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)) != X_101
| greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) = X_101 ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))))),bind(Y0,$fot(greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)))),bind(Z0,$fot(X_101))]]) ).
cnf(refute_0_1747,plain,
( greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)) != X_101
| greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) = X_101 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))),greatest_lower_bound(X_101,least_upper_bound(X_101,X_324))) )],[refute_0_1745,refute_0_1746]) ).
cnf(refute_0_1748,plain,
greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) = X_101,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_101,least_upper_bound(X_101,X_324)),X_101) )],[refute_0_1740,refute_0_1747]) ).
cnf(refute_0_1749,plain,
inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) = inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))))]]) ).
cnf(refute_0_1750,plain,
( greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) != X_101
| inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) != inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))))
| inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) = inverse(X_101) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))))) ),[1,0],$fot(X_101)]]) ).
cnf(refute_0_1751,plain,
( greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))) != X_101
| inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) = inverse(X_101) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))))) )],[refute_0_1749,refute_0_1750]) ).
cnf(refute_0_1752,plain,
inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) = inverse(X_101),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324)))),X_101) )],[refute_0_1748,refute_0_1751]) ).
cnf(refute_0_1753,plain,
multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))))]]) ).
cnf(refute_0_1754,plain,
( multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) != multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))
| inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) != inverse(X_101)
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))) ),[1,0],$fot(inverse(X_101))]]) ).
cnf(refute_0_1755,plain,
( inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))) != inverse(X_101)
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))) )],[refute_0_1753,refute_0_1754]) ).
cnf(refute_0_1756,plain,
multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),inverse(X_101)) )],[refute_0_1752,refute_0_1755]) ).
cnf(refute_0_1757,plain,
( multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) != multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) != multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))))),bind(Y0,$fot(multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))))),bind(Z0,$fot(multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))))]]) ).
cnf(refute_0_1758,plain,
( multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) != multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))) )],[refute_0_1756,refute_0_1757]) ).
cnf(refute_0_1759,plain,
multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) )],[refute_0_1739,refute_0_1758]) ).
cnf(refute_0_1760,plain,
( multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) != greatest_lower_bound(inverse(X_101),inverse(X_324))
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) != multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))))),bind(Y0,$fot(multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))),bind(Z0,$fot(greatest_lower_bound(inverse(X_101),inverse(X_324))))]]) ).
cnf(refute_0_1761,plain,
( multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))) != greatest_lower_bound(inverse(X_101),inverse(X_324))
| multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) )],[refute_0_1759,refute_0_1760]) ).
cnf(refute_0_1762,plain,
multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) = greatest_lower_bound(inverse(X_101),inverse(X_324)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))),greatest_lower_bound(inverse(X_101),inverse(X_324))) )],[refute_0_1734,refute_0_1761]) ).
cnf(refute_0_1763,plain,
( multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))) != greatest_lower_bound(inverse(X_101),inverse(X_324))
| inverse(least_upper_bound(X_101,X_324)) != multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))
| inverse(least_upper_bound(X_101,X_324)) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_101,X_324)),multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))) ),[1],$fot(greatest_lower_bound(inverse(X_101),inverse(X_324)))]]) ).
cnf(refute_0_1764,plain,
( inverse(least_upper_bound(X_101,X_324)) != multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))
| inverse(least_upper_bound(X_101,X_324)) = greatest_lower_bound(inverse(X_101),inverse(X_324)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324))))),greatest_lower_bound(inverse(X_101),inverse(X_324))) )],[refute_0_1762,refute_0_1763]) ).
cnf(refute_0_1765,plain,
inverse(least_upper_bound(X_101,X_324)) = greatest_lower_bound(inverse(X_101),inverse(X_324)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_101,X_324)),multiply(inverse(greatest_lower_bound(X_101,inverse(inverse(least_upper_bound(X_101,X_324))))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_101,inverse(X_324)))))) )],[refute_0_1719,refute_0_1764]) ).
cnf(refute_0_1766,plain,
( inverse(least_upper_bound(X_101,X_324)) != greatest_lower_bound(inverse(X_101),inverse(X_324))
| greatest_lower_bound(inverse(X_101),inverse(X_324)) = inverse(least_upper_bound(X_101,X_324)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_101,X_324)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_101),inverse(X_324))))]]) ).
cnf(refute_0_1767,plain,
greatest_lower_bound(inverse(X_101),inverse(X_324)) = inverse(least_upper_bound(X_101,X_324)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_101,X_324)),greatest_lower_bound(inverse(X_101),inverse(X_324))) )],[refute_0_1765,refute_0_1766]) ).
cnf(refute_0_1768,plain,
greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),
inference(subst,[],[refute_0_1767:[bind(X_101,$fot(least_upper_bound(X_245,X_246))),bind(X_324,$fot(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))]]) ).
cnf(refute_0_1769,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))
| inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != inverse(least_upper_bound(X_245,X_246))
| greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(X_245,X_246)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))),bind(Y0,$fot(inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))),bind(Z0,$fot(inverse(least_upper_bound(X_245,X_246))))]]) ).
cnf(refute_0_1770,plain,
( inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != inverse(least_upper_bound(X_245,X_246))
| greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(X_245,X_246)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) )],[refute_0_1768,refute_0_1769]) ).
cnf(refute_0_1771,plain,
greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) = inverse(least_upper_bound(X_245,X_246)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_245,X_246),greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),inverse(least_upper_bound(X_245,X_246))) )],[refute_0_308,refute_0_1770]) ).
cnf(refute_0_1772,plain,
inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) = inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))))]]) ).
cnf(refute_0_1773,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != inverse(least_upper_bound(X_245,X_246))
| inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) != inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))
| inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) = inverse(inverse(least_upper_bound(X_245,X_246))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))) ),[1,0],$fot(inverse(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_1774,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))) != inverse(least_upper_bound(X_245,X_246))
| inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) = inverse(inverse(least_upper_bound(X_245,X_246))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))) )],[refute_0_1772,refute_0_1773]) ).
cnf(refute_0_1775,plain,
inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) = inverse(inverse(least_upper_bound(X_245,X_246))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))),inverse(least_upper_bound(X_245,X_246))) )],[refute_0_1771,refute_0_1774]) ).
cnf(refute_0_1776,plain,
( inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) != inverse(inverse(least_upper_bound(X_245,X_246)))
| inverse(inverse(least_upper_bound(X_245,X_246))) != least_upper_bound(X_245,X_246)
| inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) = least_upper_bound(X_245,X_246) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(X_245,X_246))))),bind(Z0,$fot(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_1777,plain,
( inverse(inverse(least_upper_bound(X_245,X_246))) != least_upper_bound(X_245,X_246)
| inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) = least_upper_bound(X_245,X_246) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),inverse(inverse(least_upper_bound(X_245,X_246)))) )],[refute_0_1775,refute_0_1776]) ).
cnf(refute_0_1778,plain,
inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) = least_upper_bound(X_245,X_246),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_245,X_246))),least_upper_bound(X_245,X_246)) )],[refute_0_260,refute_0_1777]) ).
cnf(refute_0_1779,plain,
( inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))) != least_upper_bound(X_245,X_246)
| least_upper_bound(X_246,X_245) != inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))
| least_upper_bound(X_246,X_245) = least_upper_bound(X_245,X_246) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_246,X_245),inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))) ),[1],$fot(least_upper_bound(X_245,X_246))]]) ).
cnf(refute_0_1780,plain,
( least_upper_bound(X_246,X_245) != inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))
| least_upper_bound(X_246,X_245) = least_upper_bound(X_245,X_246) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245))))),least_upper_bound(X_245,X_246)) )],[refute_0_1778,refute_0_1779]) ).
cnf(refute_0_1781,plain,
least_upper_bound(X_246,X_245) = least_upper_bound(X_245,X_246),
inference(resolve,[$cnf( $equal(least_upper_bound(X_246,X_245),inverse(greatest_lower_bound(inverse(least_upper_bound(X_245,X_246)),inverse(greatest_lower_bound(identity,least_upper_bound(X_246,X_245)))))) )],[refute_0_259,refute_0_1780]) ).
cnf(refute_0_1782,plain,
( least_upper_bound(X_246,X_245) != least_upper_bound(X_245,X_246)
| least_upper_bound(X_245,X_246) = least_upper_bound(X_246,X_245) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_246,X_245))),bind(Y0,$fot(least_upper_bound(X_245,X_246)))]]) ).
cnf(refute_0_1783,plain,
least_upper_bound(X_245,X_246) = least_upper_bound(X_246,X_245),
inference(resolve,[$cnf( $equal(least_upper_bound(X_246,X_245),least_upper_bound(X_245,X_246)) )],[refute_0_1781,refute_0_1782]) ).
cnf(refute_0_1784,plain,
least_upper_bound(inverse(a),b) = least_upper_bound(b,inverse(a)),
inference(subst,[],[refute_0_1783:[bind(X_245,$fot(inverse(a))),bind(X_246,$fot(b))]]) ).
cnf(refute_0_1785,plain,
inverse(inverse(least_upper_bound(inverse(X_327),X_326))) = least_upper_bound(inverse(X_327),X_326),
inference(subst,[],[refute_0_119:[bind(X_33,$fot(least_upper_bound(inverse(X_327),X_326)))]]) ).
cnf(refute_0_1786,plain,
inverse(least_upper_bound(inverse(X_33),X_324)) = multiply(X_33,multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324)))),
inference(subst,[],[refute_0_487:[bind(X_29,$fot(inverse(least_upper_bound(inverse(X_33),X_324))))]]) ).
cnf(refute_0_1787,plain,
greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))) = multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))),
inference(subst,[],[refute_0_1713:[bind(X_180,$fot(inverse(X_33))),bind(X_181,$fot(X_324))]]) ).
cnf(refute_0_1788,plain,
( greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))) != multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324)))
| multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))) = greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))))),bind(Y0,$fot(multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324)))))]]) ).
cnf(refute_0_1789,plain,
multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))) = greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))),multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324)))) )],[refute_0_1787,refute_0_1788]) ).
cnf(refute_0_1790,plain,
( multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))) != greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))
| inverse(least_upper_bound(inverse(X_33),X_324)) != multiply(X_33,multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))))
| inverse(least_upper_bound(inverse(X_33),X_324)) = multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),X_324)),multiply(X_33,multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))))]]) ).
cnf(refute_0_1791,plain,
( inverse(least_upper_bound(inverse(X_33),X_324)) != multiply(X_33,multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))))
| inverse(least_upper_bound(inverse(X_33),X_324)) = multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))),greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) )],[refute_0_1789,refute_0_1790]) ).
cnf(refute_0_1792,plain,
inverse(least_upper_bound(inverse(X_33),X_324)) = multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),X_324)),multiply(X_33,multiply(inverse(X_33),inverse(least_upper_bound(inverse(X_33),X_324))))) )],[refute_0_1786,refute_0_1791]) ).
cnf(refute_0_1793,plain,
greatest_lower_bound(multiply(X_33,identity),inverse(X_324)) = greatest_lower_bound(multiply(X_33,identity),inverse(X_324)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_33,identity),inverse(X_324)))]]) ).
cnf(refute_0_1794,plain,
( multiply(X_33,identity) != X_33
| greatest_lower_bound(multiply(X_33,identity),inverse(X_324)) != greatest_lower_bound(multiply(X_33,identity),inverse(X_324))
| greatest_lower_bound(multiply(X_33,identity),inverse(X_324)) = greatest_lower_bound(X_33,inverse(X_324)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_33,identity),inverse(X_324)),greatest_lower_bound(multiply(X_33,identity),inverse(X_324))) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_1795,plain,
( multiply(X_33,identity) != X_33
| greatest_lower_bound(multiply(X_33,identity),inverse(X_324)) = greatest_lower_bound(X_33,inverse(X_324)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_33,identity),inverse(X_324)),greatest_lower_bound(multiply(X_33,identity),inverse(X_324))) )],[refute_0_1793,refute_0_1794]) ).
cnf(refute_0_1796,plain,
greatest_lower_bound(multiply(X_33,identity),inverse(X_324)) = greatest_lower_bound(X_33,inverse(X_324)),
inference(resolve,[$cnf( $equal(multiply(X_33,identity),X_33) )],[refute_0_116,refute_0_1795]) ).
cnf(refute_0_1797,plain,
multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))) = greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,multiply(inverse(X_85),X_29))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_85)),bind(Y,$fot(X_86)),bind(Z,$fot(multiply(inverse(X_85),X_29)))]]) ).
cnf(refute_0_1798,plain,
X_29 = multiply(X_85,multiply(inverse(X_85),X_29)),
inference(subst,[],[refute_0_487:[bind(X_33,$fot(X_85))]]) ).
cnf(refute_0_1799,plain,
( X_29 != multiply(X_85,multiply(inverse(X_85),X_29))
| multiply(X_85,multiply(inverse(X_85),X_29)) = X_29 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_29)),bind(Y0,$fot(multiply(X_85,multiply(inverse(X_85),X_29))))]]) ).
cnf(refute_0_1800,plain,
multiply(X_85,multiply(inverse(X_85),X_29)) = X_29,
inference(resolve,[$cnf( $equal(X_29,multiply(X_85,multiply(inverse(X_85),X_29))) )],[refute_0_1798,refute_0_1799]) ).
cnf(refute_0_1801,plain,
( multiply(X_85,multiply(inverse(X_85),X_29)) != X_29
| multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))) != greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,multiply(inverse(X_85),X_29)))
| multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))) = greatest_lower_bound(multiply(X_85,X_86),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,multiply(inverse(X_85),X_29)))) ),[1,1],$fot(X_29)]]) ).
cnf(refute_0_1802,plain,
( multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))) != greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,multiply(inverse(X_85),X_29)))
| multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))) = greatest_lower_bound(multiply(X_85,X_86),X_29) ),
inference(resolve,[$cnf( $equal(multiply(X_85,multiply(inverse(X_85),X_29)),X_29) )],[refute_0_1800,refute_0_1801]) ).
cnf(refute_0_1803,plain,
multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))) = greatest_lower_bound(multiply(X_85,X_86),X_29),
inference(resolve,[$cnf( $equal(multiply(X_85,greatest_lower_bound(X_86,multiply(inverse(X_85),X_29))),greatest_lower_bound(multiply(X_85,X_86),multiply(X_85,multiply(inverse(X_85),X_29)))) )],[refute_0_1797,refute_0_1802]) ).
cnf(refute_0_1804,plain,
multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) = greatest_lower_bound(multiply(X_33,identity),inverse(X_324)),
inference(subst,[],[refute_0_1803:[bind(X_29,$fot(inverse(X_324))),bind(X_85,$fot(X_33)),bind(X_86,$fot(identity))]]) ).
cnf(refute_0_1805,plain,
( multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) != greatest_lower_bound(multiply(X_33,identity),inverse(X_324))
| greatest_lower_bound(multiply(X_33,identity),inverse(X_324)) != greatest_lower_bound(X_33,inverse(X_324))
| multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) = greatest_lower_bound(X_33,inverse(X_324)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_33,identity),inverse(X_324)))),bind(Z0,$fot(greatest_lower_bound(X_33,inverse(X_324))))]]) ).
cnf(refute_0_1806,plain,
( greatest_lower_bound(multiply(X_33,identity),inverse(X_324)) != greatest_lower_bound(X_33,inverse(X_324))
| multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) = greatest_lower_bound(X_33,inverse(X_324)) ),
inference(resolve,[$cnf( $equal(multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))),greatest_lower_bound(multiply(X_33,identity),inverse(X_324))) )],[refute_0_1804,refute_0_1805]) ).
cnf(refute_0_1807,plain,
multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) = greatest_lower_bound(X_33,inverse(X_324)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_33,identity),inverse(X_324)),greatest_lower_bound(X_33,inverse(X_324))) )],[refute_0_1796,refute_0_1806]) ).
cnf(refute_0_1808,plain,
( multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))) != greatest_lower_bound(X_33,inverse(X_324))
| inverse(least_upper_bound(inverse(X_33),X_324)) != multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))))
| inverse(least_upper_bound(inverse(X_33),X_324)) = greatest_lower_bound(X_33,inverse(X_324)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),X_324)),multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))))) ),[1],$fot(greatest_lower_bound(X_33,inverse(X_324)))]]) ).
cnf(refute_0_1809,plain,
( inverse(least_upper_bound(inverse(X_33),X_324)) != multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))))
| inverse(least_upper_bound(inverse(X_33),X_324)) = greatest_lower_bound(X_33,inverse(X_324)) ),
inference(resolve,[$cnf( $equal(multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324)))),greatest_lower_bound(X_33,inverse(X_324))) )],[refute_0_1807,refute_0_1808]) ).
cnf(refute_0_1810,plain,
inverse(least_upper_bound(inverse(X_33),X_324)) = greatest_lower_bound(X_33,inverse(X_324)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_33),X_324)),multiply(X_33,greatest_lower_bound(identity,multiply(inverse(X_33),inverse(X_324))))) )],[refute_0_1792,refute_0_1809]) ).
cnf(refute_0_1811,plain,
inverse(least_upper_bound(inverse(X_327),X_326)) = greatest_lower_bound(X_327,inverse(X_326)),
inference(subst,[],[refute_0_1810:[bind(X_324,$fot(X_326)),bind(X_33,$fot(X_327))]]) ).
cnf(refute_0_1812,plain,
( inverse(inverse(least_upper_bound(inverse(X_327),X_326))) != least_upper_bound(inverse(X_327),X_326)
| inverse(least_upper_bound(inverse(X_327),X_326)) != greatest_lower_bound(X_327,inverse(X_326))
| inverse(greatest_lower_bound(X_327,inverse(X_326))) = least_upper_bound(inverse(X_327),X_326) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X_327),X_326))),least_upper_bound(inverse(X_327),X_326)) ),[0,0],$fot(greatest_lower_bound(X_327,inverse(X_326)))]]) ).
cnf(refute_0_1813,plain,
( inverse(inverse(least_upper_bound(inverse(X_327),X_326))) != least_upper_bound(inverse(X_327),X_326)
| inverse(greatest_lower_bound(X_327,inverse(X_326))) = least_upper_bound(inverse(X_327),X_326) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_327),X_326)),greatest_lower_bound(X_327,inverse(X_326))) )],[refute_0_1811,refute_0_1812]) ).
cnf(refute_0_1814,plain,
inverse(greatest_lower_bound(X_327,inverse(X_326))) = least_upper_bound(inverse(X_327),X_326),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X_327),X_326))),least_upper_bound(inverse(X_327),X_326)) )],[refute_0_1785,refute_0_1813]) ).
cnf(refute_0_1815,plain,
inverse(greatest_lower_bound(a,inverse(b))) = least_upper_bound(inverse(a),b),
inference(subst,[],[refute_0_1814:[bind(X_326,$fot(b)),bind(X_327,$fot(a))]]) ).
cnf(refute_0_1816,plain,
( inverse(greatest_lower_bound(a,inverse(b))) != least_upper_bound(inverse(a),b)
| least_upper_bound(inverse(a),b) != least_upper_bound(b,inverse(a))
| inverse(greatest_lower_bound(a,inverse(b))) = least_upper_bound(b,inverse(a)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(inverse(greatest_lower_bound(a,inverse(b))))),bind(Y0,$fot(least_upper_bound(inverse(a),b))),bind(Z0,$fot(least_upper_bound(b,inverse(a))))]]) ).
cnf(refute_0_1817,plain,
( least_upper_bound(inverse(a),b) != least_upper_bound(b,inverse(a))
| inverse(greatest_lower_bound(a,inverse(b))) = least_upper_bound(b,inverse(a)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,inverse(b))),least_upper_bound(inverse(a),b)) )],[refute_0_1815,refute_0_1816]) ).
cnf(refute_0_1818,plain,
inverse(greatest_lower_bound(a,inverse(b))) = least_upper_bound(b,inverse(a)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),b),least_upper_bound(b,inverse(a))) )],[refute_0_1784,refute_0_1817]) ).
cnf(refute_0_1819,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
introduced(tautology,[refl,[$fot(multiply(a,inverse(greatest_lower_bound(a,inverse(b)))))]]) ).
cnf(refute_0_1820,plain,
( multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != multiply(a,inverse(greatest_lower_bound(a,inverse(b))))
| inverse(greatest_lower_bound(a,inverse(b))) != least_upper_bound(b,inverse(a))
| multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = multiply(a,least_upper_bound(b,inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) ),[1,1],$fot(least_upper_bound(b,inverse(a)))]]) ).
cnf(refute_0_1821,plain,
( inverse(greatest_lower_bound(a,inverse(b))) != least_upper_bound(b,inverse(a))
| multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = multiply(a,least_upper_bound(b,inverse(a))) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) )],[refute_0_1819,refute_0_1820]) ).
cnf(refute_0_1822,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = multiply(a,least_upper_bound(b,inverse(a))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,inverse(b))),least_upper_bound(b,inverse(a))) )],[refute_0_1818,refute_0_1821]) ).
cnf(refute_0_1823,plain,
( multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != multiply(a,least_upper_bound(b,inverse(a)))
| multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b))
| multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = least_upper_bound(identity,multiply(a,b)) ),
inference(subst,[],[refute_0_209:[bind(X0,$fot(multiply(a,inverse(greatest_lower_bound(a,inverse(b)))))),bind(Y0,$fot(multiply(a,least_upper_bound(b,inverse(a))))),bind(Z0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).
cnf(refute_0_1824,plain,
( multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b))
| multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = least_upper_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),multiply(a,least_upper_bound(b,inverse(a)))) )],[refute_0_1822,refute_0_1823]) ).
cnf(refute_0_1825,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,inverse(a))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_41,refute_0_1824]) ).
cnf(refute_0_1826,plain,
( multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) ),[1],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_1827,plain,
( least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_1825,refute_0_1826]) ).
cnf(refute_0_1828,plain,
least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) )],[refute_0_1827,refute_0_8]) ).
cnf(refute_0_1829,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_1830,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))) )],[refute_0_1829,refute_0_1828]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP186-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.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 : Tue Jun 14 06:02:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14.61/14.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.61/14.78
% 14.61/14.78 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.80/15.00
%------------------------------------------------------------------------------