TSTP Solution File: GRP186-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 10:37:51 EDT 2022
% Result : Unsatisfiable 11.69s 11.86s
% Output : CNFRefutation 11.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 238
% Syntax : Number of clauses : 1143 ( 585 unt; 0 nHn; 564 RR)
% Number of literals : 1940 (1939 equ; 801 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 : 2264 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p23_1,hypothesis,
inverse(identity) = identity ).
cnf(p23_2,hypothesis,
inverse(inverse(X)) = X ).
cnf(p23_3,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(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( $equal(least_upper_bound(multiply(a,b),identity),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) )],[refute_0_7,prove_p23]) ).
cnf(refute_0_9,plain,
inverse(multiply(inverse(X),X_26)) = multiply(inverse(X_26),inverse(inverse(X))),
inference(subst,[],[p23_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_10,plain,
( inverse(multiply(inverse(X),X_26)) != multiply(inverse(X_26),inverse(inverse(X)))
| inverse(inverse(X)) != X
| inverse(multiply(inverse(X),X_26)) = multiply(inverse(X_26),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_26)),multiply(inverse(X_26),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_11,plain,
( inverse(multiply(inverse(X),X_26)) != multiply(inverse(X_26),inverse(inverse(X)))
| inverse(multiply(inverse(X),X_26)) = multiply(inverse(X_26),X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p23_2,refute_0_10]) ).
cnf(refute_0_12,plain,
inverse(multiply(inverse(X),X_26)) = multiply(inverse(X_26),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_26)),multiply(inverse(X_26),inverse(inverse(X)))) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
inverse(multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111))))) = multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_111)),bind(X_26,$fot(greatest_lower_bound(X_32,inverse(inverse(X_111)))))]]) ).
cnf(refute_0_14,plain,
multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) = greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,inverse(X_31))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(inverse(X_31)))]]) ).
cnf(refute_0_15,plain,
multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).
cnf(refute_0_16,plain,
inverse(inverse(X_1)) = X_1,
inference(subst,[],[p23_2:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_17,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| inverse(inverse(X_1)) != X_1
| multiply(X_1,inverse(X_1)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_18,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| multiply(X_1,inverse(X_1)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(X_1,inverse(X_1)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(X_31,inverse(X_31)) = identity,
inference(subst,[],[refute_0_19:[bind(X_1,$fot(X_31))]]) ).
cnf(refute_0_21,plain,
( multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) != greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,inverse(X_31)))
| multiply(X_31,inverse(X_31)) != identity
| multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) = greatest_lower_bound(multiply(X_31,X_32),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))),greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,inverse(X_31)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_22,plain,
( multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) != greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,inverse(X_31)))
| multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) = greatest_lower_bound(multiply(X_31,X_32),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_31,inverse(X_31)),identity) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) = greatest_lower_bound(multiply(X_31,X_32),identity),
inference(resolve,[$cnf( $equal(multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))),greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,inverse(X_31)))) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_25,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_24]) ).
cnf(refute_0_26,plain,
greatest_lower_bound(multiply(X_31,X_32),identity) = greatest_lower_bound(identity,multiply(X_31,X_32)),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_31,X_32)))]]) ).
cnf(refute_0_27,plain,
( multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) != greatest_lower_bound(multiply(X_31,X_32),identity)
| greatest_lower_bound(multiply(X_31,X_32),identity) != greatest_lower_bound(identity,multiply(X_31,X_32))
| multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) = greatest_lower_bound(identity,multiply(X_31,X_32)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))),greatest_lower_bound(identity,multiply(X_31,X_32))) ),[0],$fot(greatest_lower_bound(multiply(X_31,X_32),identity))]]) ).
cnf(refute_0_28,plain,
( multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) != greatest_lower_bound(multiply(X_31,X_32),identity)
| multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) = greatest_lower_bound(identity,multiply(X_31,X_32)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_31,X_32),identity),greatest_lower_bound(identity,multiply(X_31,X_32))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))) = greatest_lower_bound(identity,multiply(X_31,X_32)),
inference(resolve,[$cnf( $equal(multiply(X_31,greatest_lower_bound(X_32,inverse(X_31))),greatest_lower_bound(multiply(X_31,X_32),identity)) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111)))) = greatest_lower_bound(identity,multiply(inverse(X_111),X_32)),
inference(subst,[],[refute_0_29:[bind(X_31,$fot(inverse(X_111)))]]) ).
cnf(refute_0_31,plain,
( multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111)))) != greatest_lower_bound(identity,multiply(inverse(X_111),X_32))
| inverse(multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111))))) != multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) = multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111))))),multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_111),X_32)))]]) ).
cnf(refute_0_32,plain,
( inverse(multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111))))) != multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) = multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111)))),greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) = multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_111),greatest_lower_bound(X_32,inverse(inverse(X_111))))),multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)) )],[refute_0_13,refute_0_32]) ).
cnf(refute_0_34,plain,
inverse(inverse(X_111)) = X_111,
inference(subst,[],[p23_2:[bind(X,$fot(X_111))]]) ).
cnf(refute_0_35,plain,
greatest_lower_bound(X_32,inverse(inverse(X_111))) = greatest_lower_bound(X_32,inverse(inverse(X_111))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_32,inverse(inverse(X_111))))]]) ).
cnf(refute_0_36,plain,
( greatest_lower_bound(X_32,inverse(inverse(X_111))) != greatest_lower_bound(X_32,inverse(inverse(X_111)))
| inverse(inverse(X_111)) != X_111
| greatest_lower_bound(X_32,inverse(inverse(X_111))) = greatest_lower_bound(X_32,X_111) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_32,inverse(inverse(X_111))),greatest_lower_bound(X_32,inverse(inverse(X_111)))) ),[1,1],$fot(X_111)]]) ).
cnf(refute_0_37,plain,
( inverse(inverse(X_111)) != X_111
| greatest_lower_bound(X_32,inverse(inverse(X_111))) = greatest_lower_bound(X_32,X_111) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,inverse(inverse(X_111))),greatest_lower_bound(X_32,inverse(inverse(X_111)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
greatest_lower_bound(X_32,inverse(inverse(X_111))) = greatest_lower_bound(X_32,X_111),
inference(resolve,[$cnf( $equal(inverse(inverse(X_111)),X_111) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))) = inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))))]]) ).
cnf(refute_0_40,plain,
( greatest_lower_bound(X_32,inverse(inverse(X_111))) != greatest_lower_bound(X_32,X_111)
| inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))) != inverse(greatest_lower_bound(X_32,inverse(inverse(X_111))))
| inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))) = inverse(greatest_lower_bound(X_32,X_111)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),inverse(greatest_lower_bound(X_32,inverse(inverse(X_111))))) ),[1,0],$fot(greatest_lower_bound(X_32,X_111))]]) ).
cnf(refute_0_41,plain,
( greatest_lower_bound(X_32,inverse(inverse(X_111))) != greatest_lower_bound(X_32,X_111)
| inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))) = inverse(greatest_lower_bound(X_32,X_111)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),inverse(greatest_lower_bound(X_32,inverse(inverse(X_111))))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))) = inverse(greatest_lower_bound(X_32,X_111)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,inverse(inverse(X_111))),greatest_lower_bound(X_32,X_111)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) = multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111))]]) ).
cnf(refute_0_44,plain,
( multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) != multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)
| inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))) != inverse(greatest_lower_bound(X_32,X_111))
| multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) = multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111),multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)) ),[1,0],$fot(inverse(greatest_lower_bound(X_32,X_111)))]]) ).
cnf(refute_0_45,plain,
( inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))) != inverse(greatest_lower_bound(X_32,X_111))
| multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) = multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111),multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) = multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),inverse(greatest_lower_bound(X_32,X_111))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111) != multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) != multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) = multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))),multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111))]]) ).
cnf(refute_0_48,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) != multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) = multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111),multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))) = multiply(inverse(greatest_lower_bound(X_32,X_111)),X_111),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_111),X_32))),multiply(inverse(greatest_lower_bound(X_32,inverse(inverse(X_111)))),X_111)) )],[refute_0_33,refute_0_48]) ).
cnf(refute_0_50,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))) = multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144),
inference(subst,[],[refute_0_49:[bind(X_111,$fot(X_144)),bind(X_32,$fot(inverse(X_50)))]]) ).
cnf(refute_0_51,plain,
multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)) = greatest_lower_bound(multiply(X_50,inverse(X_50)),multiply(X_51,inverse(X_50))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_50))),bind(Y,$fot(X_50)),bind(Z,$fot(X_51))]]) ).
cnf(refute_0_52,plain,
multiply(X_50,inverse(X_50)) = identity,
inference(subst,[],[refute_0_19:[bind(X_1,$fot(X_50))]]) ).
cnf(refute_0_53,plain,
( multiply(X_50,inverse(X_50)) != identity
| multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)) != greatest_lower_bound(multiply(X_50,inverse(X_50)),multiply(X_51,inverse(X_50)))
| multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)) = greatest_lower_bound(identity,multiply(X_51,inverse(X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)),greatest_lower_bound(multiply(X_50,inverse(X_50)),multiply(X_51,inverse(X_50)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_54,plain,
( multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)) != greatest_lower_bound(multiply(X_50,inverse(X_50)),multiply(X_51,inverse(X_50)))
| multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)) = greatest_lower_bound(identity,multiply(X_51,inverse(X_50))) ),
inference(resolve,[$cnf( $equal(multiply(X_50,inverse(X_50)),identity) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)) = greatest_lower_bound(identity,multiply(X_51,inverse(X_50))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,X_51),inverse(X_50)),greatest_lower_bound(multiply(X_50,inverse(X_50)),multiply(X_51,inverse(X_50)))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50)) = greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50))),
inference(subst,[],[refute_0_55:[bind(X_51,$fot(inverse(X_144)))]]) ).
cnf(refute_0_57,plain,
( multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50)) != greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))
| greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50))) = multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))))]]) ).
cnf(refute_0_58,plain,
greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50))) = multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50)),greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50))) != multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))) != multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)
| inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) = multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))),multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)) ),[0,0],$fot(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50)))]]) ).
cnf(refute_0_60,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))) != multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)
| inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) = multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50))),multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) = multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X_50)))),multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)) )],[refute_0_50,refute_0_60]) ).
cnf(refute_0_62,plain,
inverse(multiply(X_25,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_25)),
inference(subst,[],[p23_3:[bind(X,$fot(X_25)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_63,plain,
( inverse(multiply(X_25,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_25))
| inverse(inverse(X)) != X
| inverse(multiply(X_25,inverse(X))) = multiply(X,inverse(X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_25,inverse(X))),multiply(inverse(inverse(X)),inverse(X_25))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_64,plain,
( inverse(multiply(X_25,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_25))
| inverse(multiply(X_25,inverse(X))) = multiply(X,inverse(X_25)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p23_2,refute_0_63]) ).
cnf(refute_0_65,plain,
inverse(multiply(X_25,inverse(X))) = multiply(X,inverse(X_25)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_25,inverse(X))),multiply(inverse(inverse(X)),inverse(X_25))) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) = multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))),
inference(subst,[],[refute_0_65:[bind(X,$fot(X_50)),bind(X_25,$fot(greatest_lower_bound(X_50,inverse(X_144))))]]) ).
cnf(refute_0_67,plain,
( inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) != multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144))))
| inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) != multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)
| multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) = multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))),multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)) ),[0],$fot(multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))))]]) ).
cnf(refute_0_68,plain,
( inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) != multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)
| multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) = multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))),multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144))))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X)))) = multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144),
inference(subst,[],[refute_0_49:[bind(X_111,$fot(X_144)),bind(X_32,$fot(inverse(X)))]]) ).
cnf(refute_0_70,plain,
inverse(multiply(X,X_144)) = multiply(inverse(X_144),inverse(X)),
inference(subst,[],[p23_3:[bind(Y,$fot(X_144))]]) ).
cnf(refute_0_71,plain,
( inverse(multiply(X,X_144)) != multiply(inverse(X_144),inverse(X))
| multiply(inverse(X_144),inverse(X)) = inverse(multiply(X,X_144)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X,X_144)))),bind(Y0,$fot(multiply(inverse(X_144),inverse(X))))]]) ).
cnf(refute_0_72,plain,
multiply(inverse(X_144),inverse(X)) = inverse(multiply(X,X_144)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,X_144)),multiply(inverse(X_144),inverse(X))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( multiply(inverse(X_144),inverse(X)) != inverse(multiply(X,X_144))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X)))) != multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144)
| inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))) = multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X)))),multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144)) ),[0,0,1],$fot(inverse(multiply(X,X_144)))]]) ).
cnf(refute_0_74,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X)))) != multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144)
| inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))) = multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_144),inverse(X)),inverse(multiply(X,X_144))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))) = multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_144),inverse(X)))),multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144)) )],[refute_0_69,refute_0_74]) ).
cnf(refute_0_76,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))) != multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144)
| multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144) = inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144)))]]) ).
cnf(refute_0_77,plain,
multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144) = inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X,X_144)))),multiply(inverse(greatest_lower_bound(inverse(X),X_144)),X_144)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144) = inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144)))),
inference(subst,[],[refute_0_77:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_79,plain,
( multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) != multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)
| multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144) != inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144))))
| multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) = inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))),inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144))]]) ).
cnf(refute_0_80,plain,
( multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) != multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)
| multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) = inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144),inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144))))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))) != multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)
| multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) = inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144)))) ),
inference(resolve,[$cnf( $equal(multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))),multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)) )],[refute_0_68,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(X_50,inverse(greatest_lower_bound(X_50,inverse(X_144)))) = inverse(greatest_lower_bound(identity,inverse(multiply(X_50,X_144)))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_50,inverse(X_144)),inverse(X_50))),multiply(inverse(greatest_lower_bound(inverse(X_50),X_144)),X_144)) )],[refute_0_61,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),
inference(subst,[],[refute_0_82:[bind(X_144,$fot(b)),bind(X_50,$fot(a))]]) ).
cnf(refute_0_84,plain,
( multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))
| least_upper_bound(identity,multiply(a,b)) != inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) ),[1],$fot(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))))]]) ).
cnf(refute_0_85,plain,
( least_upper_bound(identity,multiply(a,b)) != inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))
| least_upper_bound(identity,multiply(a,b)) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
least_upper_bound(identity,multiply(a,b)) != inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),multiply(a,inverse(greatest_lower_bound(a,inverse(b))))) )],[refute_0_85,refute_0_8]) ).
cnf(refute_0_87,plain,
inverse(inverse(least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(identity,multiply(a,b)),
inference(subst,[],[p23_2:[bind(X,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).
cnf(refute_0_88,plain,
multiply(multiply(inverse(X_93),X_93),X_94) = multiply(inverse(X_93),multiply(X_93,X_94)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_93))),bind(Y,$fot(X_93)),bind(Z,$fot(X_94))]]) ).
cnf(refute_0_89,plain,
multiply(inverse(X_93),X_93) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_93))]]) ).
cnf(refute_0_90,plain,
( multiply(multiply(inverse(X_93),X_93),X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| multiply(inverse(X_93),X_93) != identity
| multiply(identity,X_94) = multiply(inverse(X_93),multiply(X_93,X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_93),X_93),X_94),multiply(inverse(X_93),multiply(X_93,X_94))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_91,plain,
( multiply(multiply(inverse(X_93),X_93),X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| multiply(identity,X_94) = multiply(inverse(X_93),multiply(X_93,X_94)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_93),X_93),identity) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(identity,X_94) = multiply(inverse(X_93),multiply(X_93,X_94)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_93),X_93),X_94),multiply(inverse(X_93),multiply(X_93,X_94))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(identity,X_94) = X_94,
inference(subst,[],[left_identity:[bind(X,$fot(X_94))]]) ).
cnf(refute_0_94,plain,
( multiply(identity,X_94) != X_94
| multiply(identity,X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| X_94 = multiply(inverse(X_93),multiply(X_93,X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_94),multiply(inverse(X_93),multiply(X_93,X_94))) ),[0],$fot(X_94)]]) ).
cnf(refute_0_95,plain,
( multiply(identity,X_94) != multiply(inverse(X_93),multiply(X_93,X_94))
| X_94 = multiply(inverse(X_93),multiply(X_93,X_94)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),X_94) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
X_94 = multiply(inverse(X_93),multiply(X_93,X_94)),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),multiply(inverse(X_93),multiply(X_93,X_94))) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
X_94 = multiply(inverse(least_upper_bound(X_128,inverse(X_94))),multiply(least_upper_bound(X_128,inverse(X_94)),X_94)),
inference(subst,[],[refute_0_96:[bind(X_93,$fot(least_upper_bound(X_128,inverse(X_94))))]]) ).
cnf(refute_0_98,plain,
multiply(least_upper_bound(X_123,inverse(X_122)),X_122) = least_upper_bound(multiply(X_123,X_122),multiply(inverse(X_122),X_122)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_122)),bind(Y,$fot(X_123)),bind(Z,$fot(inverse(X_122)))]]) ).
cnf(refute_0_99,plain,
multiply(inverse(X_122),X_122) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_122))]]) ).
cnf(refute_0_100,plain,
( multiply(inverse(X_122),X_122) != identity
| multiply(least_upper_bound(X_123,inverse(X_122)),X_122) != least_upper_bound(multiply(X_123,X_122),multiply(inverse(X_122),X_122))
| multiply(least_upper_bound(X_123,inverse(X_122)),X_122) = least_upper_bound(multiply(X_123,X_122),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_123,inverse(X_122)),X_122),least_upper_bound(multiply(X_123,X_122),multiply(inverse(X_122),X_122))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_101,plain,
( multiply(least_upper_bound(X_123,inverse(X_122)),X_122) != least_upper_bound(multiply(X_123,X_122),multiply(inverse(X_122),X_122))
| multiply(least_upper_bound(X_123,inverse(X_122)),X_122) = least_upper_bound(multiply(X_123,X_122),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_122),X_122),identity) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(least_upper_bound(X_123,inverse(X_122)),X_122) = least_upper_bound(multiply(X_123,X_122),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_123,inverse(X_122)),X_122),least_upper_bound(multiply(X_123,X_122),multiply(inverse(X_122),X_122))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
least_upper_bound(multiply(X_123,X_122),identity) = least_upper_bound(identity,multiply(X_123,X_122)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_123,X_122)))]]) ).
cnf(refute_0_104,plain,
( multiply(least_upper_bound(X_123,inverse(X_122)),X_122) != least_upper_bound(multiply(X_123,X_122),identity)
| least_upper_bound(multiply(X_123,X_122),identity) != least_upper_bound(identity,multiply(X_123,X_122))
| multiply(least_upper_bound(X_123,inverse(X_122)),X_122) = least_upper_bound(identity,multiply(X_123,X_122)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_123,inverse(X_122)),X_122),least_upper_bound(identity,multiply(X_123,X_122))) ),[0],$fot(least_upper_bound(multiply(X_123,X_122),identity))]]) ).
cnf(refute_0_105,plain,
( multiply(least_upper_bound(X_123,inverse(X_122)),X_122) != least_upper_bound(multiply(X_123,X_122),identity)
| multiply(least_upper_bound(X_123,inverse(X_122)),X_122) = least_upper_bound(identity,multiply(X_123,X_122)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_123,X_122),identity),least_upper_bound(identity,multiply(X_123,X_122))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(least_upper_bound(X_123,inverse(X_122)),X_122) = least_upper_bound(identity,multiply(X_123,X_122)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_123,inverse(X_122)),X_122),least_upper_bound(multiply(X_123,X_122),identity)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
multiply(least_upper_bound(X_128,inverse(X_94)),X_94) = least_upper_bound(identity,multiply(X_128,X_94)),
inference(subst,[],[refute_0_106:[bind(X_122,$fot(X_94)),bind(X_123,$fot(X_128))]]) ).
cnf(refute_0_108,plain,
( X_94 != multiply(inverse(least_upper_bound(X_128,inverse(X_94))),multiply(least_upper_bound(X_128,inverse(X_94)),X_94))
| multiply(least_upper_bound(X_128,inverse(X_94)),X_94) != least_upper_bound(identity,multiply(X_128,X_94))
| X_94 = multiply(inverse(least_upper_bound(X_128,inverse(X_94))),least_upper_bound(identity,multiply(X_128,X_94))) ),
introduced(tautology,[equality,[$cnf( $equal(X_94,multiply(inverse(least_upper_bound(X_128,inverse(X_94))),multiply(least_upper_bound(X_128,inverse(X_94)),X_94))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_128,X_94)))]]) ).
cnf(refute_0_109,plain,
( X_94 != multiply(inverse(least_upper_bound(X_128,inverse(X_94))),multiply(least_upper_bound(X_128,inverse(X_94)),X_94))
| X_94 = multiply(inverse(least_upper_bound(X_128,inverse(X_94))),least_upper_bound(identity,multiply(X_128,X_94))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,inverse(X_94)),X_94),least_upper_bound(identity,multiply(X_128,X_94))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
X_94 = multiply(inverse(least_upper_bound(X_128,inverse(X_94))),least_upper_bound(identity,multiply(X_128,X_94))),
inference(resolve,[$cnf( $equal(X_94,multiply(inverse(least_upper_bound(X_128,inverse(X_94))),multiply(least_upper_bound(X_128,inverse(X_94)),X_94))) )],[refute_0_97,refute_0_109]) ).
cnf(refute_0_111,plain,
greatest_lower_bound(identity,inverse(X_89)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))))),
inference(subst,[],[refute_0_110:[bind(X_128,$fot(greatest_lower_bound(X_89,identity))),bind(X_94,$fot(greatest_lower_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_112,plain,
multiply(X_31,greatest_lower_bound(X_32,identity)) = greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_113,plain,
inverse(multiply(identity,X_26)) = multiply(inverse(X_26),inverse(identity)),
inference(subst,[],[p23_3:[bind(X,$fot(identity)),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_114,plain,
( inverse(multiply(identity,X_26)) != multiply(inverse(X_26),inverse(identity))
| inverse(identity) != identity
| inverse(multiply(identity,X_26)) = multiply(inverse(X_26),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_26)),multiply(inverse(X_26),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_115,plain,
( inverse(multiply(identity,X_26)) != multiply(inverse(X_26),inverse(identity))
| inverse(multiply(identity,X_26)) = multiply(inverse(X_26),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p23_1,refute_0_114]) ).
cnf(refute_0_116,plain,
inverse(multiply(identity,X_26)) = multiply(inverse(X_26),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_26)),multiply(inverse(X_26),inverse(identity))) )],[refute_0_113,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(identity,X_26) = X_26,
inference(subst,[],[left_identity:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_118,plain,
inverse(multiply(identity,X_26)) = inverse(multiply(identity,X_26)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_26)))]]) ).
cnf(refute_0_119,plain,
( multiply(identity,X_26) != X_26
| inverse(multiply(identity,X_26)) != inverse(multiply(identity,X_26))
| inverse(multiply(identity,X_26)) = inverse(X_26) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_26)),inverse(multiply(identity,X_26))) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_120,plain,
( multiply(identity,X_26) != X_26
| inverse(multiply(identity,X_26)) = inverse(X_26) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_26)),inverse(multiply(identity,X_26))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
inverse(multiply(identity,X_26)) = inverse(X_26),
inference(resolve,[$cnf( $equal(multiply(identity,X_26),X_26) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
( inverse(multiply(identity,X_26)) != multiply(inverse(X_26),identity)
| inverse(multiply(identity,X_26)) != inverse(X_26)
| inverse(X_26) = multiply(inverse(X_26),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_26)),multiply(inverse(X_26),identity)) ),[0],$fot(inverse(X_26))]]) ).
cnf(refute_0_123,plain,
( inverse(multiply(identity,X_26)) != multiply(inverse(X_26),identity)
| inverse(X_26) = multiply(inverse(X_26),identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_26)),inverse(X_26)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
inverse(X_26) = multiply(inverse(X_26),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_26)),multiply(inverse(X_26),identity)) )],[refute_0_116,refute_0_123]) ).
cnf(refute_0_125,plain,
inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
inference(subst,[],[refute_0_124:[bind(X_26,$fot(inverse(X)))]]) ).
cnf(refute_0_126,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_127,plain,
( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p23_2,refute_0_126]) ).
cnf(refute_0_128,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_125,refute_0_127]) ).
cnf(refute_0_129,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) ),[0],$fot(X)]]) ).
cnf(refute_0_130,plain,
( inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p23_2,refute_0_129]) ).
cnf(refute_0_131,plain,
X = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_128,refute_0_130]) ).
cnf(refute_0_132,plain,
X_31 = multiply(X_31,identity),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_133,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_134,plain,
multiply(X_31,identity) = X_31,
inference(resolve,[$cnf( $equal(X_31,multiply(X_31,identity)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( multiply(X_31,greatest_lower_bound(X_32,identity)) != greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,identity))
| multiply(X_31,identity) != X_31
| multiply(X_31,greatest_lower_bound(X_32,identity)) = greatest_lower_bound(multiply(X_31,X_32),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,greatest_lower_bound(X_32,identity)),greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,identity))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_136,plain,
( multiply(X_31,greatest_lower_bound(X_32,identity)) != greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,identity))
| multiply(X_31,greatest_lower_bound(X_32,identity)) = greatest_lower_bound(multiply(X_31,X_32),X_31) ),
inference(resolve,[$cnf( $equal(multiply(X_31,identity),X_31) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(X_31,greatest_lower_bound(X_32,identity)) = greatest_lower_bound(multiply(X_31,X_32),X_31),
inference(resolve,[$cnf( $equal(multiply(X_31,greatest_lower_bound(X_32,identity)),greatest_lower_bound(multiply(X_31,X_32),multiply(X_31,identity))) )],[refute_0_112,refute_0_136]) ).
cnf(refute_0_138,plain,
greatest_lower_bound(multiply(X_31,X_32),X_31) = greatest_lower_bound(X_31,multiply(X_31,X_32)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_31)),bind(Y,$fot(multiply(X_31,X_32)))]]) ).
cnf(refute_0_139,plain,
( multiply(X_31,greatest_lower_bound(X_32,identity)) != greatest_lower_bound(multiply(X_31,X_32),X_31)
| greatest_lower_bound(multiply(X_31,X_32),X_31) != greatest_lower_bound(X_31,multiply(X_31,X_32))
| multiply(X_31,greatest_lower_bound(X_32,identity)) = greatest_lower_bound(X_31,multiply(X_31,X_32)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_31,greatest_lower_bound(X_32,identity)),greatest_lower_bound(X_31,multiply(X_31,X_32))) ),[0],$fot(greatest_lower_bound(multiply(X_31,X_32),X_31))]]) ).
cnf(refute_0_140,plain,
( multiply(X_31,greatest_lower_bound(X_32,identity)) != greatest_lower_bound(multiply(X_31,X_32),X_31)
| multiply(X_31,greatest_lower_bound(X_32,identity)) = greatest_lower_bound(X_31,multiply(X_31,X_32)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_31,X_32),X_31),greatest_lower_bound(X_31,multiply(X_31,X_32))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(X_31,greatest_lower_bound(X_32,identity)) = greatest_lower_bound(X_31,multiply(X_31,X_32)),
inference(resolve,[$cnf( $equal(multiply(X_31,greatest_lower_bound(X_32,identity)),greatest_lower_bound(multiply(X_31,X_32),X_31)) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) = greatest_lower_bound(greatest_lower_bound(X_89,identity),multiply(greatest_lower_bound(X_89,identity),inverse(X_89))),
inference(subst,[],[refute_0_141:[bind(X_31,$fot(greatest_lower_bound(X_89,identity))),bind(X_32,$fot(inverse(X_89)))]]) ).
cnf(refute_0_143,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_144,plain,
multiply(identity,X_49) = X_49,
inference(subst,[],[left_identity:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_145,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))
| multiply(identity,X_49) != X_49
| multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))) ),[1,1],$fot(X_49)]]) ).
cnf(refute_0_146,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))
| multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),X_49) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_49),X_49) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(multiply(X_50,X_49),X_49),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(multiply(X_50,X_49),multiply(identity,X_49))) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
greatest_lower_bound(multiply(X_50,X_49),X_49) = greatest_lower_bound(X_49,multiply(X_50,X_49)),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_49)),bind(Y,$fot(multiply(X_50,X_49)))]]) ).
cnf(refute_0_149,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),X_49)
| greatest_lower_bound(multiply(X_50,X_49),X_49) != greatest_lower_bound(X_49,multiply(X_50,X_49))
| multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(X_49,multiply(X_50,X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(X_49,multiply(X_50,X_49))) ),[0],$fot(greatest_lower_bound(multiply(X_50,X_49),X_49))]]) ).
cnf(refute_0_150,plain,
( multiply(greatest_lower_bound(X_50,identity),X_49) != greatest_lower_bound(multiply(X_50,X_49),X_49)
| multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(X_49,multiply(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_50,X_49),X_49),greatest_lower_bound(X_49,multiply(X_50,X_49))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(greatest_lower_bound(X_50,identity),X_49) = greatest_lower_bound(X_49,multiply(X_50,X_49)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),X_49),greatest_lower_bound(multiply(X_50,X_49),X_49)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) = greatest_lower_bound(inverse(X_53),multiply(X_53,inverse(X_53))),
inference(subst,[],[refute_0_151:[bind(X_49,$fot(inverse(X_53))),bind(X_50,$fot(X_53))]]) ).
cnf(refute_0_153,plain,
multiply(X_53,inverse(X_53)) = identity,
inference(subst,[],[refute_0_19:[bind(X_1,$fot(X_53))]]) ).
cnf(refute_0_154,plain,
( multiply(X_53,inverse(X_53)) != identity
| multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) != greatest_lower_bound(inverse(X_53),multiply(X_53,inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) = greatest_lower_bound(inverse(X_53),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),inverse(X_53)),greatest_lower_bound(inverse(X_53),multiply(X_53,inverse(X_53)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_155,plain,
( multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) != greatest_lower_bound(inverse(X_53),multiply(X_53,inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) = greatest_lower_bound(inverse(X_53),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_53,inverse(X_53)),identity) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) = greatest_lower_bound(inverse(X_53),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),inverse(X_53)),greatest_lower_bound(inverse(X_53),multiply(X_53,inverse(X_53)))) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
greatest_lower_bound(inverse(X_53),identity) = greatest_lower_bound(identity,inverse(X_53)),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_53)))]]) ).
cnf(refute_0_158,plain,
( multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) != greatest_lower_bound(inverse(X_53),identity)
| greatest_lower_bound(inverse(X_53),identity) != greatest_lower_bound(identity,inverse(X_53))
| multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) = greatest_lower_bound(identity,inverse(X_53)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_53,identity),inverse(X_53)),greatest_lower_bound(identity,inverse(X_53))) ),[0],$fot(greatest_lower_bound(inverse(X_53),identity))]]) ).
cnf(refute_0_159,plain,
( multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) != greatest_lower_bound(inverse(X_53),identity)
| multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) = greatest_lower_bound(identity,inverse(X_53)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_53),identity),greatest_lower_bound(identity,inverse(X_53))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) = greatest_lower_bound(identity,inverse(X_53)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),inverse(X_53)),greatest_lower_bound(inverse(X_53),identity)) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(greatest_lower_bound(X_89,identity),inverse(X_89)) = greatest_lower_bound(identity,inverse(X_89)),
inference(subst,[],[refute_0_160:[bind(X_53,$fot(X_89))]]) ).
cnf(refute_0_162,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) != greatest_lower_bound(greatest_lower_bound(X_89,identity),multiply(greatest_lower_bound(X_89,identity),inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),inverse(X_89)) != greatest_lower_bound(identity,inverse(X_89))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) = greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)),greatest_lower_bound(greatest_lower_bound(X_89,identity),multiply(greatest_lower_bound(X_89,identity),inverse(X_89)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_89)))]]) ).
cnf(refute_0_163,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) != greatest_lower_bound(greatest_lower_bound(X_89,identity),multiply(greatest_lower_bound(X_89,identity),inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) = greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),inverse(X_89)),greatest_lower_bound(identity,inverse(X_89))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) = greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)),greatest_lower_bound(greatest_lower_bound(X_89,identity),multiply(greatest_lower_bound(X_89,identity),inverse(X_89)))) )],[refute_0_142,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) = greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(greatest_lower_bound(X_66,X_67),inverse(X_66))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(greatest_lower_bound(X_66,X_67))),bind(Z,$fot(inverse(X_66)))]]) ).
cnf(refute_0_166,plain,
multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)) = greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),
inference(subst,[],[refute_0_55:[bind(X_50,$fot(X_66)),bind(X_51,$fot(X_67))]]) ).
cnf(refute_0_167,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) != greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)))
| multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)) != greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) = greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))),greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))))]]) ).
cnf(refute_0_168,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) != greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) = greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) = greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))),greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) = greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(greatest_lower_bound(X_66,X_67))),bind(Y,$fot(inverse(X_66)))]]) ).
cnf(refute_0_171,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) != greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))
| multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)) != greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)),greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))))]]) ).
cnf(refute_0_172,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) != greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) )],[refute_0_166,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)),greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))) )],[refute_0_170,refute_0_172]) ).
cnf(refute_0_174,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_175,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_174]) ).
cnf(refute_0_176,plain,
greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))),
inference(subst,[],[refute_0_175:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_67,inverse(X_66)))),bind(Z,$fot(multiply(greatest_lower_bound(X_66,X_67),Z)))]]) ).
cnf(refute_0_177,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) != greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z))
| greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z)) != greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z)))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)),greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z)))]]) ).
cnf(refute_0_178,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) != greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z)),greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_67,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),Z))) )],[refute_0_173,refute_0_178]) ).
cnf(refute_0_180,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) != greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z)))))]]) ).
cnf(refute_0_181,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Z)),greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Z)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)),
inference(subst,[],[refute_0_181:[bind(Z,$fot(Y))]]) ).
cnf(refute_0_183,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(X_23,Y)))]]) ).
cnf(refute_0_184,plain,
greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(greatest_lower_bound(X_17,X_18))),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_185,plain,
greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_17,X_18),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(greatest_lower_bound(X_17,X_18)))]]) ).
cnf(refute_0_186,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(X_17,X_18)
| greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18)
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)),greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18)) ),[0],$fot(greatest_lower_bound(X_17,X_18))]]) ).
cnf(refute_0_187,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18)
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)),greatest_lower_bound(X_17,X_18)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
greatest_lower_bound(X_17,X_18) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)),greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18)) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_190,plain,
greatest_lower_bound(X_18,X_17) = greatest_lower_bound(X_17,X_18),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_18)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_191,plain,
( greatest_lower_bound(X_18,X_17) != greatest_lower_bound(X_17,X_18)
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_18,X_17))),bind(Y0,$fot(greatest_lower_bound(X_17,X_18)))]]) ).
cnf(refute_0_192,plain,
greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,X_17),greatest_lower_bound(X_17,X_18)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18)
| greatest_lower_bound(X_17,X_18) != greatest_lower_bound(X_18,X_17)
| greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) = greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)),greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18)) ),[0,1],$fot(greatest_lower_bound(X_18,X_17))]]) ).
cnf(refute_0_194,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18)
| greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) = greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_18,X_17)) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) = greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)),greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18)) )],[refute_0_189,refute_0_194]) ).
cnf(refute_0_196,plain,
greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)),
inference(subst,[],[refute_0_175:[bind(X,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_197,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18)
| greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18) != greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18))
| greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18))]]) ).
cnf(refute_0_198,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18)
| greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)),greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_18)) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) != greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18))
| greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)))),bind(Y0,$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18))))]]) ).
cnf(refute_0_201,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_18,X_17)),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_18))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17)) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),
inference(subst,[],[refute_0_201:[bind(X_16,$fot(X_18)),bind(X_17,$fot(greatest_lower_bound(X_17,X_18))),bind(X_18,$fot(X_17))]]) ).
cnf(refute_0_203,plain,
greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(greatest_lower_bound(X_16,X_17),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_16,X_17)))]]) ).
cnf(refute_0_204,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) = greatest_lower_bound(greatest_lower_bound(X_16,X_17),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(X))]]) ).
cnf(refute_0_205,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X)
| greatest_lower_bound(greatest_lower_bound(X_16,X_17),X) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_16,X_17),X)))]]) ).
cnf(refute_0_206,plain,
greatest_lower_bound(greatest_lower_bound(X_16,X_17),X) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)),greatest_lower_bound(greatest_lower_bound(X_16,X_17),X)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X)
| greatest_lower_bound(greatest_lower_bound(X_16,X_17),X) != greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))
| greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_16,X_17),X))]]) ).
cnf(refute_0_208,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X)
| greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_16,X_17),X),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(greatest_lower_bound(X_16,X_17),X)) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))
| greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) = greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)))),bind(Y0,$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))))]]) ).
cnf(refute_0_211,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) = greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17)),
inference(subst,[],[refute_0_211:[bind(X,$fot(X_18)),bind(X_16,$fot(greatest_lower_bound(X_17,X_18)))]]) ).
cnf(refute_0_213,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_214,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_213]) ).
cnf(refute_0_215,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17)) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17))
| greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)))),bind(Y0,$fot(greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17)))),bind(Z0,$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))))]]) ).
cnf(refute_0_216,plain,
( greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17)) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)),greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17))) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17)),greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))) )],[refute_0_202,refute_0_216]) ).
cnf(refute_0_218,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) = greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)),
inference(subst,[],[refute_0_175:[bind(X,$fot(greatest_lower_bound(X_17,X_18))),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_219,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) != greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18))
| greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)))),bind(Z0,$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))))]]) ).
cnf(refute_0_220,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18),greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_17,X_18)),greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
( greatest_lower_bound(X_17,X_18) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18)
| greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18))]]) ).
cnf(refute_0_223,plain,
( greatest_lower_bound(X_17,X_18) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18)
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18),greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_18),greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_17,X_18),X_17),X_18)) )],[refute_0_188,refute_0_223]) ).
cnf(refute_0_225,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(greatest_lower_bound(X_17,X_17),X_18),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_17)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_226,plain,
greatest_lower_bound(X_17,X_17) = X_17,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_227,plain,
( greatest_lower_bound(X_17,X_17) != X_17
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(greatest_lower_bound(X_17,X_17),X_18)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_17,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)),greatest_lower_bound(greatest_lower_bound(X_17,X_17),X_18)) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_228,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(greatest_lower_bound(X_17,X_17),X_18)
| greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_17,X_18) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_17),X_17) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_17,X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)),greatest_lower_bound(greatest_lower_bound(X_17,X_17),X_18)) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))))]]) ).
cnf(refute_0_231,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(X_17,X_18)
| greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))) ),[1,1],$fot(greatest_lower_bound(X_17,X_18))]]) ).
cnf(refute_0_232,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)) != greatest_lower_bound(X_17,X_18)
| greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)),greatest_lower_bound(X_17,X_18)) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
( greatest_lower_bound(X_17,X_18) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18))
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18))) ),[0],$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))))]]) ).
cnf(refute_0_235,plain,
( greatest_lower_bound(X_17,X_18) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18))),greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_18,greatest_lower_bound(X_17,greatest_lower_bound(X_17,X_18)))) )],[refute_0_224,refute_0_235]) ).
cnf(refute_0_237,plain,
greatest_lower_bound(X_23,Y) = greatest_lower_bound(Y,greatest_lower_bound(X_23,Y)),
inference(subst,[],[refute_0_236:[bind(X_17,$fot(X_23)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_238,plain,
( greatest_lower_bound(X_23,Y) != greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))
| greatest_lower_bound(Y,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X_23,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_23,Y))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))))]]) ).
cnf(refute_0_239,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X_23,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,Y),greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y))
| greatest_lower_bound(Y,greatest_lower_bound(X_23,Y)) != greatest_lower_bound(X_23,Y)
| greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y))) ),[0,1],$fot(greatest_lower_bound(X_23,Y))]]) ).
cnf(refute_0_241,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y))
| greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_23,Y)),greatest_lower_bound(X_23,Y)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_23,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y))) )],[refute_0_183,refute_0_241]) ).
cnf(refute_0_243,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_23,X)),Z),
inference(subst,[],[associativity_of_glb:[bind(Y,$fot(greatest_lower_bound(X_23,X)))]]) ).
cnf(refute_0_244,plain,
greatest_lower_bound(X_23,X) = greatest_lower_bound(X,greatest_lower_bound(X_23,X)),
inference(subst,[],[refute_0_236:[bind(X_17,$fot(X_23)),bind(X_18,$fot(X))]]) ).
cnf(refute_0_245,plain,
( greatest_lower_bound(X_23,X) != greatest_lower_bound(X,greatest_lower_bound(X_23,X))
| greatest_lower_bound(X,greatest_lower_bound(X_23,X)) = greatest_lower_bound(X_23,X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_23,X))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_23,X))))]]) ).
cnf(refute_0_246,plain,
greatest_lower_bound(X,greatest_lower_bound(X_23,X)) = greatest_lower_bound(X_23,X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,X),greatest_lower_bound(X,greatest_lower_bound(X_23,X))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_23,X)) != greatest_lower_bound(X_23,X)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_23,X)),Z)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(greatest_lower_bound(X_23,X),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_23,X)),Z)) ),[1,0],$fot(greatest_lower_bound(X_23,X))]]) ).
cnf(refute_0_248,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_23,X)),Z)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(greatest_lower_bound(X_23,X),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_23,X)),greatest_lower_bound(X_23,X)) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(greatest_lower_bound(X_23,X),Z),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_23,X)),Z)) )],[refute_0_243,refute_0_248]) ).
cnf(refute_0_250,plain,
greatest_lower_bound(greatest_lower_bound(X_23,X),Z) = greatest_lower_bound(X_23,greatest_lower_bound(X,Z)),
inference(subst,[],[refute_0_175:[bind(X,$fot(X_23)),bind(Y,$fot(X))]]) ).
cnf(refute_0_251,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)))]]) ).
cnf(refute_0_252,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) != greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z))
| greatest_lower_bound(greatest_lower_bound(X_23,X),Z) != greatest_lower_bound(X_23,greatest_lower_bound(X,Z))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z))) ),[1,1],$fot(greatest_lower_bound(X_23,greatest_lower_bound(X,Z)))]]) ).
cnf(refute_0_253,plain,
( greatest_lower_bound(greatest_lower_bound(X_23,X),Z) != greatest_lower_bound(X_23,greatest_lower_bound(X,Z))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_23,X),Z),greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) != greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z)))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) != greatest_lower_bound(greatest_lower_bound(X_23,X),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) = greatest_lower_bound(greatest_lower_bound(X_23,X),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) ),[0],$fot(greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))))]]) ).
cnf(refute_0_256,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) != greatest_lower_bound(greatest_lower_bound(X_23,X),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) = greatest_lower_bound(greatest_lower_bound(X_23,X),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z)))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) != greatest_lower_bound(greatest_lower_bound(X_23,X),Z)
| greatest_lower_bound(greatest_lower_bound(X_23,X),Z) != greatest_lower_bound(X_23,greatest_lower_bound(X,Z))
| greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) = greatest_lower_bound(X_23,greatest_lower_bound(X,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))),greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_23,X),Z))]]) ).
cnf(refute_0_258,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) != greatest_lower_bound(greatest_lower_bound(X_23,X),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) = greatest_lower_bound(X_23,greatest_lower_bound(X,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_23,X),Z),greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) )],[refute_0_250,refute_0_257]) ).
cnf(refute_0_259,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) != greatest_lower_bound(greatest_lower_bound(X_23,X),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) = greatest_lower_bound(X_23,greatest_lower_bound(X,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))),greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) )],[refute_0_256,refute_0_258]) ).
cnf(refute_0_260,plain,
greatest_lower_bound(X,greatest_lower_bound(X_23,greatest_lower_bound(X,Z))) = greatest_lower_bound(X_23,greatest_lower_bound(X,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_23,X),Z)),greatest_lower_bound(greatest_lower_bound(X_23,X),Z)) )],[refute_0_249,refute_0_259]) ).
cnf(refute_0_261,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)),
inference(subst,[],[refute_0_260:[bind(X,$fot(Y)),bind(Z,$fot(X_23)),bind(X_23,$fot(X))]]) ).
cnf(refute_0_262,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_23) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)),
inference(subst,[],[refute_0_175:[bind(Z,$fot(X_23))]]) ).
cnf(refute_0_263,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)))]]) ).
cnf(refute_0_264,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_23) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23))) ),[1,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_23)))]]) ).
cnf(refute_0_265,plain,
( greatest_lower_bound(greatest_lower_bound(X,Y),X_23) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_23),greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) )],[refute_0_262,refute_0_265]) ).
cnf(refute_0_267,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) != greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23)))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))))),bind(Z0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_23))))]]) ).
cnf(refute_0_268,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)),greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23)))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_23))),greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) )],[refute_0_261,refute_0_268]) ).
cnf(refute_0_270,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)),
inference(subst,[],[refute_0_211:[bind(X,$fot(Y)),bind(X_16,$fot(greatest_lower_bound(X,Y))),bind(X_17,$fot(X_23))]]) ).
cnf(refute_0_271,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)))),bind(Z0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_23))))]]) ).
cnf(refute_0_272,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_23)),greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) )],[refute_0_269,refute_0_272]) ).
cnf(refute_0_274,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_23,Y)),greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)))]]) ).
cnf(refute_0_275,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y))
| greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y)),greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_23)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_23,Y)),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_23,Y))) )],[refute_0_242,refute_0_275]) ).
cnf(refute_0_277,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) != greatest_lower_bound(X,greatest_lower_bound(Y,X_23))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X,greatest_lower_bound(X_23,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_23,Y)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_23))))]]) ).
cnf(refute_0_278,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X,greatest_lower_bound(X_23,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_23,Y)),greatest_lower_bound(X,greatest_lower_bound(Y,X_23))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y))),
inference(subst,[],[refute_0_278:[bind(X,$fot(identity)),bind(Y,$fot(multiply(greatest_lower_bound(X_66,X_67),Y))),bind(X_23,$fot(multiply(X_67,inverse(X_66))))]]) ).
cnf(refute_0_280,plain,
( greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y))) != multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))))]]) ).
cnf(refute_0_281,plain,
( greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y))) != multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))),greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y)))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_67,inverse(X_66)),multiply(greatest_lower_bound(X_66,X_67),Y))),multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))) )],[refute_0_182,refute_0_281]) ).
cnf(refute_0_283,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) = greatest_lower_bound(X_16,greatest_lower_bound(X,X_17)),
inference(subst,[],[refute_0_199:[bind(X_17,$fot(X)),bind(X_18,$fot(X_17))]]) ).
cnf(refute_0_284,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))
| greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)) != greatest_lower_bound(X_16,greatest_lower_bound(X,X_17))
| greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X,X_17)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_16,greatest_lower_bound(X,X_17))) ),[0],$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)))]]) ).
cnf(refute_0_285,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))
| greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X,X_17)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X)),greatest_lower_bound(X_16,greatest_lower_bound(X,X_17))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) = greatest_lower_bound(X_16,greatest_lower_bound(X,X_17)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X))) )],[refute_0_209,refute_0_285]) ).
cnf(refute_0_287,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) != greatest_lower_bound(X_16,greatest_lower_bound(X,X_17))
| greatest_lower_bound(X_16,greatest_lower_bound(X,X_17)) = greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)))),bind(Y0,$fot(greatest_lower_bound(X_16,greatest_lower_bound(X,X_17))))]]) ).
cnf(refute_0_288,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X,X_17)) = greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_16,X_17)),greatest_lower_bound(X_16,greatest_lower_bound(X,X_17))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))),
inference(subst,[],[refute_0_288:[bind(X,$fot(identity)),bind(X_16,$fot(multiply(greatest_lower_bound(X_66,X_67),Y))),bind(X_17,$fot(multiply(X_67,inverse(X_66))))]]) ).
cnf(refute_0_290,plain,
( greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66))))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))) != multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))
| greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))))]]) ).
cnf(refute_0_291,plain,
( greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))) != multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))
| greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))),greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66))))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),multiply(X_67,inverse(X_66)))),multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))) )],[refute_0_282,refute_0_291]) ).
cnf(refute_0_293,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) != greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66))))
| greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))) != multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))) ),[0],$fot(greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))))]]) ).
cnf(refute_0_294,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) != greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66))))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66)))),multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))),greatest_lower_bound(multiply(greatest_lower_bound(X_66,X_67),Y),greatest_lower_bound(identity,multiply(X_67,inverse(X_66))))) )],[refute_0_169,refute_0_294]) ).
cnf(refute_0_296,plain,
( multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) != multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))
| multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))))]]) ).
cnf(refute_0_297,plain,
multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y)) = multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(Y,inverse(X_66))),multiply(greatest_lower_bound(X_66,X_67),greatest_lower_bound(inverse(X_66),Y))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) = multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))),
inference(subst,[],[refute_0_297:[bind(Y,$fot(identity)),bind(X_66,$fot(X_89)),bind(X_67,$fot(identity))]]) ).
cnf(refute_0_299,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) != multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) != greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)),greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))) ),[0],$fot(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_300,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) != greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)),multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))),
inference(subst,[],[refute_0_260:[bind(X,$fot(identity)),bind(Z,$fot(inverse(X_89))),bind(X_23,$fot(X_89))]]) ).
cnf(refute_0_302,plain,
greatest_lower_bound(X_61,greatest_lower_bound(greatest_lower_bound(X,Y),X_62)) = greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y))),
inference(subst,[],[refute_0_199:[bind(X_16,$fot(X_61)),bind(X_17,$fot(X_62)),bind(X_18,$fot(greatest_lower_bound(X,Y)))]]) ).
cnf(refute_0_303,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_62)) = greatest_lower_bound(greatest_lower_bound(X,Y),X_62),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(X_62))]]) ).
cnf(refute_0_304,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_62)) != greatest_lower_bound(greatest_lower_bound(X,Y),X_62)
| greatest_lower_bound(greatest_lower_bound(X,Y),X_62) = greatest_lower_bound(X,greatest_lower_bound(Y,X_62)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_62)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),X_62)))]]) ).
cnf(refute_0_305,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_62) = greatest_lower_bound(X,greatest_lower_bound(Y,X_62)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_62)),greatest_lower_bound(greatest_lower_bound(X,Y),X_62)) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
( greatest_lower_bound(X_61,greatest_lower_bound(greatest_lower_bound(X,Y),X_62)) != greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y)))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_62) != greatest_lower_bound(X,greatest_lower_bound(Y,X_62))
| greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))) = greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_61,greatest_lower_bound(greatest_lower_bound(X,Y),X_62)),greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y)))) ),[0,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_62)))]]) ).
cnf(refute_0_307,plain,
( greatest_lower_bound(X_61,greatest_lower_bound(greatest_lower_bound(X,Y),X_62)) != greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y)))
| greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))) = greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_62),greatest_lower_bound(X,greatest_lower_bound(Y,X_62))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))) = greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_61,greatest_lower_bound(greatest_lower_bound(X,Y),X_62)),greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y)))) )],[refute_0_302,refute_0_307]) ).
cnf(refute_0_309,plain,
( greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))) != greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y)))
| greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y))) = greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))))),bind(Y0,$fot(greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y)))))]]) ).
cnf(refute_0_310,plain,
greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y))) = greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_61,greatest_lower_bound(X,greatest_lower_bound(Y,X_62))),greatest_lower_bound(X_61,greatest_lower_bound(X_62,greatest_lower_bound(X,Y)))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))) = greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))),
inference(subst,[],[refute_0_310:[bind(X,$fot(X_89)),bind(Y,$fot(identity)),bind(X_61,$fot(identity)),bind(X_62,$fot(inverse(X_89)))]]) ).
cnf(refute_0_312,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))) != greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))),bind(Z0,$fot(greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))]]) ).
cnf(refute_0_313,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))),greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))),greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_301,refute_0_313]) ).
cnf(refute_0_315,plain,
greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))),
inference(subst,[],[refute_0_278:[bind(X,$fot(identity)),bind(Y,$fot(greatest_lower_bound(X_89,identity))),bind(X_23,$fot(inverse(X_89)))]]) ).
cnf(refute_0_316,plain,
( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))))),bind(Z0,$fot(greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))]]) ).
cnf(refute_0_317,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity)))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),greatest_lower_bound(X_89,identity))),greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_314,refute_0_317]) ).
cnf(refute_0_319,plain,
greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))),
inference(subst,[],[refute_0_288:[bind(X,$fot(identity)),bind(X_16,$fot(greatest_lower_bound(X_89,identity))),bind(X_17,$fot(inverse(X_89)))]]) ).
cnf(refute_0_320,plain,
( greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89)))
| greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))))),bind(Z0,$fot(greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))]]) ).
cnf(refute_0_321,plain,
( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89)))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_89,identity),inverse(X_89))),greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) != greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))),greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_324,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) != greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))),greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)) != greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))
| multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))),greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_300,refute_0_324]) ).
cnf(refute_0_326,plain,
multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(inverse(X_89),identity)),greatest_lower_bound(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_164,refute_0_325]) ).
cnf(refute_0_327,plain,
( multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))) != greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(identity,inverse(X_89)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))))
| greatest_lower_bound(identity,inverse(X_89)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_89)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))))) ),[1,1,1],$fot(greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_328,plain,
( greatest_lower_bound(identity,inverse(X_89)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))))
| greatest_lower_bound(identity,inverse(X_89)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89))),greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
greatest_lower_bound(identity,inverse(X_89)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_89)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_89,identity),greatest_lower_bound(identity,inverse(X_89)))))) )],[refute_0_111,refute_0_328]) ).
cnf(refute_0_330,plain,
( X != multiply(X,identity)
| multiply(X,identity) = X ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).
cnf(refute_0_331,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_131,refute_0_330]) ).
cnf(refute_0_332,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),
inference(subst,[],[refute_0_331:[bind(X,$fot(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))))]]) ).
cnf(refute_0_333,plain,
least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))) = X,
inference(subst,[],[lub_absorbtion:[bind(Y,$fot(greatest_lower_bound(X_60,X_58)))]]) ).
cnf(refute_0_334,plain,
greatest_lower_bound(X_58,greatest_lower_bound(X,X_60)) = greatest_lower_bound(X,greatest_lower_bound(X_60,X_58)),
inference(subst,[],[refute_0_209:[bind(X,$fot(X_58)),bind(X_16,$fot(X)),bind(X_17,$fot(X_60))]]) ).
cnf(refute_0_335,plain,
( greatest_lower_bound(X_58,greatest_lower_bound(X,X_60)) != greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))
| greatest_lower_bound(X,greatest_lower_bound(X_60,X_58)) = greatest_lower_bound(X_58,greatest_lower_bound(X,X_60)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_58,greatest_lower_bound(X,X_60)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))))]]) ).
cnf(refute_0_336,plain,
greatest_lower_bound(X,greatest_lower_bound(X_60,X_58)) = greatest_lower_bound(X_58,greatest_lower_bound(X,X_60)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_58,greatest_lower_bound(X,X_60)),greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_60,X_58)) != greatest_lower_bound(X_58,greatest_lower_bound(X,X_60))
| least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))) != X
| least_upper_bound(X,greatest_lower_bound(X_58,greatest_lower_bound(X,X_60))) = X ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))),X) ),[0,1],$fot(greatest_lower_bound(X_58,greatest_lower_bound(X,X_60)))]]) ).
cnf(refute_0_338,plain,
( least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))) != X
| least_upper_bound(X,greatest_lower_bound(X_58,greatest_lower_bound(X,X_60))) = X ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_60,X_58)),greatest_lower_bound(X_58,greatest_lower_bound(X,X_60))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
least_upper_bound(X,greatest_lower_bound(X_58,greatest_lower_bound(X,X_60))) = X,
inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_60,X_58))),X) )],[refute_0_333,refute_0_338]) ).
cnf(refute_0_340,plain,
least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) = identity,
inference(subst,[],[refute_0_339:[bind(X,$fot(identity)),bind(X_58,$fot(X_89)),bind(X_60,$fot(inverse(X_89)))]]) ).
cnf(refute_0_341,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))))]]) ).
cnf(refute_0_342,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))
| least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) != identity
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_343,plain,
( least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))) != identity
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))),identity) )],[refute_0_340,refute_0_343]) ).
cnf(refute_0_345,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity) != inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity)
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity))),bind(Z0,$fot(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))))]]) ).
cnf(refute_0_346,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity) != inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity)) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),identity),inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))) )],[refute_0_332,refute_0_346]) ).
cnf(refute_0_348,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))) != inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))
| greatest_lower_bound(identity,inverse(X_89)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))
| greatest_lower_bound(identity,inverse(X_89)) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_89)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))) ),[1],$fot(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))))]]) ).
cnf(refute_0_349,plain,
( greatest_lower_bound(identity,inverse(X_89)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))
| greatest_lower_bound(identity,inverse(X_89)) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89))))),inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
greatest_lower_bound(identity,inverse(X_89)) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_89)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_89,greatest_lower_bound(identity,inverse(X_89)))))) )],[refute_0_329,refute_0_349]) ).
cnf(refute_0_351,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_352,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_353,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_354,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_356,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_351,refute_0_356]) ).
cnf(refute_0_358,plain,
least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)) = X_10,
inference(subst,[],[refute_0_357:[bind(X_11,$fot(greatest_lower_bound(X_16,X_17)))]]) ).
cnf(refute_0_359,plain,
greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10)) = greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_360,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10)) != greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)
| greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)))]]) ).
cnf(refute_0_361,plain,
greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10) = greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10)),greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
( greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10) != greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10))
| least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)),X_10) ),[0,1],$fot(greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10)))]]) ).
cnf(refute_0_363,plain,
( least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10))) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10),greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
least_upper_bound(X_10,greatest_lower_bound(X_16,greatest_lower_bound(X_17,X_10))) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_16,X_17),X_10)),X_10) )],[refute_0_358,refute_0_363]) ).
cnf(refute_0_365,plain,
least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,greatest_lower_bound(X_83,least_upper_bound(X_83,Y)))) = least_upper_bound(X_83,Y),
inference(subst,[],[refute_0_364:[bind(X_10,$fot(least_upper_bound(X_83,Y))),bind(X_16,$fot(X_82)),bind(X_17,$fot(X_83))]]) ).
cnf(refute_0_366,plain,
greatest_lower_bound(X_83,least_upper_bound(X_83,Y)) = X_83,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_367,plain,
( greatest_lower_bound(X_83,least_upper_bound(X_83,Y)) != X_83
| least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,greatest_lower_bound(X_83,least_upper_bound(X_83,Y)))) != least_upper_bound(X_83,Y)
| least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)) = least_upper_bound(X_83,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,greatest_lower_bound(X_83,least_upper_bound(X_83,Y)))),least_upper_bound(X_83,Y)) ),[0,1,1],$fot(X_83)]]) ).
cnf(refute_0_368,plain,
( least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,greatest_lower_bound(X_83,least_upper_bound(X_83,Y)))) != least_upper_bound(X_83,Y)
| least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)) = least_upper_bound(X_83,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_83,least_upper_bound(X_83,Y)),X_83) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)) = least_upper_bound(X_83,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,greatest_lower_bound(X_83,least_upper_bound(X_83,Y)))),least_upper_bound(X_83,Y)) )],[refute_0_365,refute_0_368]) ).
cnf(refute_0_370,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_371,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_370]) ).
cnf(refute_0_372,plain,
least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)) = least_upper_bound(X_83,least_upper_bound(Y,greatest_lower_bound(X_82,X_83))),
inference(subst,[],[refute_0_371:[bind(X,$fot(X_83)),bind(Z,$fot(greatest_lower_bound(X_82,X_83)))]]) ).
cnf(refute_0_373,plain,
( least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)) != least_upper_bound(X_83,Y)
| least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)) != least_upper_bound(X_83,least_upper_bound(Y,greatest_lower_bound(X_82,X_83)))
| least_upper_bound(X_83,least_upper_bound(Y,greatest_lower_bound(X_82,X_83))) = least_upper_bound(X_83,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)),least_upper_bound(X_83,Y)) ),[0],$fot(least_upper_bound(X_83,least_upper_bound(Y,greatest_lower_bound(X_82,X_83))))]]) ).
cnf(refute_0_374,plain,
( least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)) != least_upper_bound(X_83,Y)
| least_upper_bound(X_83,least_upper_bound(Y,greatest_lower_bound(X_82,X_83))) = least_upper_bound(X_83,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)),least_upper_bound(X_83,least_upper_bound(Y,greatest_lower_bound(X_82,X_83)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
least_upper_bound(X_83,least_upper_bound(Y,greatest_lower_bound(X_82,X_83))) = least_upper_bound(X_83,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_83,Y),greatest_lower_bound(X_82,X_83)),least_upper_bound(X_83,Y)) )],[refute_0_369,refute_0_374]) ).
cnf(refute_0_376,plain,
least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity))) = least_upper_bound(identity,X_89),
inference(subst,[],[refute_0_375:[bind(Y,$fot(X_89)),bind(X_82,$fot(X_89)),bind(X_83,$fot(identity))]]) ).
cnf(refute_0_377,plain,
least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) = least_upper_bound(X_11,X_15),
inference(subst,[],[refute_0_357:[bind(X_10,$fot(least_upper_bound(X_11,X_15)))]]) ).
cnf(refute_0_378,plain,
greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)) = X_11,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_11)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_379,plain,
( greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)) != X_11
| least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) != least_upper_bound(X_11,X_15)
| least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))),least_upper_bound(X_11,X_15)) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_380,plain,
( least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) != least_upper_bound(X_11,X_15)
| least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)),X_11) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))),least_upper_bound(X_11,X_15)) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,least_upper_bound(X_15,X_11)),
inference(subst,[],[refute_0_371:[bind(X,$fot(X_11)),bind(Y,$fot(X_15)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_383,plain,
( least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,X_15)
| least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,least_upper_bound(X_15,X_11))
| least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,X_15)) ),[0],$fot(least_upper_bound(X_11,least_upper_bound(X_15,X_11)))]]) ).
cnf(refute_0_384,plain,
( least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,X_15)
| least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,least_upper_bound(X_15,X_11))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,X_15)) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_108,X_109),X_11)) = least_upper_bound(X_11,least_upper_bound(X_108,X_109)),
inference(subst,[],[refute_0_385:[bind(X_15,$fot(least_upper_bound(X_108,X_109)))]]) ).
cnf(refute_0_387,plain,
least_upper_bound(X_108,least_upper_bound(X_109,X_11)) = least_upper_bound(least_upper_bound(X_108,X_109),X_11),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_388,plain,
( least_upper_bound(X_108,least_upper_bound(X_109,X_11)) != least_upper_bound(least_upper_bound(X_108,X_109),X_11)
| least_upper_bound(least_upper_bound(X_108,X_109),X_11) = least_upper_bound(X_108,least_upper_bound(X_109,X_11)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_108,least_upper_bound(X_109,X_11)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_108,X_109),X_11)))]]) ).
cnf(refute_0_389,plain,
least_upper_bound(least_upper_bound(X_108,X_109),X_11) = least_upper_bound(X_108,least_upper_bound(X_109,X_11)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(X_109,X_11)),least_upper_bound(least_upper_bound(X_108,X_109),X_11)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
( least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_108,X_109),X_11)) != least_upper_bound(X_11,least_upper_bound(X_108,X_109))
| least_upper_bound(least_upper_bound(X_108,X_109),X_11) != least_upper_bound(X_108,least_upper_bound(X_109,X_11))
| least_upper_bound(X_11,least_upper_bound(X_108,least_upper_bound(X_109,X_11))) = least_upper_bound(X_11,least_upper_bound(X_108,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_108,X_109),X_11)),least_upper_bound(X_11,least_upper_bound(X_108,X_109))) ),[0,1],$fot(least_upper_bound(X_108,least_upper_bound(X_109,X_11)))]]) ).
cnf(refute_0_391,plain,
( least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_108,X_109),X_11)) != least_upper_bound(X_11,least_upper_bound(X_108,X_109))
| least_upper_bound(X_11,least_upper_bound(X_108,least_upper_bound(X_109,X_11))) = least_upper_bound(X_11,least_upper_bound(X_108,X_109)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_108,X_109),X_11),least_upper_bound(X_108,least_upper_bound(X_109,X_11))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
least_upper_bound(X_11,least_upper_bound(X_108,least_upper_bound(X_109,X_11))) = least_upper_bound(X_11,least_upper_bound(X_108,X_109)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_108,X_109),X_11)),least_upper_bound(X_11,least_upper_bound(X_108,X_109))) )],[refute_0_386,refute_0_391]) ).
cnf(refute_0_393,plain,
least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) = least_upper_bound(X_328,least_upper_bound(X_326,X_327)),
inference(subst,[],[refute_0_392:[bind(X_108,$fot(X_326)),bind(X_109,$fot(X_327)),bind(X_11,$fot(X_328))]]) ).
cnf(refute_0_394,plain,
least_upper_bound(X_327,X_326) = least_upper_bound(X_326,X_327),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_327)),bind(Y,$fot(X_326))]]) ).
cnf(refute_0_395,plain,
( least_upper_bound(X_327,X_326) != least_upper_bound(X_326,X_327)
| least_upper_bound(X_326,X_327) = least_upper_bound(X_327,X_326) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_327,X_326))),bind(Y0,$fot(least_upper_bound(X_326,X_327)))]]) ).
cnf(refute_0_396,plain,
least_upper_bound(X_326,X_327) = least_upper_bound(X_327,X_326),
inference(resolve,[$cnf( $equal(least_upper_bound(X_327,X_326),least_upper_bound(X_326,X_327)) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
( least_upper_bound(X_326,X_327) != least_upper_bound(X_327,X_326)
| least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) != least_upper_bound(X_328,least_upper_bound(X_326,X_327))
| least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) = least_upper_bound(X_328,least_upper_bound(X_327,X_326)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))),least_upper_bound(X_328,least_upper_bound(X_326,X_327))) ),[1,1],$fot(least_upper_bound(X_327,X_326))]]) ).
cnf(refute_0_398,plain,
( least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) != least_upper_bound(X_328,least_upper_bound(X_326,X_327))
| least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) = least_upper_bound(X_328,least_upper_bound(X_327,X_326)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_326,X_327),least_upper_bound(X_327,X_326)) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) = least_upper_bound(X_328,least_upper_bound(X_327,X_326)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))),least_upper_bound(X_328,least_upper_bound(X_326,X_327))) )],[refute_0_393,refute_0_398]) ).
cnf(refute_0_400,plain,
( least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) != least_upper_bound(X_328,least_upper_bound(X_326,X_327))
| least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) != least_upper_bound(X_328,least_upper_bound(X_327,X_326))
| least_upper_bound(X_328,least_upper_bound(X_326,X_327)) = least_upper_bound(X_328,least_upper_bound(X_327,X_326)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))),least_upper_bound(X_328,least_upper_bound(X_327,X_326))) ),[0],$fot(least_upper_bound(X_328,least_upper_bound(X_326,X_327)))]]) ).
cnf(refute_0_401,plain,
( least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))) != least_upper_bound(X_328,least_upper_bound(X_327,X_326))
| least_upper_bound(X_328,least_upper_bound(X_326,X_327)) = least_upper_bound(X_328,least_upper_bound(X_327,X_326)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))),least_upper_bound(X_328,least_upper_bound(X_326,X_327))) )],[refute_0_393,refute_0_400]) ).
cnf(refute_0_402,plain,
least_upper_bound(X_328,least_upper_bound(X_326,X_327)) = least_upper_bound(X_328,least_upper_bound(X_327,X_326)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_328,least_upper_bound(X_326,least_upper_bound(X_327,X_328))),least_upper_bound(X_328,least_upper_bound(X_327,X_326))) )],[refute_0_399,refute_0_401]) ).
cnf(refute_0_403,plain,
( least_upper_bound(X_328,least_upper_bound(X_326,X_327)) != least_upper_bound(X_328,least_upper_bound(X_327,X_326))
| least_upper_bound(X_328,least_upper_bound(X_327,X_326)) = least_upper_bound(X_328,least_upper_bound(X_326,X_327)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_328,least_upper_bound(X_326,X_327)))),bind(Y0,$fot(least_upper_bound(X_328,least_upper_bound(X_327,X_326))))]]) ).
cnf(refute_0_404,plain,
least_upper_bound(X_328,least_upper_bound(X_327,X_326)) = least_upper_bound(X_328,least_upper_bound(X_326,X_327)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_328,least_upper_bound(X_326,X_327)),least_upper_bound(X_328,least_upper_bound(X_327,X_326))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)) = least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity))),
inference(subst,[],[refute_0_404:[bind(X_326,$fot(X_89)),bind(X_327,$fot(greatest_lower_bound(X_89,identity))),bind(X_328,$fot(identity))]]) ).
cnf(refute_0_406,plain,
( least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity))) != least_upper_bound(identity,X_89)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)) != least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)) = least_upper_bound(identity,X_89) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity))))),bind(Z0,$fot(least_upper_bound(identity,X_89)))]]) ).
cnf(refute_0_407,plain,
( least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity))) != least_upper_bound(identity,X_89)
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)) = least_upper_bound(identity,X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)),least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity)))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)) = least_upper_bound(identity,X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_89,greatest_lower_bound(X_89,identity))),least_upper_bound(identity,X_89)) )],[refute_0_376,refute_0_407]) ).
cnf(refute_0_409,plain,
least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)) = least_upper_bound(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),X_110),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_108)),bind(Y,$fot(greatest_lower_bound(X_11,X_108))),bind(Z,$fot(X_110))]]) ).
cnf(refute_0_410,plain,
least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)) = X_108,
inference(subst,[],[refute_0_357:[bind(X_10,$fot(X_108))]]) ).
cnf(refute_0_411,plain,
( least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)) != X_108
| least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)) != least_upper_bound(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),X_110)
| least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)) = least_upper_bound(X_108,X_110) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)),least_upper_bound(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),X_110)) ),[1,0],$fot(X_108)]]) ).
cnf(refute_0_412,plain,
( least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)) != least_upper_bound(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),X_110)
| least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)) = least_upper_bound(X_108,X_110) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),X_108) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)) = least_upper_bound(X_108,X_110),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(greatest_lower_bound(X_11,X_108),X_110)),least_upper_bound(least_upper_bound(X_108,greatest_lower_bound(X_11,X_108)),X_110)) )],[refute_0_409,refute_0_412]) ).
cnf(refute_0_414,plain,
least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)),X_351)) = least_upper_bound(least_upper_bound(X_22,X_15),X_351),
inference(subst,[],[refute_0_413:[bind(X_108,$fot(least_upper_bound(X_22,X_15))),bind(X_11,$fot(least_upper_bound(X_15,X_22))),bind(X_110,$fot(X_351))]]) ).
cnf(refute_0_415,plain,
greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)) = X_14,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_416,plain,
least_upper_bound(X_15,X_14) = least_upper_bound(X_14,X_15),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_417,plain,
( least_upper_bound(X_15,X_14) != least_upper_bound(X_14,X_15)
| least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_15,X_14))),bind(Y0,$fot(least_upper_bound(X_14,X_15)))]]) ).
cnf(refute_0_418,plain,
least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_14),least_upper_bound(X_14,X_15)) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
( greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)) != X_14
| least_upper_bound(X_14,X_15) != least_upper_bound(X_15,X_14)
| greatest_lower_bound(X_14,least_upper_bound(X_15,X_14)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)),X_14) ),[0,1],$fot(least_upper_bound(X_15,X_14))]]) ).
cnf(refute_0_420,plain,
( greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)) != X_14
| greatest_lower_bound(X_14,least_upper_bound(X_15,X_14)) = X_14 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_14,X_15),least_upper_bound(X_15,X_14)) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
greatest_lower_bound(X_14,least_upper_bound(X_15,X_14)) = X_14,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)),X_14) )],[refute_0_415,refute_0_420]) ).
cnf(refute_0_422,plain,
greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,least_upper_bound(X_15,X_22))) = least_upper_bound(X_15,X_22),
inference(subst,[],[refute_0_421:[bind(X_14,$fot(least_upper_bound(X_15,X_22))),bind(X_15,$fot(X_22))]]) ).
cnf(refute_0_423,plain,
least_upper_bound(X_22,least_upper_bound(X_15,X_22)) = least_upper_bound(X_22,X_15),
inference(subst,[],[refute_0_385:[bind(X_11,$fot(X_22))]]) ).
cnf(refute_0_424,plain,
( greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,least_upper_bound(X_15,X_22))) != least_upper_bound(X_15,X_22)
| least_upper_bound(X_22,least_upper_bound(X_15,X_22)) != least_upper_bound(X_22,X_15)
| greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)) = least_upper_bound(X_15,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,least_upper_bound(X_15,X_22))),least_upper_bound(X_15,X_22)) ),[0,1],$fot(least_upper_bound(X_22,X_15))]]) ).
cnf(refute_0_425,plain,
( greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,least_upper_bound(X_15,X_22))) != least_upper_bound(X_15,X_22)
| greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)) = least_upper_bound(X_15,X_22) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_15,X_22)),least_upper_bound(X_22,X_15)) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)) = least_upper_bound(X_15,X_22),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,least_upper_bound(X_15,X_22))),least_upper_bound(X_15,X_22)) )],[refute_0_422,refute_0_425]) ).
cnf(refute_0_427,plain,
( greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)) != least_upper_bound(X_15,X_22)
| least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)),X_351)) != least_upper_bound(least_upper_bound(X_22,X_15),X_351)
| least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(least_upper_bound(X_22,X_15),X_351) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)),X_351)),least_upper_bound(least_upper_bound(X_22,X_15),X_351)) ),[0,1,0],$fot(least_upper_bound(X_15,X_22))]]) ).
cnf(refute_0_428,plain,
( least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)),X_351)) != least_upper_bound(least_upper_bound(X_22,X_15),X_351)
| least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(least_upper_bound(X_22,X_15),X_351) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)),least_upper_bound(X_15,X_22)) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(least_upper_bound(X_22,X_15),X_351),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(greatest_lower_bound(least_upper_bound(X_15,X_22),least_upper_bound(X_22,X_15)),X_351)),least_upper_bound(least_upper_bound(X_22,X_15),X_351)) )],[refute_0_414,refute_0_428]) ).
cnf(refute_0_430,plain,
least_upper_bound(X_108,least_upper_bound(X_109,least_upper_bound(X_15,X_109))) = least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(least_upper_bound(X_15,X_109)))]]) ).
cnf(refute_0_431,plain,
least_upper_bound(X_109,least_upper_bound(X_15,X_109)) = least_upper_bound(X_109,X_15),
inference(subst,[],[refute_0_385:[bind(X_11,$fot(X_109))]]) ).
cnf(refute_0_432,plain,
( least_upper_bound(X_108,least_upper_bound(X_109,least_upper_bound(X_15,X_109))) != least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109))
| least_upper_bound(X_109,least_upper_bound(X_15,X_109)) != least_upper_bound(X_109,X_15)
| least_upper_bound(X_108,least_upper_bound(X_109,X_15)) = least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(X_109,least_upper_bound(X_15,X_109))),least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109))) ),[0,1],$fot(least_upper_bound(X_109,X_15))]]) ).
cnf(refute_0_433,plain,
( least_upper_bound(X_108,least_upper_bound(X_109,least_upper_bound(X_15,X_109))) != least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109))
| least_upper_bound(X_108,least_upper_bound(X_109,X_15)) = least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(X_15,X_109)),least_upper_bound(X_109,X_15)) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
least_upper_bound(X_108,least_upper_bound(X_109,X_15)) = least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(X_109,least_upper_bound(X_15,X_109))),least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109))) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
least_upper_bound(least_upper_bound(X_108,X_109),X_15) = least_upper_bound(X_108,least_upper_bound(X_109,X_15)),
inference(subst,[],[refute_0_371:[bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_436,plain,
least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)) = least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)))]]) ).
cnf(refute_0_437,plain,
( least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)) != least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15))
| least_upper_bound(least_upper_bound(X_108,X_109),X_15) != least_upper_bound(X_108,least_upper_bound(X_109,X_15))
| least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)),least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15))) ),[1,1],$fot(least_upper_bound(X_108,least_upper_bound(X_109,X_15)))]]) ).
cnf(refute_0_438,plain,
( least_upper_bound(least_upper_bound(X_108,X_109),X_15) != least_upper_bound(X_108,least_upper_bound(X_109,X_15))
| least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)),least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_108,X_109),X_15),least_upper_bound(X_108,least_upper_bound(X_109,X_15))) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
least_upper_bound(X,least_upper_bound(X_108,X_109)) = least_upper_bound(least_upper_bound(X_108,X_109),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_108,X_109)))]]) ).
cnf(refute_0_441,plain,
least_upper_bound(X_108,least_upper_bound(X_109,X)) = least_upper_bound(least_upper_bound(X_108,X_109),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(X))]]) ).
cnf(refute_0_442,plain,
( least_upper_bound(X_108,least_upper_bound(X_109,X)) != least_upper_bound(least_upper_bound(X_108,X_109),X)
| least_upper_bound(least_upper_bound(X_108,X_109),X) = least_upper_bound(X_108,least_upper_bound(X_109,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_108,least_upper_bound(X_109,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_108,X_109),X)))]]) ).
cnf(refute_0_443,plain,
least_upper_bound(least_upper_bound(X_108,X_109),X) = least_upper_bound(X_108,least_upper_bound(X_109,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(X_109,X)),least_upper_bound(least_upper_bound(X_108,X_109),X)) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
( least_upper_bound(X,least_upper_bound(X_108,X_109)) != least_upper_bound(least_upper_bound(X_108,X_109),X)
| least_upper_bound(least_upper_bound(X_108,X_109),X) != least_upper_bound(X_108,least_upper_bound(X_109,X))
| least_upper_bound(X,least_upper_bound(X_108,X_109)) = least_upper_bound(X_108,least_upper_bound(X_109,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_108,X_109)),least_upper_bound(X_108,least_upper_bound(X_109,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_108,X_109),X))]]) ).
cnf(refute_0_445,plain,
( least_upper_bound(X,least_upper_bound(X_108,X_109)) != least_upper_bound(least_upper_bound(X_108,X_109),X)
| least_upper_bound(X,least_upper_bound(X_108,X_109)) = least_upper_bound(X_108,least_upper_bound(X_109,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_108,X_109),X),least_upper_bound(X_108,least_upper_bound(X_109,X))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
least_upper_bound(X,least_upper_bound(X_108,X_109)) = least_upper_bound(X_108,least_upper_bound(X_109,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_108,X_109)),least_upper_bound(least_upper_bound(X_108,X_109),X)) )],[refute_0_440,refute_0_445]) ).
cnf(refute_0_447,plain,
( least_upper_bound(X,least_upper_bound(X_108,X_109)) != least_upper_bound(X_108,least_upper_bound(X_109,X))
| least_upper_bound(X_108,least_upper_bound(X_109,X)) = least_upper_bound(X,least_upper_bound(X_108,X_109)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_108,X_109)))),bind(Y0,$fot(least_upper_bound(X_108,least_upper_bound(X_109,X))))]]) ).
cnf(refute_0_448,plain,
least_upper_bound(X_108,least_upper_bound(X_109,X)) = least_upper_bound(X,least_upper_bound(X_108,X_109)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_108,X_109)),least_upper_bound(X_108,least_upper_bound(X_109,X))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) = least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_109)),bind(X_108,$fot(least_upper_bound(X_108,X_109))),bind(X_109,$fot(X_15))]]) ).
cnf(refute_0_450,plain,
( least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)) != least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))
| least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) != least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15))
| least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)))),bind(Y0,$fot(least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)))),bind(Z0,$fot(least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))))]]) ).
cnf(refute_0_451,plain,
( least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)) != least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))
| least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)),least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_109,least_upper_bound(least_upper_bound(X_108,X_109),X_15)),least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))) )],[refute_0_439,refute_0_451]) ).
cnf(refute_0_453,plain,
( least_upper_bound(X_108,least_upper_bound(X_109,X_15)) != least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109))
| least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)) != least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))
| least_upper_bound(X_108,least_upper_bound(X_109,X_15)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_108,least_upper_bound(X_109,X_15)),least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)))]]) ).
cnf(refute_0_454,plain,
( least_upper_bound(X_108,least_upper_bound(X_109,X_15)) != least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109))
| least_upper_bound(X_108,least_upper_bound(X_109,X_15)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109)),least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
least_upper_bound(X_108,least_upper_bound(X_109,X_15)) = least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(X_109,X_15)),least_upper_bound(least_upper_bound(X_108,X_109),least_upper_bound(X_15,X_109))) )],[refute_0_434,refute_0_454]) ).
cnf(refute_0_456,plain,
( least_upper_bound(X_108,least_upper_bound(X_109,X_15)) != least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))
| least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) = least_upper_bound(X_108,least_upper_bound(X_109,X_15)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_108,least_upper_bound(X_109,X_15)))),bind(Y0,$fot(least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))))]]) ).
cnf(refute_0_457,plain,
least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15))) = least_upper_bound(X_108,least_upper_bound(X_109,X_15)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_108,least_upper_bound(X_109,X_15)),least_upper_bound(X_109,least_upper_bound(X_108,least_upper_bound(X_109,X_15)))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)),
inference(subst,[],[refute_0_457:[bind(X_108,$fot(X_15)),bind(X_109,$fot(X_22)),bind(X_15,$fot(X_351))]]) ).
cnf(refute_0_459,plain,
least_upper_bound(X_19,least_upper_bound(X_20,X_19)) = least_upper_bound(X_19,X_20),
inference(subst,[],[refute_0_385:[bind(X_11,$fot(X_19)),bind(X_15,$fot(X_20))]]) ).
cnf(refute_0_460,plain,
least_upper_bound(X_19,X_20) = least_upper_bound(X_20,X_19),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_19)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_461,plain,
( least_upper_bound(X_19,X_20) != least_upper_bound(X_20,X_19)
| least_upper_bound(X_20,X_19) = least_upper_bound(X_19,X_20) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_19,X_20))),bind(Y0,$fot(least_upper_bound(X_20,X_19)))]]) ).
cnf(refute_0_462,plain,
least_upper_bound(X_20,X_19) = least_upper_bound(X_19,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,X_20),least_upper_bound(X_20,X_19)) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
( least_upper_bound(X_19,least_upper_bound(X_20,X_19)) != least_upper_bound(X_19,X_20)
| least_upper_bound(X_20,X_19) != least_upper_bound(X_19,X_20)
| least_upper_bound(X_19,least_upper_bound(X_19,X_20)) = least_upper_bound(X_19,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_20,X_19)),least_upper_bound(X_19,X_20)) ),[0,1],$fot(least_upper_bound(X_19,X_20))]]) ).
cnf(refute_0_464,plain,
( least_upper_bound(X_19,least_upper_bound(X_20,X_19)) != least_upper_bound(X_19,X_20)
| least_upper_bound(X_19,least_upper_bound(X_19,X_20)) = least_upper_bound(X_19,X_20) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_20,X_19),least_upper_bound(X_19,X_20)) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
least_upper_bound(X_19,least_upper_bound(X_19,X_20)) = least_upper_bound(X_19,X_20),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_20,X_19)),least_upper_bound(X_19,X_20)) )],[refute_0_459,refute_0_464]) ).
cnf(refute_0_466,plain,
least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)),
inference(subst,[],[refute_0_465:[bind(X_19,$fot(X_15)),bind(X_20,$fot(least_upper_bound(X_22,X_351)))]]) ).
cnf(refute_0_467,plain,
least_upper_bound(least_upper_bound(X_15,X_22),X_351) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)),
inference(subst,[],[refute_0_371:[bind(X,$fot(X_15)),bind(Y,$fot(X_22)),bind(Z,$fot(X_351))]]) ).
cnf(refute_0_468,plain,
least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)))]]) ).
cnf(refute_0_469,plain,
( least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))
| least_upper_bound(least_upper_bound(X_15,X_22),X_351) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) ),[1,1],$fot(least_upper_bound(X_15,least_upper_bound(X_22,X_351)))]]) ).
cnf(refute_0_470,plain,
( least_upper_bound(least_upper_bound(X_15,X_22),X_351) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_22),X_351),least_upper_bound(X_15,least_upper_bound(X_22,X_351))) )],[refute_0_467,refute_0_470]) ).
cnf(refute_0_472,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351)))
| least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)))),bind(Y0,$fot(least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))))),bind(Z0,$fot(least_upper_bound(X_15,least_upper_bound(X_22,X_351))))]]) ).
cnf(refute_0_473,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351)))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_22,X_351))),least_upper_bound(X_15,least_upper_bound(X_22,X_351))) )],[refute_0_466,refute_0_473]) ).
cnf(refute_0_475,plain,
least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) = least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))))]]) ).
cnf(refute_0_476,plain,
( least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) != least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)))
| least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) = least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))),least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)))) ),[1,1],$fot(least_upper_bound(X_15,least_upper_bound(X_22,X_351)))]]) ).
cnf(refute_0_477,plain,
( least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) = least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))),least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) = least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(X_15,least_upper_bound(X_22,X_351))) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
( least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) != least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351)))
| least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))))),bind(Z0,$fot(least_upper_bound(X_15,least_upper_bound(X_22,X_351))))]]) ).
cnf(refute_0_480,plain,
( least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))),least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351)))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(X_22,X_351))),least_upper_bound(X_15,least_upper_bound(X_22,X_351))) )],[refute_0_458,refute_0_480]) ).
cnf(refute_0_482,plain,
least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))),
inference(subst,[],[refute_0_371:[bind(X,$fot(X_22)),bind(Y,$fot(X_15)),bind(Z,$fot(least_upper_bound(least_upper_bound(X_15,X_22),X_351)))]]) ).
cnf(refute_0_483,plain,
( least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)))
| least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))))),bind(Z0,$fot(least_upper_bound(X_15,least_upper_bound(X_22,X_351))))]]) ).
cnf(refute_0_484,plain,
( least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351)))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_15,least_upper_bound(least_upper_bound(X_15,X_22),X_351))),least_upper_bound(X_15,least_upper_bound(X_22,X_351))) )],[refute_0_481,refute_0_484]) ).
cnf(refute_0_486,plain,
( least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(X_15,least_upper_bound(X_22,X_351))
| least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(least_upper_bound(X_22,X_15),X_351)
| least_upper_bound(X_15,least_upper_bound(X_22,X_351)) = least_upper_bound(least_upper_bound(X_22,X_15),X_351) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(least_upper_bound(X_22,X_15),X_351)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(X_22,X_351)))]]) ).
cnf(refute_0_487,plain,
( least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(least_upper_bound(X_22,X_15),X_351)
| least_upper_bound(X_15,least_upper_bound(X_22,X_351)) = least_upper_bound(least_upper_bound(X_22,X_15),X_351) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(X_15,least_upper_bound(X_22,X_351))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
least_upper_bound(least_upper_bound(X_22,X_15),X_351) = least_upper_bound(X_22,least_upper_bound(X_15,X_351)),
inference(subst,[],[refute_0_371:[bind(X,$fot(X_22)),bind(Y,$fot(X_15)),bind(Z,$fot(X_351))]]) ).
cnf(refute_0_489,plain,
( least_upper_bound(X_15,least_upper_bound(X_22,X_351)) != least_upper_bound(least_upper_bound(X_22,X_15),X_351)
| least_upper_bound(least_upper_bound(X_22,X_15),X_351) != least_upper_bound(X_22,least_upper_bound(X_15,X_351))
| least_upper_bound(X_15,least_upper_bound(X_22,X_351)) = least_upper_bound(X_22,least_upper_bound(X_15,X_351)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_15,least_upper_bound(X_22,X_351)),least_upper_bound(X_22,least_upper_bound(X_15,X_351))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,X_15),X_351))]]) ).
cnf(refute_0_490,plain,
( least_upper_bound(X_15,least_upper_bound(X_22,X_351)) != least_upper_bound(least_upper_bound(X_22,X_15),X_351)
| least_upper_bound(X_15,least_upper_bound(X_22,X_351)) = least_upper_bound(X_22,least_upper_bound(X_15,X_351)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_15),X_351),least_upper_bound(X_22,least_upper_bound(X_15,X_351))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
( least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)) != least_upper_bound(least_upper_bound(X_22,X_15),X_351)
| least_upper_bound(X_15,least_upper_bound(X_22,X_351)) = least_upper_bound(X_22,least_upper_bound(X_15,X_351)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_22,X_351)),least_upper_bound(least_upper_bound(X_22,X_15),X_351)) )],[refute_0_487,refute_0_490]) ).
cnf(refute_0_492,plain,
least_upper_bound(X_15,least_upper_bound(X_22,X_351)) = least_upper_bound(X_22,least_upper_bound(X_15,X_351)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_15),least_upper_bound(least_upper_bound(X_15,X_22),X_351)),least_upper_bound(least_upper_bound(X_22,X_15),X_351)) )],[refute_0_429,refute_0_491]) ).
cnf(refute_0_493,plain,
( least_upper_bound(X_15,least_upper_bound(X_22,X_351)) != least_upper_bound(X_22,least_upper_bound(X_15,X_351))
| least_upper_bound(X_22,least_upper_bound(X_15,X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_15,least_upper_bound(X_22,X_351)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_15,X_351))))]]) ).
cnf(refute_0_494,plain,
least_upper_bound(X_22,least_upper_bound(X_15,X_351)) = least_upper_bound(X_15,least_upper_bound(X_22,X_351)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_22,X_351)),least_upper_bound(X_22,least_upper_bound(X_15,X_351))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)),
inference(subst,[],[refute_0_494:[bind(X_15,$fot(identity)),bind(X_22,$fot(greatest_lower_bound(X_89,identity))),bind(X_351,$fot(X_89))]]) ).
cnf(refute_0_496,plain,
( least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)) != least_upper_bound(identity,X_89)
| least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) = least_upper_bound(identity,X_89) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)))),bind(Z0,$fot(least_upper_bound(identity,X_89)))]]) ).
cnf(refute_0_497,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)) != least_upper_bound(identity,X_89)
| least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) = least_upper_bound(identity,X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) = least_upper_bound(identity,X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_89,identity),X_89)),least_upper_bound(identity,X_89)) )],[refute_0_408,refute_0_497]) ).
cnf(refute_0_499,plain,
inverse(greatest_lower_bound(identity,inverse(X_35))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))))),
inference(subst,[],[refute_0_110:[bind(X_128,$fot(greatest_lower_bound(X_35,identity))),bind(X_94,$fot(inverse(greatest_lower_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_500,plain,
inverse(X) = multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X))),
inference(subst,[],[refute_0_96:[bind(X_93,$fot(inverse(Y))),bind(X_94,$fot(inverse(X)))]]) ).
cnf(refute_0_501,plain,
( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
| multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).
cnf(refute_0_502,plain,
multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p23_3,refute_0_501]) ).
cnf(refute_0_503,plain,
( multiply(inverse(Y),inverse(X)) != inverse(multiply(X,Y))
| inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,Y)))]]) ).
cnf(refute_0_504,plain,
( inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),inverse(X)),inverse(multiply(X,Y))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) )],[refute_0_500,refute_0_504]) ).
cnf(refute_0_506,plain,
inverse(multiply(multiply(X,Y),inverse(Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(subst,[],[refute_0_65:[bind(X,$fot(Y)),bind(X_25,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_507,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = inverse(multiply(multiply(X,Y),inverse(Y))),
inference(subst,[],[refute_0_502:[bind(X,$fot(multiply(X,Y))),bind(Y,$fot(inverse(Y)))]]) ).
cnf(refute_0_508,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != inverse(multiply(multiply(X,Y),inverse(Y)))
| inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))))),bind(Y0,$fot(inverse(multiply(multiply(X,Y),inverse(Y))))),bind(Z0,$fot(multiply(Y,inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_509,plain,
( inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),inverse(multiply(multiply(X,Y),inverse(Y)))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X,Y),inverse(Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_506,refute_0_509]) ).
cnf(refute_0_511,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != multiply(Y,inverse(multiply(X,Y)))
| inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) ),[1],$fot(multiply(Y,inverse(multiply(X,Y))))]]) ).
cnf(refute_0_512,plain,
( inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
inverse(X) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) )],[refute_0_505,refute_0_512]) ).
cnf(refute_0_514,plain,
inverse(inverse(X_35)) = multiply(greatest_lower_bound(X_35,identity),inverse(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)))),
inference(subst,[],[refute_0_513:[bind(X,$fot(inverse(X_35))),bind(Y,$fot(greatest_lower_bound(X_35,identity)))]]) ).
cnf(refute_0_515,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(inverse(X_35),multiply(inverse(X_35),X_35)),
inference(subst,[],[refute_0_141:[bind(X_31,$fot(inverse(X_35))),bind(X_32,$fot(X_35))]]) ).
cnf(refute_0_516,plain,
multiply(inverse(X_35),X_35) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_517,plain,
( multiply(inverse(X_35),X_35) != identity
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(inverse(X_35),multiply(inverse(X_35),X_35))
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(inverse(X_35),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),greatest_lower_bound(inverse(X_35),multiply(inverse(X_35),X_35))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_518,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(inverse(X_35),multiply(inverse(X_35),X_35))
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(inverse(X_35),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),X_35),identity) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(inverse(X_35),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),greatest_lower_bound(inverse(X_35),multiply(inverse(X_35),X_35))) )],[refute_0_515,refute_0_518]) ).
cnf(refute_0_520,plain,
greatest_lower_bound(inverse(X_35),identity) = greatest_lower_bound(identity,inverse(X_35)),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_35)))]]) ).
cnf(refute_0_521,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(inverse(X_35),identity)
| greatest_lower_bound(inverse(X_35),identity) != greatest_lower_bound(identity,inverse(X_35))
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(identity,inverse(X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),greatest_lower_bound(identity,inverse(X_35))) ),[0],$fot(greatest_lower_bound(inverse(X_35),identity))]]) ).
cnf(refute_0_522,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(inverse(X_35),identity)
| multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(identity,inverse(X_35)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_35),identity),greatest_lower_bound(identity,inverse(X_35))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) = greatest_lower_bound(identity,inverse(X_35)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),greatest_lower_bound(inverse(X_35),identity)) )],[refute_0_519,refute_0_522]) ).
cnf(refute_0_524,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(identity,inverse(X_35))
| inverse(inverse(X_35)) != multiply(greatest_lower_bound(X_35,identity),inverse(multiply(inverse(X_35),greatest_lower_bound(X_35,identity))))
| inverse(inverse(X_35)) = multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_35)),multiply(greatest_lower_bound(X_35,identity),inverse(multiply(inverse(X_35),greatest_lower_bound(X_35,identity))))) ),[1,1,0],$fot(greatest_lower_bound(identity,inverse(X_35)))]]) ).
cnf(refute_0_525,plain,
( inverse(inverse(X_35)) != multiply(greatest_lower_bound(X_35,identity),inverse(multiply(inverse(X_35),greatest_lower_bound(X_35,identity))))
| inverse(inverse(X_35)) = multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),greatest_lower_bound(identity,inverse(X_35))) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
inverse(inverse(X_35)) = multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),multiply(greatest_lower_bound(X_35,identity),inverse(multiply(inverse(X_35),greatest_lower_bound(X_35,identity))))) )],[refute_0_514,refute_0_525]) ).
cnf(refute_0_527,plain,
inverse(inverse(X_35)) = X_35,
inference(subst,[],[p23_2:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_528,plain,
( inverse(inverse(X_35)) != X_35
| inverse(inverse(X_35)) != multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))
| X_35 = multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_35)),multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))) ),[0],$fot(X_35)]]) ).
cnf(refute_0_529,plain,
( inverse(inverse(X_35)) != multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))
| X_35 = multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),X_35) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
X_35 = multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))) )],[refute_0_526,refute_0_529]) ).
cnf(refute_0_531,plain,
( X_35 != multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))
| multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))) = X_35 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_35)),bind(Y0,$fot(multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))))]]) ).
cnf(refute_0_532,plain,
multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))) = X_35,
inference(resolve,[$cnf( $equal(X_35,multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
( multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))) != X_35
| inverse(greatest_lower_bound(identity,inverse(X_35))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))))
| inverse(greatest_lower_bound(identity,inverse(X_35))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_35))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))))) ),[1,1,1],$fot(X_35)]]) ).
cnf(refute_0_534,plain,
( inverse(greatest_lower_bound(identity,inverse(X_35))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))))
| inverse(greatest_lower_bound(identity,inverse(X_35))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35)))),X_35) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
inverse(greatest_lower_bound(identity,inverse(X_35))) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_35))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,multiply(greatest_lower_bound(X_35,identity),inverse(greatest_lower_bound(identity,inverse(X_35))))))) )],[refute_0_499,refute_0_534]) ).
cnf(refute_0_536,plain,
multiply(least_upper_bound(X_123,identity),X_122) = least_upper_bound(multiply(X_123,X_122),multiply(identity,X_122)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_122)),bind(Y,$fot(X_123)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_537,plain,
multiply(identity,X_122) = X_122,
inference(subst,[],[left_identity:[bind(X,$fot(X_122))]]) ).
cnf(refute_0_538,plain,
( multiply(identity,X_122) != X_122
| multiply(least_upper_bound(X_123,identity),X_122) != least_upper_bound(multiply(X_123,X_122),multiply(identity,X_122))
| multiply(least_upper_bound(X_123,identity),X_122) = least_upper_bound(multiply(X_123,X_122),X_122) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_123,identity),X_122),least_upper_bound(multiply(X_123,X_122),multiply(identity,X_122))) ),[1,1],$fot(X_122)]]) ).
cnf(refute_0_539,plain,
( multiply(least_upper_bound(X_123,identity),X_122) != least_upper_bound(multiply(X_123,X_122),multiply(identity,X_122))
| multiply(least_upper_bound(X_123,identity),X_122) = least_upper_bound(multiply(X_123,X_122),X_122) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_122),X_122) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
multiply(least_upper_bound(X_123,identity),X_122) = least_upper_bound(multiply(X_123,X_122),X_122),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_123,identity),X_122),least_upper_bound(multiply(X_123,X_122),multiply(identity,X_122))) )],[refute_0_536,refute_0_539]) ).
cnf(refute_0_541,plain,
least_upper_bound(multiply(X_123,X_122),X_122) = least_upper_bound(X_122,multiply(X_123,X_122)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_122)),bind(Y,$fot(multiply(X_123,X_122)))]]) ).
cnf(refute_0_542,plain,
( multiply(least_upper_bound(X_123,identity),X_122) != least_upper_bound(multiply(X_123,X_122),X_122)
| least_upper_bound(multiply(X_123,X_122),X_122) != least_upper_bound(X_122,multiply(X_123,X_122))
| multiply(least_upper_bound(X_123,identity),X_122) = least_upper_bound(X_122,multiply(X_123,X_122)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_123,identity),X_122),least_upper_bound(X_122,multiply(X_123,X_122))) ),[0],$fot(least_upper_bound(multiply(X_123,X_122),X_122))]]) ).
cnf(refute_0_543,plain,
( multiply(least_upper_bound(X_123,identity),X_122) != least_upper_bound(multiply(X_123,X_122),X_122)
| multiply(least_upper_bound(X_123,identity),X_122) = least_upper_bound(X_122,multiply(X_123,X_122)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_123,X_122),X_122),least_upper_bound(X_122,multiply(X_123,X_122))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
multiply(least_upper_bound(X_123,identity),X_122) = least_upper_bound(X_122,multiply(X_123,X_122)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_123,identity),X_122),least_upper_bound(multiply(X_123,X_122),X_122)) )],[refute_0_540,refute_0_543]) ).
cnf(refute_0_545,plain,
multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) = least_upper_bound(greatest_lower_bound(X_35,identity),multiply(inverse(X_35),greatest_lower_bound(X_35,identity))),
inference(subst,[],[refute_0_544:[bind(X_122,$fot(greatest_lower_bound(X_35,identity))),bind(X_123,$fot(inverse(X_35)))]]) ).
cnf(refute_0_546,plain,
( multiply(inverse(X_35),greatest_lower_bound(X_35,identity)) != greatest_lower_bound(identity,inverse(X_35))
| multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) != least_upper_bound(greatest_lower_bound(X_35,identity),multiply(inverse(X_35),greatest_lower_bound(X_35,identity)))
| multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)),least_upper_bound(greatest_lower_bound(X_35,identity),multiply(inverse(X_35),greatest_lower_bound(X_35,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_35)))]]) ).
cnf(refute_0_547,plain,
( multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) != least_upper_bound(greatest_lower_bound(X_35,identity),multiply(inverse(X_35),greatest_lower_bound(X_35,identity)))
| multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),greatest_lower_bound(X_35,identity)),greatest_lower_bound(identity,inverse(X_35))) )],[refute_0_523,refute_0_546]) ).
cnf(refute_0_548,plain,
multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)),least_upper_bound(greatest_lower_bound(X_35,identity),multiply(inverse(X_35),greatest_lower_bound(X_35,identity)))) )],[refute_0_545,refute_0_547]) ).
cnf(refute_0_549,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_126,X_19))) = least_upper_bound(X_19,multiply(X_126,X_19)),
inference(subst,[],[refute_0_465:[bind(X_20,$fot(multiply(X_126,X_19)))]]) ).
cnf(refute_0_550,plain,
multiply(least_upper_bound(X_126,identity),X_19) = least_upper_bound(X_19,multiply(X_126,X_19)),
inference(subst,[],[refute_0_544:[bind(X_122,$fot(X_19)),bind(X_123,$fot(X_126))]]) ).
cnf(refute_0_551,plain,
( multiply(least_upper_bound(X_126,identity),X_19) != least_upper_bound(X_19,multiply(X_126,X_19))
| least_upper_bound(X_19,multiply(X_126,X_19)) = multiply(least_upper_bound(X_126,identity),X_19) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_126,identity),X_19))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_126,X_19))))]]) ).
cnf(refute_0_552,plain,
least_upper_bound(X_19,multiply(X_126,X_19)) = multiply(least_upper_bound(X_126,identity),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_126,identity),X_19),least_upper_bound(X_19,multiply(X_126,X_19))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
( least_upper_bound(X_19,multiply(X_126,X_19)) != multiply(least_upper_bound(X_126,identity),X_19)
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_126,X_19))) != least_upper_bound(X_19,multiply(X_126,X_19))
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = least_upper_bound(X_19,multiply(X_126,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_126,X_19))),least_upper_bound(X_19,multiply(X_126,X_19))) ),[0,1],$fot(multiply(least_upper_bound(X_126,identity),X_19))]]) ).
cnf(refute_0_554,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_126,X_19))) != least_upper_bound(X_19,multiply(X_126,X_19))
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = least_upper_bound(X_19,multiply(X_126,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_126,X_19)),multiply(least_upper_bound(X_126,identity),X_19)) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = least_upper_bound(X_19,multiply(X_126,X_19)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_126,X_19))),least_upper_bound(X_19,multiply(X_126,X_19))) )],[refute_0_549,refute_0_554]) ).
cnf(refute_0_556,plain,
least_upper_bound(identity,least_upper_bound(X_126,identity)) = least_upper_bound(identity,X_126),
inference(subst,[],[refute_0_385:[bind(X_11,$fot(identity)),bind(X_15,$fot(X_126))]]) ).
cnf(refute_0_557,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19))]]) ).
cnf(refute_0_558,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)
| least_upper_bound(identity,least_upper_bound(X_126,identity)) != least_upper_bound(identity,X_126)
| multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) = multiply(least_upper_bound(identity,X_126),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)) ),[1,0],$fot(least_upper_bound(identity,X_126))]]) ).
cnf(refute_0_559,plain,
( least_upper_bound(identity,least_upper_bound(X_126,identity)) != least_upper_bound(identity,X_126)
| multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) = multiply(least_upper_bound(identity,X_126),X_19) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) = multiply(least_upper_bound(identity,X_126),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_126,identity)),least_upper_bound(identity,X_126)) )],[refute_0_556,refute_0_559]) ).
cnf(refute_0_561,plain,
least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) = least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_124,X_122))),bind(Y,$fot(multiply(X_123,X_122)))]]) ).
cnf(refute_0_562,plain,
multiply(least_upper_bound(X_123,X_124),X_122) = least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_122)),bind(Y,$fot(X_123)),bind(Z,$fot(X_124))]]) ).
cnf(refute_0_563,plain,
( multiply(least_upper_bound(X_123,X_124),X_122) != least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122))
| least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122)) = multiply(least_upper_bound(X_123,X_124),X_122) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_123,X_124),X_122))),bind(Y0,$fot(least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122))))]]) ).
cnf(refute_0_564,plain,
least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122)) = multiply(least_upper_bound(X_123,X_124),X_122),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_123,X_124),X_122),least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
( least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122)) != multiply(least_upper_bound(X_123,X_124),X_122)
| least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) != least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122))
| least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) = multiply(least_upper_bound(X_123,X_124),X_122) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)),least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122))) ),[1],$fot(multiply(least_upper_bound(X_123,X_124),X_122))]]) ).
cnf(refute_0_566,plain,
( least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) != least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122))
| least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) = multiply(least_upper_bound(X_123,X_124),X_122) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122)),multiply(least_upper_bound(X_123,X_124),X_122)) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) = multiply(least_upper_bound(X_123,X_124),X_122),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)),least_upper_bound(multiply(X_123,X_122),multiply(X_124,X_122))) )],[refute_0_561,refute_0_566]) ).
cnf(refute_0_568,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_569,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_568]) ).
cnf(refute_0_570,plain,
least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) = multiply(least_upper_bound(X_124,X_123),X_122),
inference(subst,[],[refute_0_569:[bind(X,$fot(X_122)),bind(Y,$fot(X_124)),bind(Z,$fot(X_123))]]) ).
cnf(refute_0_571,plain,
( least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) != multiply(least_upper_bound(X_123,X_124),X_122)
| least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) != multiply(least_upper_bound(X_124,X_123),X_122)
| multiply(least_upper_bound(X_124,X_123),X_122) = multiply(least_upper_bound(X_123,X_124),X_122) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)),multiply(least_upper_bound(X_123,X_124),X_122)) ),[0],$fot(multiply(least_upper_bound(X_124,X_123),X_122))]]) ).
cnf(refute_0_572,plain,
( least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)) != multiply(least_upper_bound(X_123,X_124),X_122)
| multiply(least_upper_bound(X_124,X_123),X_122) = multiply(least_upper_bound(X_123,X_124),X_122) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)),multiply(least_upper_bound(X_124,X_123),X_122)) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
multiply(least_upper_bound(X_124,X_123),X_122) = multiply(least_upper_bound(X_123,X_124),X_122),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_124,X_122),multiply(X_123,X_122)),multiply(least_upper_bound(X_123,X_124),X_122)) )],[refute_0_567,refute_0_572]) ).
cnf(refute_0_574,plain,
( multiply(least_upper_bound(X_124,X_123),X_122) != multiply(least_upper_bound(X_123,X_124),X_122)
| multiply(least_upper_bound(X_123,X_124),X_122) = multiply(least_upper_bound(X_124,X_123),X_122) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_124,X_123),X_122))),bind(Y0,$fot(multiply(least_upper_bound(X_123,X_124),X_122)))]]) ).
cnf(refute_0_575,plain,
multiply(least_upper_bound(X_123,X_124),X_122) = multiply(least_upper_bound(X_124,X_123),X_122),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_124,X_123),X_122),multiply(least_upper_bound(X_123,X_124),X_122)) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19),
inference(subst,[],[refute_0_575:[bind(X_122,$fot(X_19)),bind(X_123,$fot(least_upper_bound(X_126,identity))),bind(X_124,$fot(identity))]]) ).
cnf(refute_0_577,plain,
( multiply(least_upper_bound(X_123,identity),X_122) != least_upper_bound(X_122,multiply(X_123,X_122))
| least_upper_bound(X_122,multiply(X_123,X_122)) = multiply(least_upper_bound(X_123,identity),X_122) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_123,identity),X_122))),bind(Y0,$fot(least_upper_bound(X_122,multiply(X_123,X_122))))]]) ).
cnf(refute_0_578,plain,
least_upper_bound(X_122,multiply(X_123,X_122)) = multiply(least_upper_bound(X_123,identity),X_122),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_123,identity),X_122),least_upper_bound(X_122,multiply(X_123,X_122))) )],[refute_0_544,refute_0_577]) ).
cnf(refute_0_579,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19),
inference(subst,[],[refute_0_578:[bind(X_122,$fot(X_19)),bind(X_123,$fot(least_upper_bound(X_126,identity)))]]) ).
cnf(refute_0_580,plain,
( multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) != multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)))]]) ).
cnf(refute_0_581,plain,
( multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)),multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19)) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_126,identity),identity),X_19),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)) )],[refute_0_576,refute_0_581]) ).
cnf(refute_0_583,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) != multiply(least_upper_bound(identity,X_126),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) != multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = multiply(least_upper_bound(identity,X_126),X_19) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_126),X_19)))]]) ).
cnf(refute_0_584,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19) != multiply(least_upper_bound(identity,X_126),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = multiply(least_upper_bound(identity,X_126),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)),multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19)) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) = multiply(least_upper_bound(identity,X_126),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_126,identity)),X_19),multiply(least_upper_bound(identity,X_126),X_19)) )],[refute_0_560,refute_0_584]) ).
cnf(refute_0_586,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) != multiply(least_upper_bound(identity,X_126),X_19)
| least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) != least_upper_bound(X_19,multiply(X_126,X_19))
| multiply(least_upper_bound(identity,X_126),X_19) = least_upper_bound(X_19,multiply(X_126,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)),least_upper_bound(X_19,multiply(X_126,X_19))) ),[0],$fot(multiply(least_upper_bound(identity,X_126),X_19))]]) ).
cnf(refute_0_587,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) != least_upper_bound(X_19,multiply(X_126,X_19))
| multiply(least_upper_bound(identity,X_126),X_19) = least_upper_bound(X_19,multiply(X_126,X_19)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)),multiply(least_upper_bound(identity,X_126),X_19)) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
( multiply(least_upper_bound(identity,X_126),X_19) != least_upper_bound(X_19,multiply(X_126,X_19))
| least_upper_bound(X_19,multiply(X_126,X_19)) != multiply(least_upper_bound(X_126,identity),X_19)
| multiply(least_upper_bound(identity,X_126),X_19) = multiply(least_upper_bound(X_126,identity),X_19) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_126),X_19),multiply(least_upper_bound(X_126,identity),X_19)) ),[0],$fot(least_upper_bound(X_19,multiply(X_126,X_19)))]]) ).
cnf(refute_0_589,plain,
( multiply(least_upper_bound(identity,X_126),X_19) != least_upper_bound(X_19,multiply(X_126,X_19))
| multiply(least_upper_bound(identity,X_126),X_19) = multiply(least_upper_bound(X_126,identity),X_19) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_126,X_19)),multiply(least_upper_bound(X_126,identity),X_19)) )],[refute_0_552,refute_0_588]) ).
cnf(refute_0_590,plain,
( least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)) != least_upper_bound(X_19,multiply(X_126,X_19))
| multiply(least_upper_bound(identity,X_126),X_19) = multiply(least_upper_bound(X_126,identity),X_19) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_126),X_19),least_upper_bound(X_19,multiply(X_126,X_19))) )],[refute_0_587,refute_0_589]) ).
cnf(refute_0_591,plain,
multiply(least_upper_bound(identity,X_126),X_19) = multiply(least_upper_bound(X_126,identity),X_19),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(least_upper_bound(X_126,identity),X_19)),least_upper_bound(X_19,multiply(X_126,X_19))) )],[refute_0_555,refute_0_590]) ).
cnf(refute_0_592,plain,
( multiply(least_upper_bound(identity,X_126),X_19) != multiply(least_upper_bound(X_126,identity),X_19)
| multiply(least_upper_bound(X_126,identity),X_19) = multiply(least_upper_bound(identity,X_126),X_19) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,X_126),X_19))),bind(Y0,$fot(multiply(least_upper_bound(X_126,identity),X_19)))]]) ).
cnf(refute_0_593,plain,
multiply(least_upper_bound(X_126,identity),X_19) = multiply(least_upper_bound(identity,X_126),X_19),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_126),X_19),multiply(least_upper_bound(X_126,identity),X_19)) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) = multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)),
inference(subst,[],[refute_0_593:[bind(X_126,$fot(inverse(X_35))),bind(X_19,$fot(greatest_lower_bound(X_35,identity)))]]) ).
cnf(refute_0_595,plain,
( multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) != multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity))
| multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) != least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)),least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)))]]) ).
cnf(refute_0_596,plain,
( multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)) != least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)),multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity))) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_35),identity),greatest_lower_bound(X_35,identity)),least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_548,refute_0_596]) ).
cnf(refute_0_598,plain,
multiply(X_113,least_upper_bound(X_114,identity)) = least_upper_bound(multiply(X_113,X_114),multiply(X_113,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_113)),bind(Y,$fot(X_114)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_599,plain,
X_113 = multiply(X_113,identity),
inference(subst,[],[refute_0_131:[bind(X,$fot(X_113))]]) ).
cnf(refute_0_600,plain,
( X_113 != multiply(X_113,identity)
| multiply(X_113,identity) = X_113 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_113)),bind(Y0,$fot(multiply(X_113,identity)))]]) ).
cnf(refute_0_601,plain,
multiply(X_113,identity) = X_113,
inference(resolve,[$cnf( $equal(X_113,multiply(X_113,identity)) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
( multiply(X_113,identity) != X_113
| multiply(X_113,least_upper_bound(X_114,identity)) != least_upper_bound(multiply(X_113,X_114),multiply(X_113,identity))
| multiply(X_113,least_upper_bound(X_114,identity)) = least_upper_bound(multiply(X_113,X_114),X_113) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_113,least_upper_bound(X_114,identity)),least_upper_bound(multiply(X_113,X_114),multiply(X_113,identity))) ),[1,1],$fot(X_113)]]) ).
cnf(refute_0_603,plain,
( multiply(X_113,least_upper_bound(X_114,identity)) != least_upper_bound(multiply(X_113,X_114),multiply(X_113,identity))
| multiply(X_113,least_upper_bound(X_114,identity)) = least_upper_bound(multiply(X_113,X_114),X_113) ),
inference(resolve,[$cnf( $equal(multiply(X_113,identity),X_113) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
multiply(X_113,least_upper_bound(X_114,identity)) = least_upper_bound(multiply(X_113,X_114),X_113),
inference(resolve,[$cnf( $equal(multiply(X_113,least_upper_bound(X_114,identity)),least_upper_bound(multiply(X_113,X_114),multiply(X_113,identity))) )],[refute_0_598,refute_0_603]) ).
cnf(refute_0_605,plain,
least_upper_bound(multiply(X_113,X_114),X_113) = least_upper_bound(X_113,multiply(X_113,X_114)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_113)),bind(Y,$fot(multiply(X_113,X_114)))]]) ).
cnf(refute_0_606,plain,
( multiply(X_113,least_upper_bound(X_114,identity)) != least_upper_bound(multiply(X_113,X_114),X_113)
| least_upper_bound(multiply(X_113,X_114),X_113) != least_upper_bound(X_113,multiply(X_113,X_114))
| multiply(X_113,least_upper_bound(X_114,identity)) = least_upper_bound(X_113,multiply(X_113,X_114)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_113,least_upper_bound(X_114,identity)),least_upper_bound(X_113,multiply(X_113,X_114))) ),[0],$fot(least_upper_bound(multiply(X_113,X_114),X_113))]]) ).
cnf(refute_0_607,plain,
( multiply(X_113,least_upper_bound(X_114,identity)) != least_upper_bound(multiply(X_113,X_114),X_113)
| multiply(X_113,least_upper_bound(X_114,identity)) = least_upper_bound(X_113,multiply(X_113,X_114)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_113,X_114),X_113),least_upper_bound(X_113,multiply(X_113,X_114))) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
multiply(X_113,least_upper_bound(X_114,identity)) = least_upper_bound(X_113,multiply(X_113,X_114)),
inference(resolve,[$cnf( $equal(multiply(X_113,least_upper_bound(X_114,identity)),least_upper_bound(multiply(X_113,X_114),X_113)) )],[refute_0_604,refute_0_607]) ).
cnf(refute_0_609,plain,
multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) = least_upper_bound(greatest_lower_bound(X_53,identity),multiply(greatest_lower_bound(X_53,identity),inverse(X_53))),
inference(subst,[],[refute_0_608:[bind(X_113,$fot(greatest_lower_bound(X_53,identity))),bind(X_114,$fot(inverse(X_53)))]]) ).
cnf(refute_0_610,plain,
( multiply(greatest_lower_bound(X_53,identity),inverse(X_53)) != greatest_lower_bound(identity,inverse(X_53))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) != least_upper_bound(greatest_lower_bound(X_53,identity),multiply(greatest_lower_bound(X_53,identity),inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) = least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)),least_upper_bound(greatest_lower_bound(X_53,identity),multiply(greatest_lower_bound(X_53,identity),inverse(X_53)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_53)))]]) ).
cnf(refute_0_611,plain,
( multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) != least_upper_bound(greatest_lower_bound(X_53,identity),multiply(greatest_lower_bound(X_53,identity),inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) = least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),inverse(X_53)),greatest_lower_bound(identity,inverse(X_53))) )],[refute_0_160,refute_0_610]) ).
cnf(refute_0_612,plain,
multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) = least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)),least_upper_bound(greatest_lower_bound(X_53,identity),multiply(greatest_lower_bound(X_53,identity),inverse(X_53)))) )],[refute_0_609,refute_0_611]) ).
cnf(refute_0_613,plain,
least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_200))) = least_upper_bound(X_19,multiply(X_19,X_200)),
inference(subst,[],[refute_0_465:[bind(X_20,$fot(multiply(X_19,X_200)))]]) ).
cnf(refute_0_614,plain,
multiply(X_19,least_upper_bound(X_200,identity)) = least_upper_bound(X_19,multiply(X_19,X_200)),
inference(subst,[],[refute_0_608:[bind(X_113,$fot(X_19)),bind(X_114,$fot(X_200))]]) ).
cnf(refute_0_615,plain,
( multiply(X_19,least_upper_bound(X_200,identity)) != least_upper_bound(X_19,multiply(X_19,X_200))
| least_upper_bound(X_19,multiply(X_19,X_200)) = multiply(X_19,least_upper_bound(X_200,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_19,least_upper_bound(X_200,identity)))),bind(Y0,$fot(least_upper_bound(X_19,multiply(X_19,X_200))))]]) ).
cnf(refute_0_616,plain,
least_upper_bound(X_19,multiply(X_19,X_200)) = multiply(X_19,least_upper_bound(X_200,identity)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(X_200,identity)),least_upper_bound(X_19,multiply(X_19,X_200))) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
( least_upper_bound(X_19,multiply(X_19,X_200)) != multiply(X_19,least_upper_bound(X_200,identity))
| least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_200))) != least_upper_bound(X_19,multiply(X_19,X_200))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = least_upper_bound(X_19,multiply(X_19,X_200)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_200))),least_upper_bound(X_19,multiply(X_19,X_200))) ),[0,1],$fot(multiply(X_19,least_upper_bound(X_200,identity)))]]) ).
cnf(refute_0_618,plain,
( least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_200))) != least_upper_bound(X_19,multiply(X_19,X_200))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = least_upper_bound(X_19,multiply(X_19,X_200)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_200)),multiply(X_19,least_upper_bound(X_200,identity))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = least_upper_bound(X_19,multiply(X_19,X_200)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,least_upper_bound(X_19,multiply(X_19,X_200))),least_upper_bound(X_19,multiply(X_19,X_200))) )],[refute_0_613,refute_0_618]) ).
cnf(refute_0_620,plain,
least_upper_bound(identity,least_upper_bound(X_200,identity)) = least_upper_bound(identity,X_200),
inference(subst,[],[refute_0_385:[bind(X_11,$fot(identity)),bind(X_15,$fot(X_200))]]) ).
cnf(refute_0_621,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))),
introduced(tautology,[refl,[$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))))]]) ).
cnf(refute_0_622,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))
| least_upper_bound(identity,least_upper_bound(X_200,identity)) != least_upper_bound(identity,X_200)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,X_200)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_200))]]) ).
cnf(refute_0_623,plain,
( least_upper_bound(identity,least_upper_bound(X_200,identity)) != least_upper_bound(identity,X_200)
| multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,X_200)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,X_200)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_200,identity)),least_upper_bound(identity,X_200)) )],[refute_0_620,refute_0_623]) ).
cnf(refute_0_625,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_426:[bind(X_15,$fot(multiply(X,Z))),bind(X_22,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_626,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_627,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_626]) ).
cnf(refute_0_628,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$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_629,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( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_625,refute_0_629]) ).
cnf(refute_0_631,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_426:[bind(X_15,$fot(Y)),bind(X_22,$fot(Z))]]) ).
cnf(refute_0_632,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_633,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_634,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( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_631,refute_0_634]) ).
cnf(refute_0_636,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_637,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_636]) ).
cnf(refute_0_638,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
inference(subst,[],[refute_0_637:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_639,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_214:[bind(X0,$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_640,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( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_635,refute_0_640]) ).
cnf(refute_0_642,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_627:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_643,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_644,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_645,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( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_214:[bind(X0,$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_648,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( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_641,refute_0_648]) ).
cnf(refute_0_650,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_25:[bind(X,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_651,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_214:[bind(X0,$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_652,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( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_649,refute_0_652]) ).
cnf(refute_0_654,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$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_655,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( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
introduced(tautology,[equality,[$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_657,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( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_642,refute_0_656]) ).
cnf(refute_0_658,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_655,refute_0_657]) ).
cnf(refute_0_659,plain,
multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_630,refute_0_658]) ).
cnf(refute_0_660,plain,
( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_661,plain,
multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity)) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))),
inference(subst,[],[refute_0_661:[bind(X,$fot(X_19)),bind(Y,$fot(identity)),bind(Z,$fot(least_upper_bound(X_200,identity)))]]) ).
cnf(refute_0_663,plain,
( multiply(X_113,least_upper_bound(X_114,identity)) != least_upper_bound(X_113,multiply(X_113,X_114))
| least_upper_bound(X_113,multiply(X_113,X_114)) = multiply(X_113,least_upper_bound(X_114,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_113,least_upper_bound(X_114,identity)))),bind(Y0,$fot(least_upper_bound(X_113,multiply(X_113,X_114))))]]) ).
cnf(refute_0_664,plain,
least_upper_bound(X_113,multiply(X_113,X_114)) = multiply(X_113,least_upper_bound(X_114,identity)),
inference(resolve,[$cnf( $equal(multiply(X_113,least_upper_bound(X_114,identity)),least_upper_bound(X_113,multiply(X_113,X_114))) )],[refute_0_608,refute_0_663]) ).
cnf(refute_0_665,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity)),
inference(subst,[],[refute_0_664:[bind(X_113,$fot(X_19)),bind(X_114,$fot(least_upper_bound(X_200,identity)))]]) ).
cnf(refute_0_666,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) != multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity)))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))))]]) ).
cnf(refute_0_667,plain,
( multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity)) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))),multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(least_upper_bound(X_200,identity),identity)),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))) )],[refute_0_662,refute_0_667]) ).
cnf(refute_0_669,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) != multiply(X_19,least_upper_bound(identity,X_200))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) != multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,X_200)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))))),bind(Y0,$fot(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))))),bind(Z0,$fot(multiply(X_19,least_upper_bound(identity,X_200))))]]) ).
cnf(refute_0_670,plain,
( multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))) != multiply(X_19,least_upper_bound(identity,X_200))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,X_200)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))),multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity)))) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) = multiply(X_19,least_upper_bound(identity,X_200)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,least_upper_bound(X_200,identity))),multiply(X_19,least_upper_bound(identity,X_200))) )],[refute_0_624,refute_0_670]) ).
cnf(refute_0_672,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) != multiply(X_19,least_upper_bound(identity,X_200))
| least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) != least_upper_bound(X_19,multiply(X_19,X_200))
| multiply(X_19,least_upper_bound(identity,X_200)) = least_upper_bound(X_19,multiply(X_19,X_200)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))),least_upper_bound(X_19,multiply(X_19,X_200))) ),[0],$fot(multiply(X_19,least_upper_bound(identity,X_200)))]]) ).
cnf(refute_0_673,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) != least_upper_bound(X_19,multiply(X_19,X_200))
| multiply(X_19,least_upper_bound(identity,X_200)) = least_upper_bound(X_19,multiply(X_19,X_200)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))),multiply(X_19,least_upper_bound(identity,X_200))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
( multiply(X_19,least_upper_bound(identity,X_200)) != least_upper_bound(X_19,multiply(X_19,X_200))
| least_upper_bound(X_19,multiply(X_19,X_200)) != multiply(X_19,least_upper_bound(X_200,identity))
| multiply(X_19,least_upper_bound(identity,X_200)) = multiply(X_19,least_upper_bound(X_200,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_19,least_upper_bound(identity,X_200)),multiply(X_19,least_upper_bound(X_200,identity))) ),[0],$fot(least_upper_bound(X_19,multiply(X_19,X_200)))]]) ).
cnf(refute_0_675,plain,
( multiply(X_19,least_upper_bound(identity,X_200)) != least_upper_bound(X_19,multiply(X_19,X_200))
| multiply(X_19,least_upper_bound(identity,X_200)) = multiply(X_19,least_upper_bound(X_200,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,X_200)),multiply(X_19,least_upper_bound(X_200,identity))) )],[refute_0_616,refute_0_674]) ).
cnf(refute_0_676,plain,
( least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))) != least_upper_bound(X_19,multiply(X_19,X_200))
| multiply(X_19,least_upper_bound(identity,X_200)) = multiply(X_19,least_upper_bound(X_200,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_200)),least_upper_bound(X_19,multiply(X_19,X_200))) )],[refute_0_673,refute_0_675]) ).
cnf(refute_0_677,plain,
multiply(X_19,least_upper_bound(identity,X_200)) = multiply(X_19,least_upper_bound(X_200,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_19,multiply(X_19,least_upper_bound(X_200,identity))),least_upper_bound(X_19,multiply(X_19,X_200))) )],[refute_0_619,refute_0_676]) ).
cnf(refute_0_678,plain,
( multiply(X_19,least_upper_bound(identity,X_200)) != multiply(X_19,least_upper_bound(X_200,identity))
| multiply(X_19,least_upper_bound(X_200,identity)) = multiply(X_19,least_upper_bound(identity,X_200)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_19,least_upper_bound(identity,X_200)))),bind(Y0,$fot(multiply(X_19,least_upper_bound(X_200,identity))))]]) ).
cnf(refute_0_679,plain,
multiply(X_19,least_upper_bound(X_200,identity)) = multiply(X_19,least_upper_bound(identity,X_200)),
inference(resolve,[$cnf( $equal(multiply(X_19,least_upper_bound(identity,X_200)),multiply(X_19,least_upper_bound(X_200,identity))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) = multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))),
inference(subst,[],[refute_0_679:[bind(X_19,$fot(greatest_lower_bound(X_53,identity))),bind(X_200,$fot(inverse(X_53)))]]) ).
cnf(refute_0_681,plain,
( multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) != multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) != least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) = least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)),least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))) ),[0],$fot(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))))]]) ).
cnf(refute_0_682,plain,
( multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) != least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) = least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)),multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53)))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) != least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))
| least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) = multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_684,plain,
least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) = multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)),least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_597,refute_0_683]) ).
cnf(refute_0_685,plain,
least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))) = multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity)),
inference(subst,[],[refute_0_684:[bind(X_35,$fot(X_53))]]) ).
cnf(refute_0_686,plain,
( multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) != least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))
| least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))) != multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) = multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))),multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))))]]) ).
cnf(refute_0_687,plain,
( multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) != least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) = multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53))),multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity))) )],[refute_0_685,refute_0_686]) ).
cnf(refute_0_688,plain,
( multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)) != least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))
| multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) = multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))),least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))) )],[refute_0_682,refute_0_687]) ).
cnf(refute_0_689,plain,
multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) = multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(inverse(X_53),identity)),least_upper_bound(greatest_lower_bound(X_53,identity),greatest_lower_bound(identity,inverse(X_53)))) )],[refute_0_612,refute_0_688]) ).
cnf(refute_0_690,plain,
( multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) != multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity))
| multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity)) = multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity))))]]) ).
cnf(refute_0_691,plain,
multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity)) = multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_53,identity),least_upper_bound(identity,inverse(X_53))),multiply(least_upper_bound(identity,inverse(X_53)),greatest_lower_bound(X_53,identity))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) = multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))),
inference(subst,[],[refute_0_691:[bind(X_53,$fot(X_35))]]) ).
cnf(refute_0_693,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) != multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))
| multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) != least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))
| multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)),least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))) ),[0],$fot(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))]]) ).
cnf(refute_0_694,plain,
( multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)) != least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))
| multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)),multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_35)),greatest_lower_bound(X_35,identity)),least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_597,refute_0_694]) ).
cnf(refute_0_696,plain,
( multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) != least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))
| least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) = multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_697,plain,
least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) = multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))),least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))) = greatest_lower_bound(identity,inverse(X_35)),
inference(subst,[],[p23_2:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_35))))]]) ).
cnf(refute_0_699,plain,
least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) = least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))))]]) ).
cnf(refute_0_700,plain,
( inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))) != greatest_lower_bound(identity,inverse(X_35))
| least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) != least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))
| least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))),least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_35)))]]) ).
cnf(refute_0_701,plain,
( inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))) != greatest_lower_bound(identity,inverse(X_35))
| least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))),least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) = least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))),greatest_lower_bound(identity,inverse(X_35))) )],[refute_0_698,refute_0_701]) ).
cnf(refute_0_703,plain,
( least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) != multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))
| least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) != least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))
| least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) = multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_704,plain,
( least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))) != multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))
| least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) = multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))),least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35)))) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) = multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,identity),greatest_lower_bound(identity,inverse(X_35))),multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) )],[refute_0_697,refute_0_704]) ).
cnf(refute_0_706,plain,
inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) = inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))))]]) ).
cnf(refute_0_707,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) != inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))))
| least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) != multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))
| inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) = inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))))) ),[1,0],$fot(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))]]) ).
cnf(refute_0_708,plain,
( least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))) != multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))
| inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) = inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))))) )],[refute_0_706,refute_0_707]) ).
cnf(refute_0_709,plain,
inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) = inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35))))),multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) )],[refute_0_705,refute_0_708]) ).
cnf(refute_0_710,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)))]]) ).
cnf(refute_0_711,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35))
| inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) != inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) = multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35))) ),[1,0],$fot(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_712,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))) != inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))
| multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) = multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)),multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35))) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) = multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))) )],[refute_0_709,refute_0_712]) ).
cnf(refute_0_714,plain,
( multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)) != multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))
| inverse(greatest_lower_bound(identity,inverse(X_35))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35))
| inverse(greatest_lower_bound(identity,inverse(X_35))) = multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_35))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35))) ),[1],$fot(multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)))]]) ).
cnf(refute_0_715,plain,
( inverse(greatest_lower_bound(identity,inverse(X_35))) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35))
| inverse(greatest_lower_bound(identity,inverse(X_35))) = multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35)),multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
inverse(greatest_lower_bound(identity,inverse(X_35))) = multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_35))),multiply(inverse(least_upper_bound(greatest_lower_bound(X_35,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_35)))))),least_upper_bound(identity,X_35))) )],[refute_0_535,refute_0_715]) ).
cnf(refute_0_717,plain,
multiply(identity,least_upper_bound(identity,X_35)) = least_upper_bound(identity,X_35),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,X_35)))]]) ).
cnf(refute_0_718,plain,
multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(multiply(inverse(X_33),X_32),multiply(inverse(X_33),X_33)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_33))),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_719,plain,
multiply(inverse(X_33),X_33) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_720,plain,
( multiply(inverse(X_33),X_33) != identity
| multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(multiply(inverse(X_33),X_32),multiply(inverse(X_33),X_33))
| multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(multiply(inverse(X_33),X_32),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)),greatest_lower_bound(multiply(inverse(X_33),X_32),multiply(inverse(X_33),X_33))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_721,plain,
( multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(multiply(inverse(X_33),X_32),multiply(inverse(X_33),X_33))
| multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(multiply(inverse(X_33),X_32),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),X_33),identity) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(multiply(inverse(X_33),X_32),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)),greatest_lower_bound(multiply(inverse(X_33),X_32),multiply(inverse(X_33),X_33))) )],[refute_0_718,refute_0_721]) ).
cnf(refute_0_723,plain,
greatest_lower_bound(multiply(inverse(X_33),X_32),identity) = greatest_lower_bound(identity,multiply(inverse(X_33),X_32)),
inference(subst,[],[refute_0_25:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_33),X_32)))]]) ).
cnf(refute_0_724,plain,
( multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(multiply(inverse(X_33),X_32),identity)
| greatest_lower_bound(multiply(inverse(X_33),X_32),identity) != greatest_lower_bound(identity,multiply(inverse(X_33),X_32))
| multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(identity,multiply(inverse(X_33),X_32)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)),greatest_lower_bound(identity,multiply(inverse(X_33),X_32))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_33),X_32),identity))]]) ).
cnf(refute_0_725,plain,
( multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(multiply(inverse(X_33),X_32),identity)
| multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(identity,multiply(inverse(X_33),X_32)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_33),X_32),identity),greatest_lower_bound(identity,multiply(inverse(X_33),X_32))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(identity,multiply(inverse(X_33),X_32)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),greatest_lower_bound(X_32,X_33)),greatest_lower_bound(multiply(inverse(X_33),X_32),identity)) )],[refute_0_722,refute_0_725]) ).
cnf(refute_0_727,plain,
multiply(inverse(least_upper_bound(X_15,X_41)),greatest_lower_bound(X_41,least_upper_bound(X_15,X_41))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41)),
inference(subst,[],[refute_0_726:[bind(X_32,$fot(X_41)),bind(X_33,$fot(least_upper_bound(X_15,X_41)))]]) ).
cnf(refute_0_728,plain,
greatest_lower_bound(X_41,least_upper_bound(X_15,X_41)) = X_41,
inference(subst,[],[refute_0_421:[bind(X_14,$fot(X_41))]]) ).
cnf(refute_0_729,plain,
( multiply(inverse(least_upper_bound(X_15,X_41)),greatest_lower_bound(X_41,least_upper_bound(X_15,X_41))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41))
| greatest_lower_bound(X_41,least_upper_bound(X_15,X_41)) != X_41
| multiply(inverse(least_upper_bound(X_15,X_41)),X_41) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_15,X_41)),greatest_lower_bound(X_41,least_upper_bound(X_15,X_41))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41))) ),[0,1],$fot(X_41)]]) ).
cnf(refute_0_730,plain,
( multiply(inverse(least_upper_bound(X_15,X_41)),greatest_lower_bound(X_41,least_upper_bound(X_15,X_41))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41))
| multiply(inverse(least_upper_bound(X_15,X_41)),X_41) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,least_upper_bound(X_15,X_41)),X_41) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
multiply(inverse(least_upper_bound(X_15,X_41)),X_41) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_15,X_41)),greatest_lower_bound(X_41,least_upper_bound(X_15,X_41))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41))) )],[refute_0_727,refute_0_730]) ).
cnf(refute_0_732,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(subst,[],[refute_0_731:[bind(X_15,$fot(identity)),bind(X_41,$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_733,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))) = least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))),
inference(subst,[],[refute_0_413:[bind(X_108,$fot(identity)),bind(X_11,$fot(X_350)),bind(X_110,$fot(greatest_lower_bound(identity,inverse(X_350))))]]) ).
cnf(refute_0_734,plain,
multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350))) = least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350))),
inference(subst,[],[refute_0_695:[bind(X_35,$fot(X_350))]]) ).
cnf(refute_0_735,plain,
( multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350))) != least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))
| least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350))) = multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))))]]) ).
cnf(refute_0_736,plain,
least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350))) = multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350))),least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
( least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350))) != multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))) != least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350)))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) = least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350)))) ),[0,1],$fot(multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350))))]]) ).
cnf(refute_0_738,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))) != least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350)))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) = least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350))),multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) = least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_350,identity),greatest_lower_bound(identity,inverse(X_350)))),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350)))) )],[refute_0_733,refute_0_738]) ).
cnf(refute_0_740,plain,
least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_350)))]]) ).
cnf(refute_0_741,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) != least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350)))
| least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))) != identity
| least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))),identity) ),[0],$fot(least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))))]]) ).
cnf(refute_0_742,plain,
( least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) != least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350)))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350))),identity) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_350,identity),least_upper_bound(identity,inverse(X_350)))),least_upper_bound(identity,greatest_lower_bound(identity,inverse(X_350)))) )],[refute_0_739,refute_0_742]) ).
cnf(refute_0_744,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = identity,
inference(subst,[],[refute_0_743:[bind(X_350,$fot(X_352))]]) ).
cnf(refute_0_745,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != identity
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) ),[1,1,0,0],$fot(identity)]]) ).
cnf(refute_0_746,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_732,refute_0_746]) ).
cnf(refute_0_748,plain,
inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))),
inference(subst,[],[p23_2:[bind(X,$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_749,plain,
multiply(X_113,least_upper_bound(X_114,inverse(X_113))) = least_upper_bound(multiply(X_113,X_114),multiply(X_113,inverse(X_113))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_113)),bind(Y,$fot(X_114)),bind(Z,$fot(inverse(X_113)))]]) ).
cnf(refute_0_750,plain,
multiply(X_113,inverse(X_113)) = identity,
inference(subst,[],[refute_0_19:[bind(X_1,$fot(X_113))]]) ).
cnf(refute_0_751,plain,
( multiply(X_113,inverse(X_113)) != identity
| multiply(X_113,least_upper_bound(X_114,inverse(X_113))) != least_upper_bound(multiply(X_113,X_114),multiply(X_113,inverse(X_113)))
| multiply(X_113,least_upper_bound(X_114,inverse(X_113))) = least_upper_bound(multiply(X_113,X_114),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_113,least_upper_bound(X_114,inverse(X_113))),least_upper_bound(multiply(X_113,X_114),multiply(X_113,inverse(X_113)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_752,plain,
( multiply(X_113,least_upper_bound(X_114,inverse(X_113))) != least_upper_bound(multiply(X_113,X_114),multiply(X_113,inverse(X_113)))
| multiply(X_113,least_upper_bound(X_114,inverse(X_113))) = least_upper_bound(multiply(X_113,X_114),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_113,inverse(X_113)),identity) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
multiply(X_113,least_upper_bound(X_114,inverse(X_113))) = least_upper_bound(multiply(X_113,X_114),identity),
inference(resolve,[$cnf( $equal(multiply(X_113,least_upper_bound(X_114,inverse(X_113))),least_upper_bound(multiply(X_113,X_114),multiply(X_113,inverse(X_113)))) )],[refute_0_749,refute_0_752]) ).
cnf(refute_0_754,plain,
least_upper_bound(multiply(X_113,X_114),identity) = least_upper_bound(identity,multiply(X_113,X_114)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_113,X_114)))]]) ).
cnf(refute_0_755,plain,
( multiply(X_113,least_upper_bound(X_114,inverse(X_113))) != least_upper_bound(multiply(X_113,X_114),identity)
| least_upper_bound(multiply(X_113,X_114),identity) != least_upper_bound(identity,multiply(X_113,X_114))
| multiply(X_113,least_upper_bound(X_114,inverse(X_113))) = least_upper_bound(identity,multiply(X_113,X_114)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_113,least_upper_bound(X_114,inverse(X_113))),least_upper_bound(identity,multiply(X_113,X_114))) ),[0],$fot(least_upper_bound(multiply(X_113,X_114),identity))]]) ).
cnf(refute_0_756,plain,
( multiply(X_113,least_upper_bound(X_114,inverse(X_113))) != least_upper_bound(multiply(X_113,X_114),identity)
| multiply(X_113,least_upper_bound(X_114,inverse(X_113))) = least_upper_bound(identity,multiply(X_113,X_114)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_113,X_114),identity),least_upper_bound(identity,multiply(X_113,X_114))) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
multiply(X_113,least_upper_bound(X_114,inverse(X_113))) = least_upper_bound(identity,multiply(X_113,X_114)),
inference(resolve,[$cnf( $equal(multiply(X_113,least_upper_bound(X_114,inverse(X_113))),least_upper_bound(multiply(X_113,X_114),identity)) )],[refute_0_753,refute_0_756]) ).
cnf(refute_0_758,plain,
multiply(inverse(X),least_upper_bound(X_117,inverse(inverse(X)))) = least_upper_bound(identity,multiply(inverse(X),X_117)),
inference(subst,[],[refute_0_757:[bind(X_113,$fot(inverse(X))),bind(X_114,$fot(X_117))]]) ).
cnf(refute_0_759,plain,
( multiply(inverse(X),least_upper_bound(X_117,inverse(inverse(X)))) != least_upper_bound(identity,multiply(inverse(X),X_117))
| inverse(inverse(X)) != X
| multiply(inverse(X),least_upper_bound(X_117,X)) = least_upper_bound(identity,multiply(inverse(X),X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_117,inverse(inverse(X)))),least_upper_bound(identity,multiply(inverse(X),X_117))) ),[0,1,1],$fot(X)]]) ).
cnf(refute_0_760,plain,
( multiply(inverse(X),least_upper_bound(X_117,inverse(inverse(X)))) != least_upper_bound(identity,multiply(inverse(X),X_117))
| multiply(inverse(X),least_upper_bound(X_117,X)) = least_upper_bound(identity,multiply(inverse(X),X_117)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p23_2,refute_0_759]) ).
cnf(refute_0_761,plain,
multiply(inverse(X),least_upper_bound(X_117,X)) = least_upper_bound(identity,multiply(inverse(X),X_117)),
inference(resolve,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_117,inverse(inverse(X)))),least_upper_bound(identity,multiply(inverse(X),X_117))) )],[refute_0_758,refute_0_760]) ).
cnf(refute_0_762,plain,
multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)),
inference(subst,[],[refute_0_761:[bind(X,$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),bind(X_117,$fot(identity))]]) ).
cnf(refute_0_763,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))
| least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) = least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_764,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))
| multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) = least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) )],[refute_0_744,refute_0_763]) ).
cnf(refute_0_765,plain,
multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) = least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) )],[refute_0_762,refute_0_764]) ).
cnf(refute_0_766,plain,
multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),
inference(subst,[],[refute_0_331:[bind(X,$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_767,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) != least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))
| inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) ),[0],$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_768,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) != least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))
| inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(subst,[],[refute_0_331:[bind(X,$fot(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))))]]) ).
cnf(refute_0_770,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_426:[bind(X_15,$fot(multiply(Z,X))),bind(X_22,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_771,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_772,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( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_569,refute_0_771]) ).
cnf(refute_0_773,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_770,refute_0_772]) ).
cnf(refute_0_774,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))]]) ).
cnf(refute_0_775,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_776,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( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_631,refute_0_776]) ).
cnf(refute_0_778,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_779,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_778]) ).
cnf(refute_0_780,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
inference(subst,[],[refute_0_779:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_781,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_214:[bind(X0,$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_782,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( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_777,refute_0_782]) ).
cnf(refute_0_784,plain,
least_upper_bound(multiply(Z,X),multiply(Y,X)) = multiply(least_upper_bound(Z,Y),X),
inference(subst,[],[refute_0_569:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_785,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_786,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_787,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( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_785,refute_0_786]) ).
cnf(refute_0_788,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_784,refute_0_787]) ).
cnf(refute_0_789,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_214:[bind(X0,$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_790,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( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_783,refute_0_790]) ).
cnf(refute_0_792,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_25:[bind(X,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y,$fot(least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_793,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_214:[bind(X0,$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_794,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( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_791,refute_0_794]) ).
cnf(refute_0_796,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$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_797,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( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
introduced(tautology,[equality,[$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_799,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( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_784,refute_0_798]) ).
cnf(refute_0_800,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_797,refute_0_799]) ).
cnf(refute_0_801,plain,
multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_773,refute_0_800]) ).
cnf(refute_0_802,plain,
( multiply(least_upper_bound(Y,Z),X) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(multiply(least_upper_bound(Z,Y),X)))]]) ).
cnf(refute_0_803,plain,
multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_801,refute_0_802]) ).
cnf(refute_0_804,plain,
multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) = multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity),
inference(subst,[],[refute_0_803:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_805,plain,
( multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) != multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity)
| multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))))]]) ).
cnf(refute_0_806,plain,
( multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity),multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity)) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_769,refute_0_806]) ).
cnf(refute_0_808,plain,
least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) = multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity),
inference(subst,[],[refute_0_578:[bind(X_122,$fot(identity)),bind(X_123,$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_809,plain,
( multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) != multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity)
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))))]]) ).
cnf(refute_0_810,plain,
( multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)),multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity)) )],[refute_0_808,refute_0_809]) ).
cnf(refute_0_811,plain,
least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_807,refute_0_810]) ).
cnf(refute_0_812,plain,
( inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))]]) ).
cnf(refute_0_813,plain,
( inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))
| inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) != least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))
| inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) )],[refute_0_768,refute_0_813]) ).
cnf(refute_0_815,plain,
inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) )],[refute_0_765,refute_0_814]) ).
cnf(refute_0_816,plain,
( inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))))]]) ).
cnf(refute_0_817,plain,
least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_815,refute_0_816]) ).
cnf(refute_0_818,plain,
( multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) != least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_819,plain,
( least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity),least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_769,refute_0_818]) ).
cnf(refute_0_820,plain,
multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) )],[refute_0_817,refute_0_819]) ).
cnf(refute_0_821,plain,
( multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) != multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity)
| multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_822,plain,
( multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity),multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity)) )],[refute_0_804,refute_0_821]) ).
cnf(refute_0_823,plain,
multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity),inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) )],[refute_0_820,refute_0_822]) ).
cnf(refute_0_824,plain,
( multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) != multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity)
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_825,plain,
( multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)),multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity)) )],[refute_0_808,refute_0_824]) ).
cnf(refute_0_826,plain,
least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) = inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity),identity),inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) )],[refute_0_823,refute_0_825]) ).
cnf(refute_0_827,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))))]]) ).
cnf(refute_0_828,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))
| least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) = inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))),inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))) ),[1,0],$fot(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_829,plain,
( least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)) != inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) = inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))),inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) = inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)),inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) )],[refute_0_826,refute_0_829]) ).
cnf(refute_0_831,plain,
( inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) != inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) = multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))))),bind(Y0,$fot(inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_832,plain,
( inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) = multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))),inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) = multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) )],[refute_0_748,refute_0_832]) ).
cnf(refute_0_834,plain,
multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(multiply(inverse(X_32),X_32),multiply(inverse(X_32),X_33)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_32))),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_835,plain,
multiply(inverse(X_32),X_32) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_836,plain,
( multiply(inverse(X_32),X_32) != identity
| multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(multiply(inverse(X_32),X_32),multiply(inverse(X_32),X_33))
| multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(identity,multiply(inverse(X_32),X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)),greatest_lower_bound(multiply(inverse(X_32),X_32),multiply(inverse(X_32),X_33))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_837,plain,
( multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(multiply(inverse(X_32),X_32),multiply(inverse(X_32),X_33))
| multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(identity,multiply(inverse(X_32),X_33)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_32),X_32),identity) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(identity,multiply(inverse(X_32),X_33)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_32),greatest_lower_bound(X_32,X_33)),greatest_lower_bound(multiply(inverse(X_32),X_32),multiply(inverse(X_32),X_33))) )],[refute_0_834,refute_0_837]) ).
cnf(refute_0_839,plain,
multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))) = greatest_lower_bound(identity,multiply(inverse(X_43),inverse(X))),
inference(subst,[],[refute_0_838:[bind(X_32,$fot(X_43)),bind(X_33,$fot(inverse(X)))]]) ).
cnf(refute_0_840,plain,
inverse(multiply(X,X_43)) = multiply(inverse(X_43),inverse(X)),
inference(subst,[],[p23_3:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_841,plain,
( inverse(multiply(X,X_43)) != multiply(inverse(X_43),inverse(X))
| multiply(inverse(X_43),inverse(X)) = inverse(multiply(X,X_43)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X,X_43)))),bind(Y0,$fot(multiply(inverse(X_43),inverse(X))))]]) ).
cnf(refute_0_842,plain,
multiply(inverse(X_43),inverse(X)) = inverse(multiply(X,X_43)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,X_43)),multiply(inverse(X_43),inverse(X))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
( multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))) != greatest_lower_bound(identity,multiply(inverse(X_43),inverse(X)))
| multiply(inverse(X_43),inverse(X)) != inverse(multiply(X,X_43))
| multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))) = greatest_lower_bound(identity,inverse(multiply(X,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))),greatest_lower_bound(identity,multiply(inverse(X_43),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,X_43)))]]) ).
cnf(refute_0_844,plain,
( multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))) != greatest_lower_bound(identity,multiply(inverse(X_43),inverse(X)))
| multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))) = greatest_lower_bound(identity,inverse(multiply(X,X_43))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_43),inverse(X)),inverse(multiply(X,X_43))) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))) = greatest_lower_bound(identity,inverse(multiply(X,X_43))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_43),greatest_lower_bound(X_43,inverse(X))),greatest_lower_bound(identity,multiply(inverse(X_43),inverse(X)))) )],[refute_0_839,refute_0_844]) ).
cnf(refute_0_846,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = greatest_lower_bound(identity,inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279)))),
inference(subst,[],[refute_0_845:[bind(X,$fot(inverse(X_279))),bind(X_43,$fot(least_upper_bound(X_280,X_279)))]]) ).
cnf(refute_0_847,plain,
multiply(inverse(X_279),least_upper_bound(X_280,X_279)) = least_upper_bound(identity,multiply(inverse(X_279),X_280)),
inference(subst,[],[refute_0_761:[bind(X,$fot(X_279)),bind(X_117,$fot(X_280))]]) ).
cnf(refute_0_848,plain,
( multiply(inverse(X_279),least_upper_bound(X_280,X_279)) != least_upper_bound(identity,multiply(inverse(X_279),X_280))
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != greatest_lower_bound(identity,inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))))
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))),greatest_lower_bound(identity,inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))))) ),[1,1,0],$fot(least_upper_bound(identity,multiply(inverse(X_279),X_280)))]]) ).
cnf(refute_0_849,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != greatest_lower_bound(identity,inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))))
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_279),least_upper_bound(X_280,X_279)),least_upper_bound(identity,multiply(inverse(X_279),X_280))) )],[refute_0_847,refute_0_848]) ).
cnf(refute_0_850,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))),greatest_lower_bound(identity,inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))))) )],[refute_0_846,refute_0_849]) ).
cnf(refute_0_851,plain,
( multiply(inverse(least_upper_bound(X_15,X_41)),X_41) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41)) = multiply(inverse(least_upper_bound(X_15,X_41)),X_41) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_15,X_41)),X_41))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41))))]]) ).
cnf(refute_0_852,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41)) = multiply(inverse(least_upper_bound(X_15,X_41)),X_41),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_15,X_41)),X_41),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_15,X_41)),X_41))) )],[refute_0_731,refute_0_851]) ).
cnf(refute_0_853,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279),
inference(subst,[],[refute_0_852:[bind(X_15,$fot(X_280)),bind(X_41,$fot(X_279))]]) ).
cnf(refute_0_854,plain,
inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_279)),bind(X_26,$fot(least_upper_bound(X_280,X_279)))]]) ).
cnf(refute_0_855,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))) = inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))),
inference(subst,[],[refute_0_502:[bind(X,$fot(inverse(X_279))),bind(Y,$fot(least_upper_bound(X_280,X_279)))]]) ).
cnf(refute_0_856,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))) != inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279)))
| inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))),bind(Y0,$fot(inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_280,X_279)),X_279)))]]) ).
cnf(refute_0_857,plain,
( inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))),inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279)))) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_279),least_upper_bound(X_280,X_279))),multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) )],[refute_0_854,refute_0_857]) ).
cnf(refute_0_859,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))))]]) ).
cnf(refute_0_860,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))) ),[1,1],$fot(multiply(inverse(least_upper_bound(X_280,X_279)),X_279))]]) ).
cnf(refute_0_861,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))),multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) )],[refute_0_858,refute_0_861]) ).
cnf(refute_0_863,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_280,X_279)),X_279)))]]) ).
cnf(refute_0_864,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279))) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),X_279)),multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) )],[refute_0_853,refute_0_864]) ).
cnf(refute_0_866,plain,
multiply(inverse(multiply(inverse(X_43),X_44)),greatest_lower_bound(identity,multiply(inverse(X_43),X_44))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)),
inference(subst,[],[refute_0_726:[bind(X_32,$fot(identity)),bind(X_33,$fot(multiply(inverse(X_43),X_44)))]]) ).
cnf(refute_0_867,plain,
multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(identity,multiply(inverse(X_43),X_44)),
inference(subst,[],[refute_0_838:[bind(X_32,$fot(X_43)),bind(X_33,$fot(X_44))]]) ).
cnf(refute_0_868,plain,
( multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)) != greatest_lower_bound(identity,multiply(inverse(X_43),X_44))
| greatest_lower_bound(identity,multiply(inverse(X_43),X_44)) = multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_43),X_44))))]]) ).
cnf(refute_0_869,plain,
greatest_lower_bound(identity,multiply(inverse(X_43),X_44)) = multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)),greatest_lower_bound(identity,multiply(inverse(X_43),X_44))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),greatest_lower_bound(identity,multiply(inverse(X_43),X_44))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| greatest_lower_bound(identity,multiply(inverse(X_43),X_44)) != multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),greatest_lower_bound(identity,multiply(inverse(X_43),X_44))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))) ),[0,1],$fot(multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))]]) ).
cnf(refute_0_871,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),greatest_lower_bound(identity,multiply(inverse(X_43),X_44))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),greatest_lower_bound(identity,multiply(inverse(X_43),X_44))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))) )],[refute_0_866,refute_0_871]) ).
cnf(refute_0_873,plain,
multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_44))),bind(Y,$fot(X_43)),bind(Z,$fot(multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))]]) ).
cnf(refute_0_874,plain,
inverse(multiply(inverse(X_43),X_44)) = multiply(inverse(X_44),X_43),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_43)),bind(X_26,$fot(X_44))]]) ).
cnf(refute_0_875,plain,
multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))]]) ).
cnf(refute_0_876,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))
| inverse(multiply(inverse(X_43),X_44)) != multiply(inverse(X_44),X_43)
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) ),[1,0],$fot(multiply(inverse(X_44),X_43))]]) ).
cnf(refute_0_877,plain,
( inverse(multiply(inverse(X_43),X_44)) != multiply(inverse(X_44),X_43)
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_44),X_43)) )],[refute_0_874,refute_0_877]) ).
cnf(refute_0_879,plain,
( multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))),bind(Y0,$fot(multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))),bind(Z0,$fot(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))))]]) ).
cnf(refute_0_880,plain,
( multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_44),X_43),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))) )],[refute_0_873,refute_0_880]) ).
cnf(refute_0_882,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))
| multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))) ),[0],$fot(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))))]]) ).
cnf(refute_0_883,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))) )],[refute_0_881,refute_0_882]) ).
cnf(refute_0_884,plain,
multiply(inverse(multiply(inverse(X_43),X_44)),identity) = inverse(multiply(inverse(X_43),X_44)),
inference(subst,[],[refute_0_331:[bind(X,$fot(inverse(multiply(inverse(X_43),X_44))))]]) ).
cnf(refute_0_885,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),identity) != inverse(multiply(inverse(X_43),X_44))
| inverse(multiply(inverse(X_43),X_44)) != multiply(inverse(X_44),X_43)
| multiply(inverse(multiply(inverse(X_43),X_44)),identity) = multiply(inverse(X_44),X_43) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(multiply(inverse(X_43),X_44)),identity))),bind(Y0,$fot(inverse(multiply(inverse(X_43),X_44)))),bind(Z0,$fot(multiply(inverse(X_44),X_43)))]]) ).
cnf(refute_0_886,plain,
( inverse(multiply(inverse(X_43),X_44)) != multiply(inverse(X_44),X_43)
| multiply(inverse(multiply(inverse(X_43),X_44)),identity) = multiply(inverse(X_44),X_43) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),identity),inverse(multiply(inverse(X_43),X_44))) )],[refute_0_884,refute_0_885]) ).
cnf(refute_0_887,plain,
multiply(inverse(multiply(inverse(X_43),X_44)),identity) = multiply(inverse(X_44),X_43),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_44),X_43)) )],[refute_0_874,refute_0_886]) ).
cnf(refute_0_888,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)))]]) ).
cnf(refute_0_889,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),identity) != multiply(inverse(X_44),X_43)
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))) ),[1,1],$fot(multiply(inverse(X_44),X_43))]]) ).
cnf(refute_0_890,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),identity) != multiply(inverse(X_44),X_43)
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))) )],[refute_0_888,refute_0_889]) ).
cnf(refute_0_891,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),identity),multiply(inverse(X_44),X_43)) )],[refute_0_887,refute_0_890]) ).
cnf(refute_0_892,plain,
( multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)) != greatest_lower_bound(identity,multiply(inverse(X_44),X_43))
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),greatest_lower_bound(identity,multiply(inverse(X_44),X_43))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)))]]) ).
cnf(refute_0_893,plain,
( multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity)),greatest_lower_bound(identity,multiply(inverse(X_44),X_43))) )],[refute_0_891,refute_0_892]) ).
cnf(refute_0_894,plain,
( multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))) )],[refute_0_883,refute_0_893]) ).
cnf(refute_0_895,plain,
multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_43),X_44)),multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),greatest_lower_bound(identity,multiply(inverse(multiply(inverse(X_43),X_44)),identity))) )],[refute_0_872,refute_0_894]) ).
cnf(refute_0_896,plain,
multiply(multiply(X_92,inverse(X_92)),X_94) = multiply(X_92,multiply(inverse(X_92),X_94)),
inference(subst,[],[associativity:[bind(X,$fot(X_92)),bind(Y,$fot(inverse(X_92))),bind(Z,$fot(X_94))]]) ).
cnf(refute_0_897,plain,
multiply(X_92,inverse(X_92)) = identity,
inference(subst,[],[refute_0_19:[bind(X_1,$fot(X_92))]]) ).
cnf(refute_0_898,plain,
( multiply(X_92,inverse(X_92)) != identity
| multiply(multiply(X_92,inverse(X_92)),X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| multiply(identity,X_94) = multiply(X_92,multiply(inverse(X_92),X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_92,inverse(X_92)),X_94),multiply(X_92,multiply(inverse(X_92),X_94))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_899,plain,
( multiply(multiply(X_92,inverse(X_92)),X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| multiply(identity,X_94) = multiply(X_92,multiply(inverse(X_92),X_94)) ),
inference(resolve,[$cnf( $equal(multiply(X_92,inverse(X_92)),identity) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
multiply(identity,X_94) = multiply(X_92,multiply(inverse(X_92),X_94)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_92,inverse(X_92)),X_94),multiply(X_92,multiply(inverse(X_92),X_94))) )],[refute_0_896,refute_0_899]) ).
cnf(refute_0_901,plain,
( multiply(identity,X_94) != X_94
| multiply(identity,X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| X_94 = multiply(X_92,multiply(inverse(X_92),X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_94),multiply(X_92,multiply(inverse(X_92),X_94))) ),[0],$fot(X_94)]]) ).
cnf(refute_0_902,plain,
( multiply(identity,X_94) != multiply(X_92,multiply(inverse(X_92),X_94))
| X_94 = multiply(X_92,multiply(inverse(X_92),X_94)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),X_94) )],[refute_0_93,refute_0_901]) ).
cnf(refute_0_903,plain,
X_94 = multiply(X_92,multiply(inverse(X_92),X_94)),
inference(resolve,[$cnf( $equal(multiply(identity,X_94),multiply(X_92,multiply(inverse(X_92),X_94))) )],[refute_0_900,refute_0_902]) ).
cnf(refute_0_904,plain,
( X_94 != multiply(X_92,multiply(inverse(X_92),X_94))
| multiply(X_92,multiply(inverse(X_92),X_94)) = X_94 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_94)),bind(Y0,$fot(multiply(X_92,multiply(inverse(X_92),X_94))))]]) ).
cnf(refute_0_905,plain,
multiply(X_92,multiply(inverse(X_92),X_94)) = X_94,
inference(resolve,[$cnf( $equal(X_94,multiply(X_92,multiply(inverse(X_92),X_94))) )],[refute_0_903,refute_0_904]) ).
cnf(refute_0_906,plain,
multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) = greatest_lower_bound(X_43,X_44),
inference(subst,[],[refute_0_905:[bind(X_92,$fot(X_43)),bind(X_94,$fot(greatest_lower_bound(X_43,X_44)))]]) ).
cnf(refute_0_907,plain,
multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))))]]) ).
cnf(refute_0_908,plain,
( multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != greatest_lower_bound(X_43,X_44)
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) != multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = multiply(inverse(X_44),greatest_lower_bound(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))) ),[1,1],$fot(greatest_lower_bound(X_43,X_44))]]) ).
cnf(refute_0_909,plain,
( multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))) != greatest_lower_bound(X_43,X_44)
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = multiply(inverse(X_44),greatest_lower_bound(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))))) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) = multiply(inverse(X_44),greatest_lower_bound(X_43,X_44)),
inference(resolve,[$cnf( $equal(multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44))),greatest_lower_bound(X_43,X_44)) )],[refute_0_906,refute_0_909]) ).
cnf(refute_0_911,plain,
( multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) != multiply(inverse(X_44),greatest_lower_bound(X_43,X_44))
| multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) != greatest_lower_bound(identity,multiply(inverse(X_44),X_43))
| multiply(inverse(X_44),greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),greatest_lower_bound(identity,multiply(inverse(X_44),X_43))) ),[0],$fot(multiply(inverse(X_44),greatest_lower_bound(X_43,X_44)))]]) ).
cnf(refute_0_912,plain,
( multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))) != greatest_lower_bound(identity,multiply(inverse(X_44),X_43))
| multiply(inverse(X_44),greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),multiply(inverse(X_44),greatest_lower_bound(X_43,X_44))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
multiply(inverse(X_44),greatest_lower_bound(X_43,X_44)) = greatest_lower_bound(identity,multiply(inverse(X_44),X_43)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),multiply(X_43,multiply(inverse(X_43),greatest_lower_bound(X_43,X_44)))),greatest_lower_bound(identity,multiply(inverse(X_44),X_43))) )],[refute_0_895,refute_0_912]) ).
cnf(refute_0_914,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))),
inference(subst,[],[refute_0_913:[bind(X_43,$fot(inverse(inverse(X_279)))),bind(X_44,$fot(least_upper_bound(X_280,X_279)))]]) ).
cnf(refute_0_915,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
inference(subst,[],[refute_0_229:[bind(X_17,$fot(multiply(X,Y))),bind(X_18,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_916,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) ),[1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_917,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_637,refute_0_916]) ).
cnf(refute_0_918,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[refute_0_915,refute_0_917]) ).
cnf(refute_0_919,plain,
( greatest_lower_bound(X_17,X_18) != greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18))
| greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_17,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_17,X_18))),bind(Y0,$fot(greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18))))]]) ).
cnf(refute_0_920,plain,
greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18)) = greatest_lower_bound(X_17,X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_18,greatest_lower_bound(X_17,X_18))) )],[refute_0_236,refute_0_919]) ).
cnf(refute_0_921,plain,
greatest_lower_bound(Y,greatest_lower_bound(Z,Y)) = greatest_lower_bound(Z,Y),
inference(subst,[],[refute_0_920:[bind(X_17,$fot(Z)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_922,plain,
multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_923,plain,
( multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))
| greatest_lower_bound(Y,greatest_lower_bound(Z,Y)) != greatest_lower_bound(Z,Y)
| multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))) ),[1,1],$fot(greatest_lower_bound(Z,Y))]]) ).
cnf(refute_0_924,plain,
( greatest_lower_bound(Y,greatest_lower_bound(Z,Y)) != greatest_lower_bound(Z,Y)
| multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))) )],[refute_0_922,refute_0_923]) ).
cnf(refute_0_925,plain,
multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(Z,Y)),greatest_lower_bound(Z,Y)) )],[refute_0_921,refute_0_924]) ).
cnf(refute_0_926,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))),
inference(subst,[],[refute_0_637:[bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_927,plain,
greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))) = greatest_lower_bound(X_59,greatest_lower_bound(multiply(X,Y),multiply(X,Z))),
inference(subst,[],[refute_0_209:[bind(X,$fot(multiply(X,Z))),bind(X_16,$fot(X_59)),bind(X_17,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_928,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))) != greatest_lower_bound(X_59,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))
| greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))) = greatest_lower_bound(X_59,multiply(X,greatest_lower_bound(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))),greatest_lower_bound(X_59,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_929,plain,
( greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))) != greatest_lower_bound(X_59,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))
| greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))) = greatest_lower_bound(X_59,multiply(X,greatest_lower_bound(Y,Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_637,refute_0_928]) ).
cnf(refute_0_930,plain,
greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))) = greatest_lower_bound(X_59,multiply(X,greatest_lower_bound(Y,Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),greatest_lower_bound(X_59,multiply(X,Y))),greatest_lower_bound(X_59,greatest_lower_bound(multiply(X,Y),multiply(X,Z)))) )],[refute_0_927,refute_0_929]) ).
cnf(refute_0_931,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y))),
inference(subst,[],[refute_0_930:[bind(Y,$fot(Z)),bind(Z,$fot(Y)),bind(X_59,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_932,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y)))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))))]]) ).
cnf(refute_0_933,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y)))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))) )],[refute_0_926,refute_0_933]) ).
cnf(refute_0_935,plain,
( multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Z,Y))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_936,plain,
( multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Z,Y))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y)))) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_925,refute_0_936]) ).
cnf(refute_0_938,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),multiply(X,greatest_lower_bound(Y,Z))) ),[0],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_939,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_918,refute_0_939]) ).
cnf(refute_0_941,plain,
( multiply(X,greatest_lower_bound(Z,Y)) != multiply(X,greatest_lower_bound(Y,Z))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Z,Y)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_942,plain,
multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Z,Y)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279))),
inference(subst,[],[refute_0_942:[bind(X,$fot(inverse(least_upper_bound(X_280,X_279)))),bind(Y,$fot(least_upper_bound(X_280,X_279))),bind(Z,$fot(inverse(inverse(X_279))))]]) ).
cnf(refute_0_944,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279)))
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))))]]) ).
cnf(refute_0_945,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))),multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279)))) )],[refute_0_943,refute_0_944]) ).
cnf(refute_0_946,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(inverse(inverse(X_279)),least_upper_bound(X_280,X_279))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))) )],[refute_0_914,refute_0_945]) ).
cnf(refute_0_947,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_280,X_279)),X_279)))]]) ).
cnf(refute_0_948,plain,
( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279))))) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) = multiply(inverse(least_upper_bound(X_280,X_279)),X_279),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_280,X_279)),inverse(inverse(X_279)))),multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) )],[refute_0_865,refute_0_948]) ).
cnf(refute_0_950,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != multiply(inverse(least_upper_bound(X_280,X_279)),X_279)
| multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))
| multiply(inverse(least_upper_bound(X_280,X_279)),X_279) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))) ),[0],$fot(multiply(inverse(least_upper_bound(X_280,X_279)),X_279))]]) ).
cnf(refute_0_951,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))
| multiply(inverse(least_upper_bound(X_280,X_279)),X_279) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))),multiply(inverse(least_upper_bound(X_280,X_279)),X_279)) )],[refute_0_949,refute_0_950]) ).
cnf(refute_0_952,plain,
multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) = greatest_lower_bound(identity,inverse(X_40)),
inference(subst,[],[refute_0_523:[bind(X_35,$fot(X_40))]]) ).
cnf(refute_0_953,plain,
greatest_lower_bound(identity,X_40) = greatest_lower_bound(X_40,identity),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_954,plain,
( greatest_lower_bound(identity,X_40) != greatest_lower_bound(X_40,identity)
| greatest_lower_bound(X_40,identity) = greatest_lower_bound(identity,X_40) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(identity,X_40))),bind(Y0,$fot(greatest_lower_bound(X_40,identity)))]]) ).
cnf(refute_0_955,plain,
greatest_lower_bound(X_40,identity) = greatest_lower_bound(identity,X_40),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_40),greatest_lower_bound(X_40,identity)) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
( multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) != greatest_lower_bound(identity,inverse(X_40))
| greatest_lower_bound(X_40,identity) != greatest_lower_bound(identity,X_40)
| multiply(inverse(X_40),greatest_lower_bound(identity,X_40)) = greatest_lower_bound(identity,inverse(X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_40),greatest_lower_bound(X_40,identity)),greatest_lower_bound(identity,inverse(X_40))) ),[0,1],$fot(greatest_lower_bound(identity,X_40))]]) ).
cnf(refute_0_957,plain,
( multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) != greatest_lower_bound(identity,inverse(X_40))
| multiply(inverse(X_40),greatest_lower_bound(identity,X_40)) = greatest_lower_bound(identity,inverse(X_40)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,X_40)) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
multiply(inverse(X_40),greatest_lower_bound(identity,X_40)) = greatest_lower_bound(identity,inverse(X_40)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),greatest_lower_bound(X_40,identity)),greatest_lower_bound(identity,inverse(X_40))) )],[refute_0_952,refute_0_957]) ).
cnf(refute_0_959,plain,
multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(subst,[],[refute_0_958:[bind(X_40,$fot(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_960,plain,
greatest_lower_bound(identity,least_upper_bound(identity,Y)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_961,plain,
( multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| greatest_lower_bound(identity,least_upper_bound(identity,Y)) != identity
| multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_962,plain,
( multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,Y)),identity) )],[refute_0_960,refute_0_961]) ).
cnf(refute_0_963,plain,
multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_959,refute_0_962]) ).
cnf(refute_0_964,plain,
multiply(inverse(least_upper_bound(identity,Y)),identity) = inverse(least_upper_bound(identity,Y)),
inference(subst,[],[refute_0_331:[bind(X,$fot(inverse(least_upper_bound(identity,Y))))]]) ).
cnf(refute_0_965,plain,
( multiply(inverse(least_upper_bound(identity,Y)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| multiply(inverse(least_upper_bound(identity,Y)),identity) != inverse(least_upper_bound(identity,Y))
| inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0],$fot(inverse(least_upper_bound(identity,Y)))]]) ).
cnf(refute_0_966,plain,
( multiply(inverse(least_upper_bound(identity,Y)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),inverse(least_upper_bound(identity,Y))) )],[refute_0_964,refute_0_965]) ).
cnf(refute_0_967,plain,
inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_963,refute_0_966]) ).
cnf(refute_0_968,plain,
( inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,Y)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))))]]) ).
cnf(refute_0_969,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) = inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))),
inference(subst,[],[refute_0_969:[bind(Y,$fot(multiply(inverse(X_279),X_280)))]]) ).
cnf(refute_0_971,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),X_279) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))
| greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) != inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))
| multiply(inverse(least_upper_bound(X_280,X_279)),X_279) = inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(X_280,X_279)),X_279),inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))))]]) ).
cnf(refute_0_972,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),X_279) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))
| multiply(inverse(least_upper_bound(X_280,X_279)),X_279) = inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))),inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280)))) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
( multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))
| multiply(inverse(least_upper_bound(X_280,X_279)),X_279) = inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),X_279),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))) )],[refute_0_951,refute_0_972]) ).
cnf(refute_0_974,plain,
multiply(inverse(least_upper_bound(X_280,X_279)),X_279) = inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_280,X_279)),greatest_lower_bound(least_upper_bound(X_280,X_279),inverse(inverse(X_279)))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_279),X_280))))) )],[refute_0_850,refute_0_973]) ).
cnf(refute_0_975,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))),
inference(subst,[],[refute_0_974:[bind(X_279,$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),bind(X_280,$fot(identity))]]) ).
cnf(refute_0_976,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))
| inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) != multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_977,plain,
( inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))) != multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity)))) )],[refute_0_975,refute_0_976]) ).
cnf(refute_0_978,plain,
multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) )],[refute_0_833,refute_0_977]) ).
cnf(refute_0_979,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))
| multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) ),[0],$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))]]) ).
cnf(refute_0_980,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) )],[refute_0_978,refute_0_979]) ).
cnf(refute_0_981,plain,
multiply(identity,identity) = identity,
inference(subst,[],[refute_0_331:[bind(X,$fot(identity))]]) ).
cnf(refute_0_982,plain,
greatest_lower_bound(identity,least_upper_bound(X_352,identity)) = identity,
inference(subst,[],[refute_0_421:[bind(X_14,$fot(identity)),bind(X_15,$fot(X_352))]]) ).
cnf(refute_0_983,plain,
multiply(least_upper_bound(X_352,identity),identity) = least_upper_bound(X_352,identity),
inference(subst,[],[refute_0_331:[bind(X,$fot(least_upper_bound(X_352,identity)))]]) ).
cnf(refute_0_984,plain,
least_upper_bound(identity,multiply(X_352,identity)) = multiply(least_upper_bound(X_352,identity),identity),
inference(subst,[],[refute_0_578:[bind(X_122,$fot(identity)),bind(X_123,$fot(X_352))]]) ).
cnf(refute_0_985,plain,
( multiply(least_upper_bound(X_352,identity),identity) != least_upper_bound(X_352,identity)
| least_upper_bound(identity,multiply(X_352,identity)) != multiply(least_upper_bound(X_352,identity),identity)
| least_upper_bound(identity,multiply(X_352,identity)) = least_upper_bound(X_352,identity) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(identity,multiply(X_352,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_352,identity),identity))),bind(Z0,$fot(least_upper_bound(X_352,identity)))]]) ).
cnf(refute_0_986,plain,
( multiply(least_upper_bound(X_352,identity),identity) != least_upper_bound(X_352,identity)
| least_upper_bound(identity,multiply(X_352,identity)) = least_upper_bound(X_352,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_352,identity)),multiply(least_upper_bound(X_352,identity),identity)) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
least_upper_bound(identity,multiply(X_352,identity)) = least_upper_bound(X_352,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_352,identity),identity),least_upper_bound(X_352,identity)) )],[refute_0_983,refute_0_986]) ).
cnf(refute_0_988,plain,
multiply(X_352,least_upper_bound(identity,inverse(X_352))) = least_upper_bound(identity,multiply(X_352,identity)),
inference(subst,[],[refute_0_757:[bind(X_113,$fot(X_352)),bind(X_114,$fot(identity))]]) ).
cnf(refute_0_989,plain,
( multiply(X_352,least_upper_bound(identity,inverse(X_352))) != least_upper_bound(identity,multiply(X_352,identity))
| least_upper_bound(identity,multiply(X_352,identity)) != least_upper_bound(X_352,identity)
| multiply(X_352,least_upper_bound(identity,inverse(X_352))) = least_upper_bound(X_352,identity) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(X_352,least_upper_bound(identity,inverse(X_352))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_352,identity)))),bind(Z0,$fot(least_upper_bound(X_352,identity)))]]) ).
cnf(refute_0_990,plain,
( least_upper_bound(identity,multiply(X_352,identity)) != least_upper_bound(X_352,identity)
| multiply(X_352,least_upper_bound(identity,inverse(X_352))) = least_upper_bound(X_352,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_352,least_upper_bound(identity,inverse(X_352))),least_upper_bound(identity,multiply(X_352,identity))) )],[refute_0_988,refute_0_989]) ).
cnf(refute_0_991,plain,
multiply(X_352,least_upper_bound(identity,inverse(X_352))) = least_upper_bound(X_352,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_352,identity)),least_upper_bound(X_352,identity)) )],[refute_0_987,refute_0_990]) ).
cnf(refute_0_992,plain,
greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_993,plain,
( multiply(X_352,least_upper_bound(identity,inverse(X_352))) != least_upper_bound(X_352,identity)
| greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352))))
| greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,least_upper_bound(X_352,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352))))) ),[1,1],$fot(least_upper_bound(X_352,identity))]]) ).
cnf(refute_0_994,plain,
( multiply(X_352,least_upper_bound(identity,inverse(X_352))) != least_upper_bound(X_352,identity)
| greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,least_upper_bound(X_352,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352))))) )],[refute_0_992,refute_0_993]) ).
cnf(refute_0_995,plain,
greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,least_upper_bound(X_352,identity)),
inference(resolve,[$cnf( $equal(multiply(X_352,least_upper_bound(identity,inverse(X_352))),least_upper_bound(X_352,identity)) )],[refute_0_991,refute_0_994]) ).
cnf(refute_0_996,plain,
( greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,least_upper_bound(X_352,identity))
| greatest_lower_bound(identity,least_upper_bound(X_352,identity)) != identity
| greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) = identity ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_352,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_997,plain,
( greatest_lower_bound(identity,least_upper_bound(X_352,identity)) != identity
| greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,least_upper_bound(X_352,identity))) )],[refute_0_995,refute_0_996]) ).
cnf(refute_0_998,plain,
greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_352,identity)),identity) )],[refute_0_982,refute_0_997]) ).
cnf(refute_0_999,plain,
greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)) = greatest_lower_bound(greatest_lower_bound(X_16,least_upper_bound(X_16,Y)),X_18),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_16)),bind(Y,$fot(least_upper_bound(X_16,Y))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_1000,plain,
greatest_lower_bound(X_16,least_upper_bound(X_16,Y)) = X_16,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_1001,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)) != greatest_lower_bound(greatest_lower_bound(X_16,least_upper_bound(X_16,Y)),X_18)
| greatest_lower_bound(X_16,least_upper_bound(X_16,Y)) != X_16
| greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)) = greatest_lower_bound(X_16,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)),greatest_lower_bound(greatest_lower_bound(X_16,least_upper_bound(X_16,Y)),X_18)) ),[1,0],$fot(X_16)]]) ).
cnf(refute_0_1002,plain,
( greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)) != greatest_lower_bound(greatest_lower_bound(X_16,least_upper_bound(X_16,Y)),X_18)
| greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)) = greatest_lower_bound(X_16,X_18) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,least_upper_bound(X_16,Y)),X_16) )],[refute_0_1000,refute_0_1001]) ).
cnf(refute_0_1003,plain,
greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)) = greatest_lower_bound(X_16,X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,greatest_lower_bound(least_upper_bound(X_16,Y),X_18)),greatest_lower_bound(greatest_lower_bound(X_16,least_upper_bound(X_16,Y)),X_18)) )],[refute_0_999,refute_0_1002]) ).
cnf(refute_0_1004,plain,
greatest_lower_bound(X_158,greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))) = greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157))),
inference(subst,[],[refute_0_1003:[bind(Y,$fot(X_157)),bind(X_16,$fot(X_158)),bind(X_18,$fot(multiply(X_50,least_upper_bound(X_158,X_157))))]]) ).
cnf(refute_0_1005,plain,
multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157)) = greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157))),
inference(subst,[],[refute_0_151:[bind(X_49,$fot(least_upper_bound(X_158,X_157)))]]) ).
cnf(refute_0_1006,plain,
( multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157)) != greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))
| greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157))) = multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))))]]) ).
cnf(refute_0_1007,plain,
greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157))) = multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157)),greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
( greatest_lower_bound(X_158,greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))) != greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157)))
| greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157))) != multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157))
| greatest_lower_bound(X_158,multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157))) = greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_158,greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))),greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157)))) ),[0,1],$fot(multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157)))]]) ).
cnf(refute_0_1009,plain,
( greatest_lower_bound(X_158,greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))) != greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157)))
| greatest_lower_bound(X_158,multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157))) = greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157))),multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157))) )],[refute_0_1007,refute_0_1008]) ).
cnf(refute_0_1010,plain,
greatest_lower_bound(X_158,multiply(greatest_lower_bound(X_50,identity),least_upper_bound(X_158,X_157))) = greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_158,greatest_lower_bound(least_upper_bound(X_158,X_157),multiply(X_50,least_upper_bound(X_158,X_157)))),greatest_lower_bound(X_158,multiply(X_50,least_upper_bound(X_158,X_157)))) )],[refute_0_1004,refute_0_1009]) ).
cnf(refute_0_1011,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))),
inference(subst,[],[refute_0_1010:[bind(X_157,$fot(inverse(X_352))),bind(X_158,$fot(identity)),bind(X_50,$fot(X_352))]]) ).
cnf(refute_0_1012,plain,
( greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = identity ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1013,plain,
( greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352))))) )],[refute_0_1011,refute_0_1012]) ).
cnf(refute_0_1014,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_352,least_upper_bound(identity,inverse(X_352)))),identity) )],[refute_0_998,refute_0_1013]) ).
cnf(refute_0_1015,plain,
multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
introduced(tautology,[refl,[$fot(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_1016,plain,
( multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != identity
| multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1017,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != identity
| multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),identity) )],[refute_0_1014,refute_0_1017]) ).
cnf(refute_0_1019,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_1020,plain,
( multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| inverse(identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1021,plain,
( inverse(identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_1019,refute_0_1020]) ).
cnf(refute_0_1022,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p23_1,refute_0_1021]) ).
cnf(refute_0_1023,plain,
( multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(identity,identity)
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,identity) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))),bind(Z0,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_1024,plain,
( multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(identity,identity)
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(identity,identity)) )],[refute_0_1018,refute_0_1024]) ).
cnf(refute_0_1026,plain,
( multiply(identity,identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(identity,identity)
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = identity ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))),bind(Y0,$fot(multiply(identity,identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1027,plain,
( multiply(identity,identity) != identity
| multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(identity,identity)) )],[refute_0_1025,refute_0_1026]) ).
cnf(refute_0_1028,plain,
multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = identity,
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_981,refute_0_1027]) ).
cnf(refute_0_1029,plain,
multiply(inverse(multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))),
inference(subst,[],[refute_0_838:[bind(X_32,$fot(multiply(X,Y))),bind(X_33,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_1030,plain,
( multiply(inverse(multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))) ),[0,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_1031,plain,
( multiply(inverse(multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_637,refute_0_1030]) ).
cnf(refute_0_1032,plain,
multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))) )],[refute_0_1029,refute_0_1031]) ).
cnf(refute_0_1033,plain,
multiply(multiply(inverse(multiply(Y,X_105)),Y),Z) = multiply(inverse(multiply(Y,X_105)),multiply(Y,Z)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(multiply(Y,X_105))))]]) ).
cnf(refute_0_1034,plain,
inverse(multiply(inverse(X_95),multiply(X_95,X_96))) = multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))),
inference(subst,[],[p23_3:[bind(X,$fot(inverse(X_95))),bind(Y,$fot(multiply(X_95,X_96)))]]) ).
cnf(refute_0_1035,plain,
X_96 = multiply(inverse(X_95),multiply(X_95,X_96)),
inference(subst,[],[refute_0_96:[bind(X_93,$fot(X_95)),bind(X_94,$fot(X_96))]]) ).
cnf(refute_0_1036,plain,
( X_96 != multiply(inverse(X_95),multiply(X_95,X_96))
| multiply(inverse(X_95),multiply(X_95,X_96)) = X_96 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_96)),bind(Y0,$fot(multiply(inverse(X_95),multiply(X_95,X_96))))]]) ).
cnf(refute_0_1037,plain,
multiply(inverse(X_95),multiply(X_95,X_96)) = X_96,
inference(resolve,[$cnf( $equal(X_96,multiply(inverse(X_95),multiply(X_95,X_96))) )],[refute_0_1035,refute_0_1036]) ).
cnf(refute_0_1038,plain,
( multiply(inverse(X_95),multiply(X_95,X_96)) != X_96
| inverse(multiply(inverse(X_95),multiply(X_95,X_96))) != multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))
| inverse(X_96) = multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_95),multiply(X_95,X_96))),multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))) ),[0,0],$fot(X_96)]]) ).
cnf(refute_0_1039,plain,
( inverse(multiply(inverse(X_95),multiply(X_95,X_96))) != multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))
| inverse(X_96) = multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),multiply(X_95,X_96)),X_96) )],[refute_0_1037,refute_0_1038]) ).
cnf(refute_0_1040,plain,
inverse(X_96) = multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_95),multiply(X_95,X_96))),multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))) )],[refute_0_1034,refute_0_1039]) ).
cnf(refute_0_1041,plain,
inverse(multiply(inverse(X_95),multiply(X_95,X_96))) = multiply(inverse(multiply(X_95,X_96)),X_95),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_95)),bind(X_26,$fot(multiply(X_95,X_96)))]]) ).
cnf(refute_0_1042,plain,
multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) = inverse(multiply(inverse(X_95),multiply(X_95,X_96))),
inference(subst,[],[refute_0_502:[bind(X,$fot(inverse(X_95))),bind(Y,$fot(multiply(X_95,X_96)))]]) ).
cnf(refute_0_1043,plain,
( multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) != inverse(multiply(inverse(X_95),multiply(X_95,X_96)))
| inverse(multiply(inverse(X_95),multiply(X_95,X_96))) != multiply(inverse(multiply(X_95,X_96)),X_95)
| multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) = multiply(inverse(multiply(X_95,X_96)),X_95) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))))),bind(Y0,$fot(inverse(multiply(inverse(X_95),multiply(X_95,X_96))))),bind(Z0,$fot(multiply(inverse(multiply(X_95,X_96)),X_95)))]]) ).
cnf(refute_0_1044,plain,
( inverse(multiply(inverse(X_95),multiply(X_95,X_96))) != multiply(inverse(multiply(X_95,X_96)),X_95)
| multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) = multiply(inverse(multiply(X_95,X_96)),X_95) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))),inverse(multiply(inverse(X_95),multiply(X_95,X_96)))) )],[refute_0_1042,refute_0_1043]) ).
cnf(refute_0_1045,plain,
multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) = multiply(inverse(multiply(X_95,X_96)),X_95),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_95),multiply(X_95,X_96))),multiply(inverse(multiply(X_95,X_96)),X_95)) )],[refute_0_1041,refute_0_1044]) ).
cnf(refute_0_1046,plain,
( multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))) != multiply(inverse(multiply(X_95,X_96)),X_95)
| inverse(X_96) != multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))
| inverse(X_96) = multiply(inverse(multiply(X_95,X_96)),X_95) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_96),multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))) ),[1],$fot(multiply(inverse(multiply(X_95,X_96)),X_95))]]) ).
cnf(refute_0_1047,plain,
( inverse(X_96) != multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))
| inverse(X_96) = multiply(inverse(multiply(X_95,X_96)),X_95) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95))),multiply(inverse(multiply(X_95,X_96)),X_95)) )],[refute_0_1045,refute_0_1046]) ).
cnf(refute_0_1048,plain,
inverse(X_96) = multiply(inverse(multiply(X_95,X_96)),X_95),
inference(resolve,[$cnf( $equal(inverse(X_96),multiply(inverse(multiply(X_95,X_96)),inverse(inverse(X_95)))) )],[refute_0_1040,refute_0_1047]) ).
cnf(refute_0_1049,plain,
inverse(X_105) = multiply(inverse(multiply(Y,X_105)),Y),
inference(subst,[],[refute_0_1048:[bind(X_95,$fot(Y)),bind(X_96,$fot(X_105))]]) ).
cnf(refute_0_1050,plain,
( inverse(X_105) != multiply(inverse(multiply(Y,X_105)),Y)
| multiply(inverse(multiply(Y,X_105)),Y) = inverse(X_105) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_105))),bind(Y0,$fot(multiply(inverse(multiply(Y,X_105)),Y)))]]) ).
cnf(refute_0_1051,plain,
multiply(inverse(multiply(Y,X_105)),Y) = inverse(X_105),
inference(resolve,[$cnf( $equal(inverse(X_105),multiply(inverse(multiply(Y,X_105)),Y)) )],[refute_0_1049,refute_0_1050]) ).
cnf(refute_0_1052,plain,
( multiply(multiply(inverse(multiply(Y,X_105)),Y),Z) != multiply(inverse(multiply(Y,X_105)),multiply(Y,Z))
| multiply(inverse(multiply(Y,X_105)),Y) != inverse(X_105)
| multiply(inverse(X_105),Z) = multiply(inverse(multiply(Y,X_105)),multiply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(multiply(Y,X_105)),Y),Z),multiply(inverse(multiply(Y,X_105)),multiply(Y,Z))) ),[0,0],$fot(inverse(X_105))]]) ).
cnf(refute_0_1053,plain,
( multiply(multiply(inverse(multiply(Y,X_105)),Y),Z) != multiply(inverse(multiply(Y,X_105)),multiply(Y,Z))
| multiply(inverse(X_105),Z) = multiply(inverse(multiply(Y,X_105)),multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(Y,X_105)),Y),inverse(X_105)) )],[refute_0_1051,refute_0_1052]) ).
cnf(refute_0_1054,plain,
multiply(inverse(X_105),Z) = multiply(inverse(multiply(Y,X_105)),multiply(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(Y,X_105)),Y),Z),multiply(inverse(multiply(Y,X_105)),multiply(Y,Z))) )],[refute_0_1033,refute_0_1053]) ).
cnf(refute_0_1055,plain,
( multiply(inverse(X_105),Z) != multiply(inverse(multiply(Y,X_105)),multiply(Y,Z))
| multiply(inverse(multiply(Y,X_105)),multiply(Y,Z)) = multiply(inverse(X_105),Z) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_105),Z))),bind(Y0,$fot(multiply(inverse(multiply(Y,X_105)),multiply(Y,Z))))]]) ).
cnf(refute_0_1056,plain,
multiply(inverse(multiply(Y,X_105)),multiply(Y,Z)) = multiply(inverse(X_105),Z),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),Z),multiply(inverse(multiply(Y,X_105)),multiply(Y,Z))) )],[refute_0_1054,refute_0_1055]) ).
cnf(refute_0_1057,plain,
multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(inverse(Y),greatest_lower_bound(Y,Z)),
inference(subst,[],[refute_0_1056:[bind(Y,$fot(X)),bind(Z,$fot(greatest_lower_bound(Y,Z))),bind(X_105,$fot(Y))]]) ).
cnf(refute_0_1058,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != multiply(inverse(Y),greatest_lower_bound(Y,Z))
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| multiply(inverse(Y),greatest_lower_bound(Y,Z)) = greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))) ),[0],$fot(multiply(inverse(Y),greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_1059,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| multiply(inverse(Y),greatest_lower_bound(Y,Z)) = greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),multiply(inverse(Y),greatest_lower_bound(Y,Z))) )],[refute_0_1057,refute_0_1058]) ).
cnf(refute_0_1060,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(Y),Z),
inference(subst,[],[refute_0_1056:[bind(Y,$fot(X)),bind(X_105,$fot(Y))]]) ).
cnf(refute_0_1061,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) = greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))))]]) ).
cnf(refute_0_1062,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,Z)) != multiply(inverse(Y),Z)
| greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) = greatest_lower_bound(identity,multiply(inverse(Y),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))),greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))) ),[1,1],$fot(multiply(inverse(Y),Z))]]) ).
cnf(refute_0_1063,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,Z)) != multiply(inverse(Y),Z)
| greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) = greatest_lower_bound(identity,multiply(inverse(Y),Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))),greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))) )],[refute_0_1061,refute_0_1062]) ).
cnf(refute_0_1064,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) = greatest_lower_bound(identity,multiply(inverse(Y),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(Y),Z)) )],[refute_0_1060,refute_0_1063]) ).
cnf(refute_0_1065,plain,
( multiply(inverse(Y),greatest_lower_bound(Y,Z)) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))) != greatest_lower_bound(identity,multiply(inverse(Y),Z))
| multiply(inverse(Y),greatest_lower_bound(Y,Z)) = greatest_lower_bound(identity,multiply(inverse(Y),Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(Y),greatest_lower_bound(Y,Z)),greatest_lower_bound(identity,multiply(inverse(Y),Z))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))))]]) ).
cnf(refute_0_1066,plain,
( multiply(inverse(Y),greatest_lower_bound(Y,Z)) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| multiply(inverse(Y),greatest_lower_bound(Y,Z)) = greatest_lower_bound(identity,multiply(inverse(Y),Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z))),greatest_lower_bound(identity,multiply(inverse(Y),Z))) )],[refute_0_1064,refute_0_1065]) ).
cnf(refute_0_1067,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))
| multiply(inverse(Y),greatest_lower_bound(Y,Z)) = greatest_lower_bound(identity,multiply(inverse(Y),Z)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),greatest_lower_bound(Y,Z)),greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))) )],[refute_0_1059,refute_0_1066]) ).
cnf(refute_0_1068,plain,
multiply(inverse(Y),greatest_lower_bound(Y,Z)) = greatest_lower_bound(identity,multiply(inverse(Y),Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(identity,multiply(inverse(multiply(X,Y)),multiply(X,Z)))) )],[refute_0_1032,refute_0_1067]) ).
cnf(refute_0_1069,plain,
( multiply(inverse(Y),greatest_lower_bound(Y,Z)) != greatest_lower_bound(identity,multiply(inverse(Y),Z))
| greatest_lower_bound(identity,multiply(inverse(Y),Z)) = multiply(inverse(Y),greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(Y),greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(Y),Z))))]]) ).
cnf(refute_0_1070,plain,
greatest_lower_bound(identity,multiply(inverse(Y),Z)) = multiply(inverse(Y),greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),greatest_lower_bound(Y,Z)),greatest_lower_bound(identity,multiply(inverse(Y),Z))) )],[refute_0_1068,refute_0_1069]) ).
cnf(refute_0_1071,plain,
greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),
inference(subst,[],[refute_0_1070:[bind(Y,$fot(identity)),bind(Z,$fot(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))]]) ).
cnf(refute_0_1072,plain,
( multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != identity
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = identity ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))),bind(Y0,$fot(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1073,plain,
( multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != identity
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_1071,refute_0_1072]) ).
cnf(refute_0_1074,plain,
greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) )],[refute_0_1028,refute_0_1073]) ).
cnf(refute_0_1075,plain,
( multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))) != identity
| multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))))]]) ).
cnf(refute_0_1076,plain,
( multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),identity) )],[refute_0_1074,refute_0_1075]) ).
cnf(refute_0_1077,plain,
( multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))) != greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))
| multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))),greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_980,refute_0_1076]) ).
cnf(refute_0_1078,plain,
multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352))))),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))),greatest_lower_bound(identity,multiply(inverse(identity),multiply(greatest_lower_bound(X_352,identity),least_upper_bound(identity,inverse(X_352)))))) )],[refute_0_747,refute_0_1077]) ).
cnf(refute_0_1079,plain,
multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) = identity,
inference(subst,[],[refute_0_1078:[bind(X_352,$fot(X_35))]]) ).
cnf(refute_0_1080,plain,
inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) = inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),
introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))))]]) ).
cnf(refute_0_1081,plain,
( multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) != identity
| inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) != inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))
| inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1082,plain,
( multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))) != identity
| inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))))) )],[refute_0_1080,refute_0_1081]) ).
cnf(refute_0_1083,plain,
inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35))),identity) )],[refute_0_1079,refute_0_1082]) ).
cnf(refute_0_1084,plain,
( inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) != inverse(identity)
| inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) = identity ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1085,plain,
( inverse(identity) != identity
| inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),inverse(identity)) )],[refute_0_1083,refute_0_1084]) ).
cnf(refute_0_1086,plain,
inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p23_1,refute_0_1085]) ).
cnf(refute_0_1087,plain,
multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) = multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)))]]) ).
cnf(refute_0_1088,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) != multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))
| inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) = multiply(identity,least_upper_bound(identity,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)),multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1089,plain,
( inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))) != identity
| multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) = multiply(identity,least_upper_bound(identity,X_35)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)),multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))) )],[refute_0_1087,refute_0_1088]) ).
cnf(refute_0_1090,plain,
multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) = multiply(identity,least_upper_bound(identity,X_35)),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),identity) )],[refute_0_1086,refute_0_1089]) ).
cnf(refute_0_1091,plain,
( multiply(identity,least_upper_bound(identity,X_35)) != least_upper_bound(identity,X_35)
| multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) != multiply(identity,least_upper_bound(identity,X_35))
| multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) = least_upper_bound(identity,X_35) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,X_35)))),bind(Z0,$fot(least_upper_bound(identity,X_35)))]]) ).
cnf(refute_0_1092,plain,
( multiply(identity,least_upper_bound(identity,X_35)) != least_upper_bound(identity,X_35)
| multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) = least_upper_bound(identity,X_35) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)),multiply(identity,least_upper_bound(identity,X_35))) )],[refute_0_1090,refute_0_1091]) ).
cnf(refute_0_1093,plain,
multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) = least_upper_bound(identity,X_35),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,X_35)),least_upper_bound(identity,X_35)) )],[refute_0_717,refute_0_1092]) ).
cnf(refute_0_1094,plain,
( multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)) != least_upper_bound(identity,X_35)
| inverse(greatest_lower_bound(identity,inverse(X_35))) != multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))
| inverse(greatest_lower_bound(identity,inverse(X_35))) = least_upper_bound(identity,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_35))),multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))) ),[1],$fot(least_upper_bound(identity,X_35))]]) ).
cnf(refute_0_1095,plain,
( inverse(greatest_lower_bound(identity,inverse(X_35))) != multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))
| inverse(greatest_lower_bound(identity,inverse(X_35))) = least_upper_bound(identity,X_35) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35)),least_upper_bound(identity,X_35)) )],[refute_0_1093,refute_0_1094]) ).
cnf(refute_0_1096,plain,
inverse(greatest_lower_bound(identity,inverse(X_35))) = least_upper_bound(identity,X_35),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_35))),multiply(inverse(multiply(greatest_lower_bound(X_35,identity),least_upper_bound(identity,inverse(X_35)))),least_upper_bound(identity,X_35))) )],[refute_0_716,refute_0_1095]) ).
cnf(refute_0_1097,plain,
inverse(greatest_lower_bound(identity,inverse(X_89))) = least_upper_bound(identity,X_89),
inference(subst,[],[refute_0_1096:[bind(X_35,$fot(X_89))]]) ).
cnf(refute_0_1098,plain,
least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))),
introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))]]) ).
cnf(refute_0_1099,plain,
( inverse(greatest_lower_bound(identity,inverse(X_89))) != least_upper_bound(identity,X_89)
| least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) != least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))
| least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))),least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) ),[1,1],$fot(least_upper_bound(identity,X_89))]]) ).
cnf(refute_0_1100,plain,
( inverse(greatest_lower_bound(identity,inverse(X_89))) != least_upper_bound(identity,X_89)
| least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))),least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_89))),least_upper_bound(identity,X_89)) )],[refute_0_1097,refute_0_1100]) ).
cnf(refute_0_1102,plain,
( least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) != least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89))
| least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) != least_upper_bound(identity,X_89)
| least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) = least_upper_bound(identity,X_89) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)))),bind(Z0,$fot(least_upper_bound(identity,X_89)))]]) ).
cnf(refute_0_1103,plain,
( least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)) != least_upper_bound(identity,X_89)
| least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) = least_upper_bound(identity,X_89) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))),least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89))) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) = least_upper_bound(identity,X_89),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_89,identity),least_upper_bound(identity,X_89)),least_upper_bound(identity,X_89)) )],[refute_0_498,refute_0_1103]) ).
cnf(refute_0_1105,plain,
inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) = inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))))]]) ).
cnf(refute_0_1106,plain,
( inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) != inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))
| least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) != least_upper_bound(identity,X_89)
| inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) = inverse(least_upper_bound(identity,X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))) ),[1,0],$fot(least_upper_bound(identity,X_89))]]) ).
cnf(refute_0_1107,plain,
( least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))) != least_upper_bound(identity,X_89)
| inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) = inverse(least_upper_bound(identity,X_89)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))) )],[refute_0_1105,refute_0_1106]) ).
cnf(refute_0_1108,plain,
inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) = inverse(least_upper_bound(identity,X_89)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))),least_upper_bound(identity,X_89)) )],[refute_0_1104,refute_0_1107]) ).
cnf(refute_0_1109,plain,
( greatest_lower_bound(identity,inverse(X_89)) != inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))
| inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))) != inverse(least_upper_bound(identity,X_89))
| greatest_lower_bound(identity,inverse(X_89)) = inverse(least_upper_bound(identity,X_89)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,inverse(X_89)),inverse(least_upper_bound(identity,X_89))) ),[0],$fot(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))))]]) ).
cnf(refute_0_1110,plain,
( greatest_lower_bound(identity,inverse(X_89)) != inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))
| greatest_lower_bound(identity,inverse(X_89)) = inverse(least_upper_bound(identity,X_89)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89))))),inverse(least_upper_bound(identity,X_89))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
greatest_lower_bound(identity,inverse(X_89)) = inverse(least_upper_bound(identity,X_89)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_89)),inverse(least_upper_bound(greatest_lower_bound(X_89,identity),inverse(greatest_lower_bound(identity,inverse(X_89)))))) )],[refute_0_350,refute_0_1110]) ).
cnf(refute_0_1112,plain,
greatest_lower_bound(identity,inverse(multiply(a,b))) = inverse(least_upper_bound(identity,multiply(a,b))),
inference(subst,[],[refute_0_1111:[bind(X_89,$fot(multiply(a,b)))]]) ).
cnf(refute_0_1113,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))))]]) ).
cnf(refute_0_1114,plain,
( greatest_lower_bound(identity,inverse(multiply(a,b))) != inverse(least_upper_bound(identity,multiply(a,b)))
| inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) != inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))
| inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = inverse(inverse(least_upper_bound(identity,multiply(a,b)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))) ),[1,0],$fot(inverse(least_upper_bound(identity,multiply(a,b))))]]) ).
cnf(refute_0_1115,plain,
( greatest_lower_bound(identity,inverse(multiply(a,b))) != inverse(least_upper_bound(identity,multiply(a,b)))
| inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = inverse(inverse(least_upper_bound(identity,multiply(a,b)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))) )],[refute_0_1113,refute_0_1114]) ).
cnf(refute_0_1116,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = inverse(inverse(least_upper_bound(identity,multiply(a,b)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(a,b))),inverse(least_upper_bound(identity,multiply(a,b)))) )],[refute_0_1112,refute_0_1115]) ).
cnf(refute_0_1117,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) != inverse(inverse(least_upper_bound(identity,multiply(a,b))))
| inverse(inverse(least_upper_bound(identity,multiply(a,b)))) != least_upper_bound(identity,multiply(a,b))
| inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = least_upper_bound(identity,multiply(a,b)) ),
inference(subst,[],[refute_0_214:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(identity,multiply(a,b)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).
cnf(refute_0_1118,plain,
( inverse(inverse(least_upper_bound(identity,multiply(a,b)))) != least_upper_bound(identity,multiply(a,b))
| inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = least_upper_bound(identity,multiply(a,b)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),inverse(inverse(least_upper_bound(identity,multiply(a,b))))) )],[refute_0_1116,refute_0_1117]) ).
cnf(refute_0_1119,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(a,b)))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_87,refute_0_1118]) ).
cnf(refute_0_1120,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(a,b)),inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))) ),[1],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_1121,plain,
( least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b))
| least_upper_bound(identity,multiply(a,b)) = inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_1119,refute_0_1120]) ).
cnf(refute_0_1122,plain,
least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(a,b)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))) )],[refute_0_1121,refute_0_86]) ).
cnf(refute_0_1123,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(a,b)))]]) ).
cnf(refute_0_1124,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))) )],[refute_0_1123,refute_0_1122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 19:13:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 11.69/11.86 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.69/11.86
% 11.69/11.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.81/11.98
%------------------------------------------------------------------------------