TSTP Solution File: GRP183-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP183-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 10:37:46 EDT 2022
% Result : Unsatisfiable 30.00s 30.18s
% Output : CNFRefutation 30.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 526
% Syntax : Number of clauses : 2550 (1308 unt; 0 nHn;1246 RR)
% Number of literals : 4334 (4333 equ;1790 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 5165 ( 102 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p20x_1,hypothesis,
inverse(identity) = identity ).
cnf(p20x_2,hypothesis,
inverse(inverse(X)) = X ).
cnf(p20x_3,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).
cnf(prove_20x,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity ).
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( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(inverse(a),identity) = least_upper_bound(identity,inverse(a)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_6,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)))]]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity))
| least_upper_bound(inverse(a),identity) != least_upper_bound(identity,inverse(a))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity))) ),[1,1],$fot(least_upper_bound(identity,inverse(a)))]]) ).
cnf(refute_0_8,plain,
( least_upper_bound(inverse(a),identity) != least_upper_bound(identity,inverse(a))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),identity),least_upper_bound(identity,inverse(a))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a)))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a)))) ),[1],$fot(identity)]]) ).
cnf(refute_0_11,plain,
( greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),identity) )],[refute_0_11,prove_20x]) ).
cnf(refute_0_13,plain,
multiply(greatest_lower_bound(X_43,identity),X_42) = greatest_lower_bound(multiply(X_43,X_42),multiply(identity,X_42)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_14,plain,
multiply(identity,X_42) = X_42,
inference(subst,[],[left_identity:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_15,plain,
( multiply(greatest_lower_bound(X_43,identity),X_42) != greatest_lower_bound(multiply(X_43,X_42),multiply(identity,X_42))
| multiply(identity,X_42) != X_42
| multiply(greatest_lower_bound(X_43,identity),X_42) = greatest_lower_bound(multiply(X_43,X_42),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_43,identity),X_42),greatest_lower_bound(multiply(X_43,X_42),multiply(identity,X_42))) ),[1,1],$fot(X_42)]]) ).
cnf(refute_0_16,plain,
( multiply(greatest_lower_bound(X_43,identity),X_42) != greatest_lower_bound(multiply(X_43,X_42),multiply(identity,X_42))
| multiply(greatest_lower_bound(X_43,identity),X_42) = greatest_lower_bound(multiply(X_43,X_42),X_42) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_42),X_42) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(greatest_lower_bound(X_43,identity),X_42) = greatest_lower_bound(multiply(X_43,X_42),X_42),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,identity),X_42),greatest_lower_bound(multiply(X_43,X_42),multiply(identity,X_42))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
greatest_lower_bound(X_28,X_27) = greatest_lower_bound(X_27,X_28),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_28)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_19,plain,
greatest_lower_bound(multiply(X_43,X_42),X_42) = greatest_lower_bound(X_42,multiply(X_43,X_42)),
inference(subst,[],[refute_0_18:[bind(X_27,$fot(X_42)),bind(X_28,$fot(multiply(X_43,X_42)))]]) ).
cnf(refute_0_20,plain,
( multiply(greatest_lower_bound(X_43,identity),X_42) != greatest_lower_bound(multiply(X_43,X_42),X_42)
| greatest_lower_bound(multiply(X_43,X_42),X_42) != greatest_lower_bound(X_42,multiply(X_43,X_42))
| multiply(greatest_lower_bound(X_43,identity),X_42) = greatest_lower_bound(X_42,multiply(X_43,X_42)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_43,identity),X_42),greatest_lower_bound(X_42,multiply(X_43,X_42))) ),[0],$fot(greatest_lower_bound(multiply(X_43,X_42),X_42))]]) ).
cnf(refute_0_21,plain,
( multiply(greatest_lower_bound(X_43,identity),X_42) != greatest_lower_bound(multiply(X_43,X_42),X_42)
| multiply(greatest_lower_bound(X_43,identity),X_42) = greatest_lower_bound(X_42,multiply(X_43,X_42)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_43,X_42),X_42),greatest_lower_bound(X_42,multiply(X_43,X_42))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(greatest_lower_bound(X_43,identity),X_42) = greatest_lower_bound(X_42,multiply(X_43,X_42)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,identity),X_42),greatest_lower_bound(multiply(X_43,X_42),X_42)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) = greatest_lower_bound(least_upper_bound(X_95,identity),multiply(inverse(X_95),least_upper_bound(X_95,identity))),
inference(subst,[],[refute_0_22:[bind(X_42,$fot(least_upper_bound(X_95,identity))),bind(X_43,$fot(inverse(X_95)))]]) ).
cnf(refute_0_24,plain,
multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_75)),bind(Y,$fot(X_76)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_25,plain,
inverse(multiply(identity,X_23)) = multiply(inverse(X_23),inverse(identity)),
inference(subst,[],[p20x_3:[bind(X,$fot(identity)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_26,plain,
( inverse(multiply(identity,X_23)) != multiply(inverse(X_23),inverse(identity))
| inverse(identity) != identity
| inverse(multiply(identity,X_23)) = multiply(inverse(X_23),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_23)),multiply(inverse(X_23),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_27,plain,
( inverse(multiply(identity,X_23)) != multiply(inverse(X_23),inverse(identity))
| inverse(multiply(identity,X_23)) = multiply(inverse(X_23),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p20x_1,refute_0_26]) ).
cnf(refute_0_28,plain,
inverse(multiply(identity,X_23)) = multiply(inverse(X_23),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_23)),multiply(inverse(X_23),inverse(identity))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(identity,X_23) = X_23,
inference(subst,[],[left_identity:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_30,plain,
inverse(multiply(identity,X_23)) = inverse(multiply(identity,X_23)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_23)))]]) ).
cnf(refute_0_31,plain,
( multiply(identity,X_23) != X_23
| inverse(multiply(identity,X_23)) != inverse(multiply(identity,X_23))
| inverse(multiply(identity,X_23)) = inverse(X_23) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_23)),inverse(multiply(identity,X_23))) ),[1,0],$fot(X_23)]]) ).
cnf(refute_0_32,plain,
( multiply(identity,X_23) != X_23
| inverse(multiply(identity,X_23)) = inverse(X_23) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_23)),inverse(multiply(identity,X_23))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
inverse(multiply(identity,X_23)) = inverse(X_23),
inference(resolve,[$cnf( $equal(multiply(identity,X_23),X_23) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( inverse(multiply(identity,X_23)) != multiply(inverse(X_23),identity)
| inverse(multiply(identity,X_23)) != inverse(X_23)
| inverse(X_23) = multiply(inverse(X_23),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_23)),multiply(inverse(X_23),identity)) ),[0],$fot(inverse(X_23))]]) ).
cnf(refute_0_35,plain,
( inverse(multiply(identity,X_23)) != multiply(inverse(X_23),identity)
| inverse(X_23) = multiply(inverse(X_23),identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_23)),inverse(X_23)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
inverse(X_23) = multiply(inverse(X_23),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_23)),multiply(inverse(X_23),identity)) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
inference(subst,[],[refute_0_36:[bind(X_23,$fot(inverse(X)))]]) ).
cnf(refute_0_38,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_39,plain,
( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_38]) ).
cnf(refute_0_40,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) ),[0],$fot(X)]]) ).
cnf(refute_0_42,plain,
( inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_41]) ).
cnf(refute_0_43,plain,
X = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
X_75 = multiply(X_75,identity),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_75))]]) ).
cnf(refute_0_45,plain,
( X_75 != multiply(X_75,identity)
| multiply(X_75,identity) = X_75 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_75)),bind(Y0,$fot(multiply(X_75,identity)))]]) ).
cnf(refute_0_46,plain,
multiply(X_75,identity) = X_75,
inference(resolve,[$cnf( $equal(X_75,multiply(X_75,identity)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( multiply(X_75,identity) != X_75
| multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))) ),[1,1],$fot(X_75)]]) ).
cnf(refute_0_48,plain,
( multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),X_75) ),
inference(resolve,[$cnf( $equal(multiply(X_75,identity),X_75) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(multiply(X_75,X_76),X_75),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,identity))) )],[refute_0_24,refute_0_48]) ).
cnf(refute_0_50,plain,
least_upper_bound(multiply(X_75,X_76),X_75) = least_upper_bound(X_75,multiply(X_75,X_76)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_75)),bind(Y,$fot(multiply(X_75,X_76)))]]) ).
cnf(refute_0_51,plain,
( multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),X_75)
| least_upper_bound(multiply(X_75,X_76),X_75) != least_upper_bound(X_75,multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(X_75,multiply(X_75,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(X_75,multiply(X_75,X_76))) ),[0],$fot(least_upper_bound(multiply(X_75,X_76),X_75))]]) ).
cnf(refute_0_52,plain,
( multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(multiply(X_75,X_76),X_75)
| multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(X_75,multiply(X_75,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_75,X_76),X_75),least_upper_bound(X_75,multiply(X_75,X_76))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(X_75,least_upper_bound(X_76,identity)) = least_upper_bound(X_75,multiply(X_75,X_76)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(multiply(X_75,X_76),X_75)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(inverse(X_94),multiply(inverse(X_94),X_94)),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(inverse(X_94))),bind(X_76,$fot(X_94))]]) ).
cnf(refute_0_55,plain,
multiply(inverse(X_94),X_94) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_94))]]) ).
cnf(refute_0_56,plain,
( multiply(inverse(X_94),X_94) != identity
| multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(inverse(X_94),multiply(inverse(X_94),X_94))
| multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(inverse(X_94),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),least_upper_bound(inverse(X_94),multiply(inverse(X_94),X_94))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_57,plain,
( multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(inverse(X_94),multiply(inverse(X_94),X_94))
| multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(inverse(X_94),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_94),X_94),identity) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(inverse(X_94),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),least_upper_bound(inverse(X_94),multiply(inverse(X_94),X_94))) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
least_upper_bound(inverse(X_94),identity) = least_upper_bound(identity,inverse(X_94)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_94)))]]) ).
cnf(refute_0_60,plain,
( multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(inverse(X_94),identity)
| least_upper_bound(inverse(X_94),identity) != least_upper_bound(identity,inverse(X_94))
| multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(identity,inverse(X_94)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),least_upper_bound(identity,inverse(X_94))) ),[0],$fot(least_upper_bound(inverse(X_94),identity))]]) ).
cnf(refute_0_61,plain,
( multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(inverse(X_94),identity)
| multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(identity,inverse(X_94)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_94),identity),least_upper_bound(identity,inverse(X_94))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(identity,inverse(X_94)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),least_upper_bound(inverse(X_94),identity)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(inverse(X_95),least_upper_bound(X_95,identity)) = least_upper_bound(identity,inverse(X_95)),
inference(subst,[],[refute_0_62:[bind(X_94,$fot(X_95))]]) ).
cnf(refute_0_64,plain,
( multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) != greatest_lower_bound(least_upper_bound(X_95,identity),multiply(inverse(X_95),least_upper_bound(X_95,identity)))
| multiply(inverse(X_95),least_upper_bound(X_95,identity)) != least_upper_bound(identity,inverse(X_95))
| multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)),greatest_lower_bound(least_upper_bound(X_95,identity),multiply(inverse(X_95),least_upper_bound(X_95,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_95)))]]) ).
cnf(refute_0_65,plain,
( multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) != greatest_lower_bound(least_upper_bound(X_95,identity),multiply(inverse(X_95),least_upper_bound(X_95,identity)))
| multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(X_95,identity)),least_upper_bound(identity,inverse(X_95))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)),greatest_lower_bound(least_upper_bound(X_95,identity),multiply(inverse(X_95),least_upper_bound(X_95,identity)))) )],[refute_0_23,refute_0_65]) ).
cnf(refute_0_67,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)) = greatest_lower_bound(greatest_lower_bound(X_27,X_27),X_28),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_27)),bind(Y,$fot(X_27)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_68,plain,
greatest_lower_bound(X_27,X_27) = X_27,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_69,plain,
( greatest_lower_bound(X_27,X_27) != X_27
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)) != greatest_lower_bound(greatest_lower_bound(X_27,X_27),X_28)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)) = greatest_lower_bound(X_27,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)),greatest_lower_bound(greatest_lower_bound(X_27,X_27),X_28)) ),[1,0],$fot(X_27)]]) ).
cnf(refute_0_70,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)) != greatest_lower_bound(greatest_lower_bound(X_27,X_27),X_28)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)) = greatest_lower_bound(X_27,X_28) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,X_27),X_27) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)) = greatest_lower_bound(X_27,X_28),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,X_28)),greatest_lower_bound(greatest_lower_bound(X_27,X_27),X_28)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = greatest_lower_bound(X_27,multiply(X_88,X_27)),
inference(subst,[],[refute_0_71:[bind(X_28,$fot(multiply(X_88,X_27)))]]) ).
cnf(refute_0_73,plain,
multiply(greatest_lower_bound(X_88,identity),X_27) = greatest_lower_bound(X_27,multiply(X_88,X_27)),
inference(subst,[],[refute_0_22:[bind(X_42,$fot(X_27)),bind(X_43,$fot(X_88))]]) ).
cnf(refute_0_74,plain,
( multiply(greatest_lower_bound(X_88,identity),X_27) != greatest_lower_bound(X_27,multiply(X_88,X_27))
| greatest_lower_bound(X_27,multiply(X_88,X_27)) = multiply(greatest_lower_bound(X_88,identity),X_27) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_88,identity),X_27))),bind(Y0,$fot(greatest_lower_bound(X_27,multiply(X_88,X_27))))]]) ).
cnf(refute_0_75,plain,
greatest_lower_bound(X_27,multiply(X_88,X_27)) = multiply(greatest_lower_bound(X_88,identity),X_27),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),X_27),greatest_lower_bound(X_27,multiply(X_88,X_27))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( greatest_lower_bound(X_27,multiply(X_88,X_27)) != multiply(greatest_lower_bound(X_88,identity),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) != greatest_lower_bound(X_27,multiply(X_88,X_27))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(X_88,identity),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))),greatest_lower_bound(X_27,multiply(X_88,X_27))) ),[1],$fot(multiply(greatest_lower_bound(X_88,identity),X_27))]]) ).
cnf(refute_0_77,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) != greatest_lower_bound(X_27,multiply(X_88,X_27))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(X_88,identity),X_27) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_88,X_27)),multiply(greatest_lower_bound(X_88,identity),X_27)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(X_88,identity),X_27),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))),greatest_lower_bound(X_27,multiply(X_88,X_27))) )],[refute_0_72,refute_0_77]) ).
cnf(refute_0_79,plain,
greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) = X_12,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_80,plain,
least_upper_bound(X_13,X_12) = least_upper_bound(X_12,X_13),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_81,plain,
( least_upper_bound(X_13,X_12) != least_upper_bound(X_12,X_13)
| least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_13,X_12))),bind(Y0,$fot(least_upper_bound(X_12,X_13)))]]) ).
cnf(refute_0_82,plain,
least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,X_12),least_upper_bound(X_12,X_13)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,X_13) != least_upper_bound(X_13,X_12)
| greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) ),[0,1],$fot(least_upper_bound(X_13,X_12))]]) ).
cnf(refute_0_84,plain,
( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
| greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_12,X_13),least_upper_bound(X_13,X_12)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) )],[refute_0_79,refute_0_84]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))) = greatest_lower_bound(X_21,Y),
inference(subst,[],[refute_0_85:[bind(X_12,$fot(greatest_lower_bound(X_21,Y))),bind(X_13,$fot(X_21))]]) ).
cnf(refute_0_87,plain,
least_upper_bound(X_21,greatest_lower_bound(X_21,Y)) = X_21,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_88,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))) != greatest_lower_bound(X_21,Y)
| least_upper_bound(X_21,greatest_lower_bound(X_21,Y)) != X_21
| greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))),greatest_lower_bound(X_21,Y)) ),[0,1],$fot(X_21)]]) ).
cnf(refute_0_89,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))) != greatest_lower_bound(X_21,Y)
| greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,greatest_lower_bound(X_21,Y)),X_21) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),least_upper_bound(X_21,greatest_lower_bound(X_21,Y))),greatest_lower_bound(X_21,Y)) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_92,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_91]) ).
cnf(refute_0_93,plain,
greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) = greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_21)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_94,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) != greatest_lower_bound(X_21,Y)
| greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) != greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))
| greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) = greatest_lower_bound(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21),greatest_lower_bound(X_21,Y)) ),[0],$fot(greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)))]]) ).
cnf(refute_0_95,plain,
( greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21) != greatest_lower_bound(X_21,Y)
| greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) = greatest_lower_bound(X_21,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21),greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
greatest_lower_bound(X_21,greatest_lower_bound(Y,X_21)) = greatest_lower_bound(X_21,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_21,Y),X_21),greatest_lower_bound(X_21,Y)) )],[refute_0_90,refute_0_95]) ).
cnf(refute_0_97,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)) = greatest_lower_bound(identity,X_88),
inference(subst,[],[refute_0_96:[bind(Y,$fot(X_88)),bind(X_21,$fot(identity))]]) ).
cnf(refute_0_98,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27))]]) ).
cnf(refute_0_99,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)
| greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)) != greatest_lower_bound(identity,X_88)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) = multiply(greatest_lower_bound(identity,X_88),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)) ),[1,0],$fot(greatest_lower_bound(identity,X_88))]]) ).
cnf(refute_0_100,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)) != greatest_lower_bound(identity,X_88)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) = multiply(greatest_lower_bound(identity,X_88),X_27) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) = multiply(greatest_lower_bound(identity,X_88),X_27),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),greatest_lower_bound(identity,X_88)) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) = greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_44,X_42))),bind(Y,$fot(multiply(X_43,X_42)))]]) ).
cnf(refute_0_103,plain,
multiply(greatest_lower_bound(X_43,X_44),X_42) = greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_104,plain,
( multiply(greatest_lower_bound(X_43,X_44),X_42) != greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42))
| greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42)) = multiply(greatest_lower_bound(X_43,X_44),X_42) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_43,X_44),X_42))),bind(Y0,$fot(greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42))))]]) ).
cnf(refute_0_105,plain,
greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42)) = multiply(greatest_lower_bound(X_43,X_44),X_42),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,X_44),X_42),greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42)) != multiply(greatest_lower_bound(X_43,X_44),X_42)
| greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) != greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42))
| greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) = multiply(greatest_lower_bound(X_43,X_44),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)),greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42))) ),[1],$fot(multiply(greatest_lower_bound(X_43,X_44),X_42))]]) ).
cnf(refute_0_107,plain,
( greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) != greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42))
| greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) = multiply(greatest_lower_bound(X_43,X_44),X_42) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42)),multiply(greatest_lower_bound(X_43,X_44),X_42)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) = multiply(greatest_lower_bound(X_43,X_44),X_42),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)),greatest_lower_bound(multiply(X_43,X_42),multiply(X_44,X_42))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_110,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_109]) ).
cnf(refute_0_111,plain,
greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) = multiply(greatest_lower_bound(X_44,X_43),X_42),
inference(subst,[],[refute_0_110:[bind(X,$fot(X_42)),bind(Y,$fot(X_44)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_112,plain,
( greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) != multiply(greatest_lower_bound(X_43,X_44),X_42)
| greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) != multiply(greatest_lower_bound(X_44,X_43),X_42)
| multiply(greatest_lower_bound(X_44,X_43),X_42) = multiply(greatest_lower_bound(X_43,X_44),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)),multiply(greatest_lower_bound(X_43,X_44),X_42)) ),[0],$fot(multiply(greatest_lower_bound(X_44,X_43),X_42))]]) ).
cnf(refute_0_113,plain,
( greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)) != multiply(greatest_lower_bound(X_43,X_44),X_42)
| multiply(greatest_lower_bound(X_44,X_43),X_42) = multiply(greatest_lower_bound(X_43,X_44),X_42) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)),multiply(greatest_lower_bound(X_44,X_43),X_42)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(greatest_lower_bound(X_44,X_43),X_42) = multiply(greatest_lower_bound(X_43,X_44),X_42),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_44,X_42),multiply(X_43,X_42)),multiply(greatest_lower_bound(X_43,X_44),X_42)) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
( multiply(greatest_lower_bound(X_44,X_43),X_42) != multiply(greatest_lower_bound(X_43,X_44),X_42)
| multiply(greatest_lower_bound(X_43,X_44),X_42) = multiply(greatest_lower_bound(X_44,X_43),X_42) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_44,X_43),X_42))),bind(Y0,$fot(multiply(greatest_lower_bound(X_43,X_44),X_42)))]]) ).
cnf(refute_0_116,plain,
multiply(greatest_lower_bound(X_43,X_44),X_42) = multiply(greatest_lower_bound(X_44,X_43),X_42),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_44,X_43),X_42),multiply(greatest_lower_bound(X_43,X_44),X_42)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27),
inference(subst,[],[refute_0_116:[bind(X_42,$fot(X_27)),bind(X_43,$fot(greatest_lower_bound(X_88,identity))),bind(X_44,$fot(identity))]]) ).
cnf(refute_0_118,plain,
( multiply(greatest_lower_bound(X_43,identity),X_42) != greatest_lower_bound(X_42,multiply(X_43,X_42))
| greatest_lower_bound(X_42,multiply(X_43,X_42)) = multiply(greatest_lower_bound(X_43,identity),X_42) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_43,identity),X_42))),bind(Y0,$fot(greatest_lower_bound(X_42,multiply(X_43,X_42))))]]) ).
cnf(refute_0_119,plain,
greatest_lower_bound(X_42,multiply(X_43,X_42)) = multiply(greatest_lower_bound(X_43,identity),X_42),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,identity),X_42),greatest_lower_bound(X_42,multiply(X_43,X_42))) )],[refute_0_22,refute_0_118]) ).
cnf(refute_0_120,plain,
greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)) = multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27),
inference(subst,[],[refute_0_119:[bind(X_42,$fot(X_27)),bind(X_43,$fot(greatest_lower_bound(X_88,identity)))]]) ).
cnf(refute_0_121,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_122,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_121]) ).
cnf(refute_0_123,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)
| greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)) != multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27)
| greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)))),bind(Y0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)))]]) ).
cnf(refute_0_124,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)
| greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)),multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27)) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_88,identity),identity),X_27),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)) )],[refute_0_117,refute_0_124]) ).
cnf(refute_0_126,plain,
greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_26,X_27)))]]) ).
cnf(refute_0_127,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X))]]) ).
cnf(refute_0_128,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),X) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)))]]) ).
cnf(refute_0_129,plain,
greatest_lower_bound(greatest_lower_bound(X_26,X_27),X) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),X) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))
| greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X))]]) ).
cnf(refute_0_131,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)
| greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X)) )],[refute_0_126,refute_0_131]) ).
cnf(refute_0_133,plain,
greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_88,X_27))),
inference(subst,[],[refute_0_132:[bind(X,$fot(multiply(X_88,X_27)))]]) ).
cnf(refute_0_134,plain,
( greatest_lower_bound(X_27,multiply(X_88,X_27)) != multiply(greatest_lower_bound(X_88,identity),X_27)
| greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_88,X_27)))
| greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_88,X_27)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_88,identity),X_27))]]) ).
cnf(refute_0_135,plain,
( greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_88,X_27)))
| greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_88,X_27)),multiply(greatest_lower_bound(X_88,identity),X_27)) )],[refute_0_75,refute_0_134]) ).
cnf(refute_0_136,plain,
greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_88,X_27)))) )],[refute_0_133,refute_0_135]) ).
cnf(refute_0_137,plain,
greatest_lower_bound(X_45,greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45)),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_45)),bind(X_26,$fot(X_46)),bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_138,plain,
greatest_lower_bound(X_47,X_46) = greatest_lower_bound(X_46,X_47),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_47)),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_139,plain,
( greatest_lower_bound(X_47,X_46) != greatest_lower_bound(X_46,X_47)
| greatest_lower_bound(X_46,X_47) = greatest_lower_bound(X_47,X_46) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_47,X_46))),bind(Y0,$fot(greatest_lower_bound(X_46,X_47)))]]) ).
cnf(refute_0_140,plain,
greatest_lower_bound(X_46,X_47) = greatest_lower_bound(X_47,X_46),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_47,X_46),greatest_lower_bound(X_46,X_47)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( greatest_lower_bound(X_45,greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45))
| greatest_lower_bound(X_46,X_47) != greatest_lower_bound(X_47,X_46)
| greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_45,greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45))) ),[0,1],$fot(greatest_lower_bound(X_47,X_46))]]) ).
cnf(refute_0_142,plain,
( greatest_lower_bound(X_45,greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45))
| greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_46,X_47),greatest_lower_bound(X_47,X_46)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_45,greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45))) )],[refute_0_137,refute_0_142]) ).
cnf(refute_0_144,plain,
( greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45))
| greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45)) = greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)))),bind(Y0,$fot(greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45))))]]) ).
cnf(refute_0_145,plain,
greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45)) = greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_45,greatest_lower_bound(X_47,X_46)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_45))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_88,X_27))),
inference(subst,[],[refute_0_145:[bind(X_45,$fot(X_27)),bind(X_46,$fot(multiply(X_88,X_27))),bind(X_47,$fot(X_26))]]) ).
cnf(refute_0_147,plain,
( greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27))
| greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_88,X_27)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_88,X_27))) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27))) ),[0],$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_88,X_27))))]]) ).
cnf(refute_0_148,plain,
( greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_88,X_27))) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_88,X_27)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_88,X_27))) = greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_27),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(greatest_lower_bound(X_88,identity),X_27))) )],[refute_0_136,refute_0_148]) ).
cnf(refute_0_150,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)),
inference(subst,[],[refute_0_149:[bind(X_26,$fot(X_27))]]) ).
cnf(refute_0_151,plain,
( greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) != greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))))),bind(Y0,$fot(greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)))]]) ).
cnf(refute_0_152,plain,
( greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))),greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(greatest_lower_bound(X_88,identity),X_27)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)) )],[refute_0_125,refute_0_152]) ).
cnf(refute_0_154,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) != multiply(greatest_lower_bound(identity,X_88),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(identity,X_88),X_27) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_88),X_27)))]]) ).
cnf(refute_0_155,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27) != multiply(greatest_lower_bound(identity,X_88),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(identity,X_88),X_27) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) = multiply(greatest_lower_bound(identity,X_88),X_27),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_88,identity)),X_27),multiply(greatest_lower_bound(identity,X_88),X_27)) )],[refute_0_101,refute_0_155]) ).
cnf(refute_0_157,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) != multiply(greatest_lower_bound(X_88,identity),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) != multiply(greatest_lower_bound(identity,X_88),X_27)
| multiply(greatest_lower_bound(identity,X_88),X_27) = multiply(greatest_lower_bound(X_88,identity),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))),multiply(greatest_lower_bound(X_88,identity),X_27)) ),[0],$fot(multiply(greatest_lower_bound(identity,X_88),X_27))]]) ).
cnf(refute_0_158,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))) != multiply(greatest_lower_bound(X_88,identity),X_27)
| multiply(greatest_lower_bound(identity,X_88),X_27) = multiply(greatest_lower_bound(X_88,identity),X_27) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))),multiply(greatest_lower_bound(identity,X_88),X_27)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(greatest_lower_bound(identity,X_88),X_27) = multiply(greatest_lower_bound(X_88,identity),X_27),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_88,X_27))),multiply(greatest_lower_bound(X_88,identity),X_27)) )],[refute_0_78,refute_0_158]) ).
cnf(refute_0_160,plain,
( multiply(greatest_lower_bound(identity,X_88),X_27) != multiply(greatest_lower_bound(X_88,identity),X_27)
| multiply(greatest_lower_bound(X_88,identity),X_27) = multiply(greatest_lower_bound(identity,X_88),X_27) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_88),X_27))),bind(Y0,$fot(multiply(greatest_lower_bound(X_88,identity),X_27)))]]) ).
cnf(refute_0_161,plain,
multiply(greatest_lower_bound(X_88,identity),X_27) = multiply(greatest_lower_bound(identity,X_88),X_27),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_88),X_27),multiply(greatest_lower_bound(X_88,identity),X_27)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) = multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)),
inference(subst,[],[refute_0_161:[bind(X_27,$fot(least_upper_bound(X_95,identity))),bind(X_88,$fot(inverse(X_95)))]]) ).
cnf(refute_0_163,plain,
( multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) != multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity))
| multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) != greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))
| multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)),greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)))]]) ).
cnf(refute_0_164,plain,
( multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)) != greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))
| multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)),multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_95),identity),least_upper_bound(X_95,identity)),greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))) )],[refute_0_66,refute_0_164]) ).
cnf(refute_0_166,plain,
( multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) != greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))
| greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) = multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))))]]) ).
cnf(refute_0_167,plain,
greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) = multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)),greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) = multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),
inference(subst,[],[refute_0_167:[bind(X_95,$fot(a))]]) ).
cnf(refute_0_169,plain,
( multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity))
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity))) ),[1],$fot(identity)]]) ).
cnf(refute_0_170,plain,
( multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != identity
| greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))),identity) )],[refute_0_170,refute_0_12]) ).
cnf(refute_0_172,plain,
multiply(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_35)),bind(Y,$fot(X_36)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_173,plain,
X_35 = multiply(X_35,identity),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_174,plain,
( X_35 != multiply(X_35,identity)
| multiply(X_35,identity) = X_35 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_35)),bind(Y0,$fot(multiply(X_35,identity)))]]) ).
cnf(refute_0_175,plain,
multiply(X_35,identity) = X_35,
inference(resolve,[$cnf( $equal(X_35,multiply(X_35,identity)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
( multiply(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,identity))
| multiply(X_35,identity) != X_35
| multiply(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(multiply(X_35,X_36),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,identity))) ),[1,1],$fot(X_35)]]) ).
cnf(refute_0_177,plain,
( multiply(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,identity))
| multiply(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(multiply(X_35,X_36),X_35) ),
inference(resolve,[$cnf( $equal(multiply(X_35,identity),X_35) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
multiply(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(multiply(X_35,X_36),X_35),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,identity))) )],[refute_0_172,refute_0_177]) ).
cnf(refute_0_179,plain,
greatest_lower_bound(multiply(X_35,X_36),X_35) = greatest_lower_bound(X_35,multiply(X_35,X_36)),
inference(subst,[],[refute_0_18:[bind(X_27,$fot(X_35)),bind(X_28,$fot(multiply(X_35,X_36)))]]) ).
cnf(refute_0_180,plain,
( multiply(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(multiply(X_35,X_36),X_35)
| greatest_lower_bound(multiply(X_35,X_36),X_35) != greatest_lower_bound(X_35,multiply(X_35,X_36))
| multiply(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_35,multiply(X_35,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_35,multiply(X_35,X_36))) ),[0],$fot(greatest_lower_bound(multiply(X_35,X_36),X_35))]]) ).
cnf(refute_0_181,plain,
( multiply(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(multiply(X_35,X_36),X_35)
| multiply(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_35,multiply(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_35,X_36),X_35),greatest_lower_bound(X_35,multiply(X_35,X_36))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
multiply(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_35,multiply(X_35,X_36)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(multiply(X_35,X_36),X_35)) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) = greatest_lower_bound(least_upper_bound(X_139,identity),multiply(least_upper_bound(X_139,identity),inverse(X_139))),
inference(subst,[],[refute_0_182:[bind(X_35,$fot(least_upper_bound(X_139,identity))),bind(X_36,$fot(inverse(X_139)))]]) ).
cnf(refute_0_184,plain,
multiply(identity,least_upper_bound(inverse(X_137),identity)) = least_upper_bound(identity,multiply(identity,inverse(X_137))),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(identity)),bind(X_76,$fot(inverse(X_137)))]]) ).
cnf(refute_0_185,plain,
multiply(least_upper_bound(inverse(X_80),X_82),X_80) = least_upper_bound(multiply(inverse(X_80),X_80),multiply(X_82,X_80)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_80)),bind(Y,$fot(inverse(X_80))),bind(Z,$fot(X_82))]]) ).
cnf(refute_0_186,plain,
multiply(inverse(X_80),X_80) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_80))]]) ).
cnf(refute_0_187,plain,
( multiply(inverse(X_80),X_80) != identity
| multiply(least_upper_bound(inverse(X_80),X_82),X_80) != least_upper_bound(multiply(inverse(X_80),X_80),multiply(X_82,X_80))
| multiply(least_upper_bound(inverse(X_80),X_82),X_80) = least_upper_bound(identity,multiply(X_82,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_80),X_82),X_80),least_upper_bound(multiply(inverse(X_80),X_80),multiply(X_82,X_80))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_188,plain,
( multiply(least_upper_bound(inverse(X_80),X_82),X_80) != least_upper_bound(multiply(inverse(X_80),X_80),multiply(X_82,X_80))
| multiply(least_upper_bound(inverse(X_80),X_82),X_80) = least_upper_bound(identity,multiply(X_82,X_80)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),X_80),identity) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(least_upper_bound(inverse(X_80),X_82),X_80) = least_upper_bound(identity,multiply(X_82,X_80)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_80),X_82),X_80),least_upper_bound(multiply(inverse(X_80),X_80),multiply(X_82,X_80))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(least_upper_bound(inverse(inverse(X)),X_86),inverse(X)) = least_upper_bound(identity,multiply(X_86,inverse(X))),
inference(subst,[],[refute_0_189:[bind(X_80,$fot(inverse(X))),bind(X_82,$fot(X_86))]]) ).
cnf(refute_0_191,plain,
( multiply(least_upper_bound(inverse(inverse(X)),X_86),inverse(X)) != least_upper_bound(identity,multiply(X_86,inverse(X)))
| inverse(inverse(X)) != X
| multiply(least_upper_bound(X,X_86),inverse(X)) = least_upper_bound(identity,multiply(X_86,inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X)),X_86),inverse(X)),least_upper_bound(identity,multiply(X_86,inverse(X)))) ),[0,0,0],$fot(X)]]) ).
cnf(refute_0_192,plain,
( multiply(least_upper_bound(inverse(inverse(X)),X_86),inverse(X)) != least_upper_bound(identity,multiply(X_86,inverse(X)))
| multiply(least_upper_bound(X,X_86),inverse(X)) = least_upper_bound(identity,multiply(X_86,inverse(X))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(least_upper_bound(X,X_86),inverse(X)) = least_upper_bound(identity,multiply(X_86,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X)),X_86),inverse(X)),least_upper_bound(identity,multiply(X_86,inverse(X)))) )],[refute_0_190,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(least_upper_bound(X_137,identity),inverse(X_137)) = least_upper_bound(identity,multiply(identity,inverse(X_137))),
inference(subst,[],[refute_0_193:[bind(X,$fot(X_137)),bind(X_86,$fot(identity))]]) ).
cnf(refute_0_195,plain,
( multiply(least_upper_bound(X_137,identity),inverse(X_137)) != least_upper_bound(identity,multiply(identity,inverse(X_137)))
| least_upper_bound(identity,multiply(identity,inverse(X_137))) = multiply(least_upper_bound(X_137,identity),inverse(X_137)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_137,identity),inverse(X_137)))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,inverse(X_137)))))]]) ).
cnf(refute_0_196,plain,
least_upper_bound(identity,multiply(identity,inverse(X_137))) = multiply(least_upper_bound(X_137,identity),inverse(X_137)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_137,identity),inverse(X_137)),least_upper_bound(identity,multiply(identity,inverse(X_137)))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
( multiply(identity,least_upper_bound(inverse(X_137),identity)) != least_upper_bound(identity,multiply(identity,inverse(X_137)))
| least_upper_bound(identity,multiply(identity,inverse(X_137))) != multiply(least_upper_bound(X_137,identity),inverse(X_137))
| multiply(identity,least_upper_bound(inverse(X_137),identity)) = multiply(least_upper_bound(X_137,identity),inverse(X_137)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,least_upper_bound(inverse(X_137),identity)),multiply(least_upper_bound(X_137,identity),inverse(X_137))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(X_137))))]]) ).
cnf(refute_0_198,plain,
( multiply(identity,least_upper_bound(inverse(X_137),identity)) != least_upper_bound(identity,multiply(identity,inverse(X_137)))
| multiply(identity,least_upper_bound(inverse(X_137),identity)) = multiply(least_upper_bound(X_137,identity),inverse(X_137)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(X_137))),multiply(least_upper_bound(X_137,identity),inverse(X_137))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
multiply(identity,least_upper_bound(inverse(X_137),identity)) = multiply(least_upper_bound(X_137,identity),inverse(X_137)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_137),identity)),least_upper_bound(identity,multiply(identity,inverse(X_137)))) )],[refute_0_184,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(identity,least_upper_bound(identity,inverse(X_137))) = least_upper_bound(identity,inverse(X_137)),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(X_137))))]]) ).
cnf(refute_0_201,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| least_upper_bound(X,greatest_lower_bound(X,Y)) != X
| least_upper_bound(X,greatest_lower_bound(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X) ),[0,1],$fot(greatest_lower_bound(Y,X))]]) ).
cnf(refute_0_202,plain,
( least_upper_bound(X,greatest_lower_bound(X,Y)) != X
| least_upper_bound(X,greatest_lower_bound(Y,X)) = X ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_201]) ).
cnf(refute_0_203,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X) )],[lub_absorbtion,refute_0_202]) ).
cnf(refute_0_204,plain,
least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) = least_upper_bound(X_15,Y),
inference(subst,[],[refute_0_203:[bind(X,$fot(least_upper_bound(X_15,Y))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_205,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_206,plain,
( greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) != X_15
| least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_207,plain,
( least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_210,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_209]) ).
cnf(refute_0_211,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_212,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(Y,X_15)))]]) ).
cnf(refute_0_213,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_208,refute_0_213]) ).
cnf(refute_0_215,plain,
least_upper_bound(X_17,least_upper_bound(X_16,X_17)) = least_upper_bound(X_17,X_16),
inference(subst,[],[refute_0_214:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_216,plain,
least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_217,plain,
( least_upper_bound(X_17,X_16) != least_upper_bound(X_16,X_17)
| least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_17,X_16))),bind(Y0,$fot(least_upper_bound(X_16,X_17)))]]) ).
cnf(refute_0_218,plain,
least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),least_upper_bound(X_16,X_17)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
( least_upper_bound(X_16,X_17) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) ),[0,1],$fot(least_upper_bound(X_17,X_16))]]) ).
cnf(refute_0_220,plain,
( least_upper_bound(X_17,least_upper_bound(X_16,X_17)) != least_upper_bound(X_17,X_16)
| least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_16,X_17),least_upper_bound(X_17,X_16)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
least_upper_bound(X_17,least_upper_bound(X_17,X_16)) = least_upper_bound(X_17,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) )],[refute_0_215,refute_0_220]) ).
cnf(refute_0_222,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_94))) = least_upper_bound(X_17,multiply(X_17,X_94)),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(multiply(X_17,X_94)))]]) ).
cnf(refute_0_223,plain,
multiply(X_17,least_upper_bound(X_94,identity)) = least_upper_bound(X_17,multiply(X_17,X_94)),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(X_17)),bind(X_76,$fot(X_94))]]) ).
cnf(refute_0_224,plain,
( multiply(X_17,least_upper_bound(X_94,identity)) != least_upper_bound(X_17,multiply(X_17,X_94))
| least_upper_bound(X_17,multiply(X_17,X_94)) = multiply(X_17,least_upper_bound(X_94,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,least_upper_bound(X_94,identity)))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_17,X_94))))]]) ).
cnf(refute_0_225,plain,
least_upper_bound(X_17,multiply(X_17,X_94)) = multiply(X_17,least_upper_bound(X_94,identity)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(X_94,identity)),least_upper_bound(X_17,multiply(X_17,X_94))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
( least_upper_bound(X_17,multiply(X_17,X_94)) != multiply(X_17,least_upper_bound(X_94,identity))
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_94))) != least_upper_bound(X_17,multiply(X_17,X_94))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = least_upper_bound(X_17,multiply(X_17,X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_94))),least_upper_bound(X_17,multiply(X_17,X_94))) ),[0,1],$fot(multiply(X_17,least_upper_bound(X_94,identity)))]]) ).
cnf(refute_0_227,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_94))) != least_upper_bound(X_17,multiply(X_17,X_94))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = least_upper_bound(X_17,multiply(X_17,X_94)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,X_94)),multiply(X_17,least_upper_bound(X_94,identity))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = least_upper_bound(X_17,multiply(X_17,X_94)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_17,X_94))),least_upper_bound(X_17,multiply(X_17,X_94))) )],[refute_0_222,refute_0_227]) ).
cnf(refute_0_229,plain,
least_upper_bound(identity,least_upper_bound(X_94,identity)) = least_upper_bound(identity,X_94),
inference(subst,[],[refute_0_214:[bind(Y,$fot(X_94)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_230,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))),
introduced(tautology,[refl,[$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))))]]) ).
cnf(refute_0_231,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))
| least_upper_bound(identity,least_upper_bound(X_94,identity)) != least_upper_bound(identity,X_94)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_94))]]) ).
cnf(refute_0_232,plain,
( least_upper_bound(identity,least_upper_bound(X_94,identity)) != least_upper_bound(identity,X_94)
| multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,X_94)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,X_94)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_94,identity)),least_upper_bound(identity,X_94)) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,least_upper_bound(Y,X_21))) = least_upper_bound(Y,X_21),
inference(subst,[],[refute_0_85:[bind(X_12,$fot(least_upper_bound(Y,X_21))),bind(X_13,$fot(X_21))]]) ).
cnf(refute_0_235,plain,
least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y),
inference(subst,[],[refute_0_214:[bind(X_15,$fot(X_21))]]) ).
cnf(refute_0_236,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,least_upper_bound(Y,X_21))) != least_upper_bound(Y,X_21)
| least_upper_bound(X_21,least_upper_bound(Y,X_21)) != least_upper_bound(X_21,Y)
| greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)) = least_upper_bound(Y,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,least_upper_bound(Y,X_21))),least_upper_bound(Y,X_21)) ),[0,1],$fot(least_upper_bound(X_21,Y))]]) ).
cnf(refute_0_237,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,least_upper_bound(Y,X_21))) != least_upper_bound(Y,X_21)
| greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)) = least_upper_bound(Y,X_21) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(Y,X_21)),least_upper_bound(X_21,Y)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)) = least_upper_bound(Y,X_21),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,least_upper_bound(Y,X_21))),least_upper_bound(Y,X_21)) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))) = least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),
inference(subst,[],[refute_0_238:[bind(Y,$fot(multiply(X_75,X_77))),bind(X_21,$fot(multiply(X_75,X_76)))]]) ).
cnf(refute_0_240,plain,
multiply(X_75,least_upper_bound(X_76,X_77)) = least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_75)),bind(Y,$fot(X_76)),bind(Z,$fot(X_77))]]) ).
cnf(refute_0_241,plain,
( multiply(X_75,least_upper_bound(X_76,X_77)) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))
| least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77)) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_75,least_upper_bound(X_76,X_77)))),bind(Y0,$fot(least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))))]]) ).
cnf(refute_0_242,plain,
least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77)) = multiply(X_75,least_upper_bound(X_76,X_77)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))) != least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))
| least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77)) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) = least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) ),[0,1],$fot(multiply(X_75,least_upper_bound(X_76,X_77)))]]) ).
cnf(refute_0_244,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))) != least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))
| greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) = least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77)),multiply(X_75,least_upper_bound(X_76,X_77))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) = least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),least_upper_bound(multiply(X_75,X_76),multiply(X_75,X_77))),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) )],[refute_0_239,refute_0_244]) ).
cnf(refute_0_246,plain,
greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)) = least_upper_bound(X_76,X_77),
inference(subst,[],[refute_0_238:[bind(Y,$fot(X_76)),bind(X_21,$fot(X_77))]]) ).
cnf(refute_0_247,plain,
multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))) = multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))),
introduced(tautology,[refl,[$fot(multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))))]]) ).
cnf(refute_0_248,plain,
( multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))) != multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)))
| greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)) != least_upper_bound(X_76,X_77)
| multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))),multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)))) ),[1,1],$fot(least_upper_bound(X_76,X_77))]]) ).
cnf(refute_0_249,plain,
( greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)) != least_upper_bound(X_76,X_77)
| multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(resolve,[$cnf( $equal(multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))),multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)),least_upper_bound(X_76,X_77)) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_252,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_251]) ).
cnf(refute_0_253,plain,
greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) = multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))),
inference(subst,[],[refute_0_252:[bind(X,$fot(X_75)),bind(Y,$fot(least_upper_bound(X_76,X_77))),bind(Z,$fot(least_upper_bound(X_77,X_76)))]]) ).
cnf(refute_0_254,plain,
( multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) != multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))))),bind(Y0,$fot(multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))))),bind(Z0,$fot(multiply(X_75,least_upper_bound(X_76,X_77))))]]) ).
cnf(refute_0_255,plain,
( multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))),multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76)))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)),
inference(resolve,[$cnf( $equal(multiply(X_75,greatest_lower_bound(least_upper_bound(X_76,X_77),least_upper_bound(X_77,X_76))),multiply(X_75,least_upper_bound(X_76,X_77))) )],[refute_0_250,refute_0_255]) ).
cnf(refute_0_257,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_258,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_257]) ).
cnf(refute_0_259,plain,
least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) = multiply(X_75,least_upper_bound(X_77,X_76)),
inference(subst,[],[refute_0_258:[bind(X,$fot(X_75)),bind(Y,$fot(X_77)),bind(Z,$fot(X_76))]]) ).
cnf(refute_0_260,plain,
greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) = greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))))]]) ).
cnf(refute_0_261,plain,
( greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) != greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)))
| least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) != multiply(X_75,least_upper_bound(X_77,X_76))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) = greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))),greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)))) ),[1,1],$fot(multiply(X_75,least_upper_bound(X_77,X_76)))]]) ).
cnf(refute_0_262,plain,
( least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) != multiply(X_75,least_upper_bound(X_77,X_76))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) = greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))),greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) = greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_77,X_76))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
( greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) != greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76)))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))))),bind(Z0,$fot(multiply(X_75,least_upper_bound(X_76,X_77))))]]) ).
cnf(refute_0_265,plain,
( greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))),greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76)))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) = multiply(X_75,least_upper_bound(X_76,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))),multiply(X_75,least_upper_bound(X_76,X_77))) )],[refute_0_256,refute_0_265]) ).
cnf(refute_0_267,plain,
greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) = greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))),
inference(subst,[],[refute_0_18:[bind(X_27,$fot(multiply(X_75,least_upper_bound(X_76,X_77)))),bind(X_28,$fot(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))))]]) ).
cnf(refute_0_268,plain,
( greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) != greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)))
| greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))))),bind(Z0,$fot(multiply(X_75,least_upper_bound(X_76,X_77))))]]) ).
cnf(refute_0_269,plain,
( greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))),greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) = multiply(X_75,least_upper_bound(X_76,X_77)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))),multiply(X_75,least_upper_bound(X_76,X_77))) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) != multiply(X_75,least_upper_bound(X_76,X_77))
| greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) != least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,X_77)) = least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) ),[0],$fot(multiply(X_75,least_upper_bound(X_76,X_77)))]]) ).
cnf(refute_0_272,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) != least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,X_77)) = least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))),multiply(X_75,least_upper_bound(X_76,X_77))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
( multiply(X_75,least_upper_bound(X_76,X_77)) != least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))
| least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)) != multiply(X_75,least_upper_bound(X_77,X_76))
| multiply(X_75,least_upper_bound(X_76,X_77)) = multiply(X_75,least_upper_bound(X_77,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) ),[0],$fot(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)))]]) ).
cnf(refute_0_274,plain,
( multiply(X_75,least_upper_bound(X_76,X_77)) != least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,X_77)) = multiply(X_75,least_upper_bound(X_77,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_77,X_76))) )],[refute_0_259,refute_0_273]) ).
cnf(refute_0_275,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))) != least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,X_77)) = multiply(X_75,least_upper_bound(X_77,X_76)) ),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,X_77)),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) )],[refute_0_272,refute_0_274]) ).
cnf(refute_0_276,plain,
multiply(X_75,least_upper_bound(X_76,X_77)) = multiply(X_75,least_upper_bound(X_77,X_76)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76)),multiply(X_75,least_upper_bound(X_76,X_77))),least_upper_bound(multiply(X_75,X_77),multiply(X_75,X_76))) )],[refute_0_245,refute_0_275]) ).
cnf(refute_0_277,plain,
( multiply(X_75,least_upper_bound(X_76,X_77)) != multiply(X_75,least_upper_bound(X_77,X_76))
| multiply(X_75,least_upper_bound(X_77,X_76)) = multiply(X_75,least_upper_bound(X_76,X_77)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_75,least_upper_bound(X_76,X_77)))),bind(Y0,$fot(multiply(X_75,least_upper_bound(X_77,X_76))))]]) ).
cnf(refute_0_278,plain,
multiply(X_75,least_upper_bound(X_77,X_76)) = multiply(X_75,least_upper_bound(X_76,X_77)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,X_77)),multiply(X_75,least_upper_bound(X_77,X_76))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity)) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))),
inference(subst,[],[refute_0_278:[bind(X_75,$fot(X_17)),bind(X_76,$fot(identity)),bind(X_77,$fot(least_upper_bound(X_94,identity)))]]) ).
cnf(refute_0_280,plain,
( multiply(X_75,least_upper_bound(X_76,identity)) != least_upper_bound(X_75,multiply(X_75,X_76))
| least_upper_bound(X_75,multiply(X_75,X_76)) = multiply(X_75,least_upper_bound(X_76,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_75,least_upper_bound(X_76,identity)))),bind(Y0,$fot(least_upper_bound(X_75,multiply(X_75,X_76))))]]) ).
cnf(refute_0_281,plain,
least_upper_bound(X_75,multiply(X_75,X_76)) = multiply(X_75,least_upper_bound(X_76,identity)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,identity)),least_upper_bound(X_75,multiply(X_75,X_76))) )],[refute_0_53,refute_0_280]) ).
cnf(refute_0_282,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity)),
inference(subst,[],[refute_0_281:[bind(X_75,$fot(X_17)),bind(X_76,$fot(least_upper_bound(X_94,identity)))]]) ).
cnf(refute_0_283,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) != multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))))),bind(Y0,$fot(multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity)))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))))]]) ).
cnf(refute_0_284,plain,
( multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity)) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))),multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(least_upper_bound(X_94,identity),identity)),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))) )],[refute_0_279,refute_0_284]) ).
cnf(refute_0_286,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) != multiply(X_17,least_upper_bound(identity,X_94))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) != multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,X_94)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))))),bind(Y0,$fot(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))))),bind(Z0,$fot(multiply(X_17,least_upper_bound(identity,X_94))))]]) ).
cnf(refute_0_287,plain,
( multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))) != multiply(X_17,least_upper_bound(identity,X_94))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,X_94)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))),multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity)))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) = multiply(X_17,least_upper_bound(identity,X_94)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,least_upper_bound(X_94,identity))),multiply(X_17,least_upper_bound(identity,X_94))) )],[refute_0_233,refute_0_287]) ).
cnf(refute_0_289,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) != multiply(X_17,least_upper_bound(identity,X_94))
| least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) != least_upper_bound(X_17,multiply(X_17,X_94))
| multiply(X_17,least_upper_bound(identity,X_94)) = least_upper_bound(X_17,multiply(X_17,X_94)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))),least_upper_bound(X_17,multiply(X_17,X_94))) ),[0],$fot(multiply(X_17,least_upper_bound(identity,X_94)))]]) ).
cnf(refute_0_290,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) != least_upper_bound(X_17,multiply(X_17,X_94))
| multiply(X_17,least_upper_bound(identity,X_94)) = least_upper_bound(X_17,multiply(X_17,X_94)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))),multiply(X_17,least_upper_bound(identity,X_94))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
( multiply(X_17,least_upper_bound(identity,X_94)) != least_upper_bound(X_17,multiply(X_17,X_94))
| least_upper_bound(X_17,multiply(X_17,X_94)) != multiply(X_17,least_upper_bound(X_94,identity))
| multiply(X_17,least_upper_bound(identity,X_94)) = multiply(X_17,least_upper_bound(X_94,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_17,least_upper_bound(identity,X_94)),multiply(X_17,least_upper_bound(X_94,identity))) ),[0],$fot(least_upper_bound(X_17,multiply(X_17,X_94)))]]) ).
cnf(refute_0_292,plain,
( multiply(X_17,least_upper_bound(identity,X_94)) != least_upper_bound(X_17,multiply(X_17,X_94))
| multiply(X_17,least_upper_bound(identity,X_94)) = multiply(X_17,least_upper_bound(X_94,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,X_94)),multiply(X_17,least_upper_bound(X_94,identity))) )],[refute_0_225,refute_0_291]) ).
cnf(refute_0_293,plain,
( least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))) != least_upper_bound(X_17,multiply(X_17,X_94))
| multiply(X_17,least_upper_bound(identity,X_94)) = multiply(X_17,least_upper_bound(X_94,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,X_94)),least_upper_bound(X_17,multiply(X_17,X_94))) )],[refute_0_290,refute_0_292]) ).
cnf(refute_0_294,plain,
multiply(X_17,least_upper_bound(identity,X_94)) = multiply(X_17,least_upper_bound(X_94,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_17,least_upper_bound(X_94,identity))),least_upper_bound(X_17,multiply(X_17,X_94))) )],[refute_0_228,refute_0_293]) ).
cnf(refute_0_295,plain,
( multiply(X_17,least_upper_bound(identity,X_94)) != multiply(X_17,least_upper_bound(X_94,identity))
| multiply(X_17,least_upper_bound(X_94,identity)) = multiply(X_17,least_upper_bound(identity,X_94)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_17,least_upper_bound(identity,X_94)))),bind(Y0,$fot(multiply(X_17,least_upper_bound(X_94,identity))))]]) ).
cnf(refute_0_296,plain,
multiply(X_17,least_upper_bound(X_94,identity)) = multiply(X_17,least_upper_bound(identity,X_94)),
inference(resolve,[$cnf( $equal(multiply(X_17,least_upper_bound(identity,X_94)),multiply(X_17,least_upper_bound(X_94,identity))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
multiply(identity,least_upper_bound(inverse(X_137),identity)) = multiply(identity,least_upper_bound(identity,inverse(X_137))),
inference(subst,[],[refute_0_296:[bind(X_17,$fot(identity)),bind(X_94,$fot(inverse(X_137)))]]) ).
cnf(refute_0_298,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_137))) != least_upper_bound(identity,inverse(X_137))
| multiply(identity,least_upper_bound(inverse(X_137),identity)) != multiply(identity,least_upper_bound(identity,inverse(X_137)))
| multiply(identity,least_upper_bound(inverse(X_137),identity)) = least_upper_bound(identity,inverse(X_137)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(X_137),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(X_137))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_137))))]]) ).
cnf(refute_0_299,plain,
( multiply(identity,least_upper_bound(identity,inverse(X_137))) != least_upper_bound(identity,inverse(X_137))
| multiply(identity,least_upper_bound(inverse(X_137),identity)) = least_upper_bound(identity,inverse(X_137)) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_137),identity)),multiply(identity,least_upper_bound(identity,inverse(X_137)))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
multiply(identity,least_upper_bound(inverse(X_137),identity)) = least_upper_bound(identity,inverse(X_137)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(X_137))),least_upper_bound(identity,inverse(X_137))) )],[refute_0_200,refute_0_299]) ).
cnf(refute_0_301,plain,
( multiply(identity,least_upper_bound(inverse(X_137),identity)) != multiply(least_upper_bound(X_137,identity),inverse(X_137))
| multiply(identity,least_upper_bound(inverse(X_137),identity)) != least_upper_bound(identity,inverse(X_137))
| least_upper_bound(identity,inverse(X_137)) = multiply(least_upper_bound(X_137,identity),inverse(X_137)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_137),identity)),multiply(least_upper_bound(X_137,identity),inverse(X_137))) ),[0],$fot(least_upper_bound(identity,inverse(X_137)))]]) ).
cnf(refute_0_302,plain,
( multiply(identity,least_upper_bound(inverse(X_137),identity)) != multiply(least_upper_bound(X_137,identity),inverse(X_137))
| least_upper_bound(identity,inverse(X_137)) = multiply(least_upper_bound(X_137,identity),inverse(X_137)) ),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_137),identity)),least_upper_bound(identity,inverse(X_137))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
least_upper_bound(identity,inverse(X_137)) = multiply(least_upper_bound(X_137,identity),inverse(X_137)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(X_137),identity)),multiply(least_upper_bound(X_137,identity),inverse(X_137))) )],[refute_0_199,refute_0_302]) ).
cnf(refute_0_304,plain,
least_upper_bound(identity,inverse(X_139)) = multiply(least_upper_bound(X_139,identity),inverse(X_139)),
inference(subst,[],[refute_0_303:[bind(X_137,$fot(X_139))]]) ).
cnf(refute_0_305,plain,
( least_upper_bound(identity,inverse(X_139)) != multiply(least_upper_bound(X_139,identity),inverse(X_139))
| multiply(least_upper_bound(X_139,identity),inverse(X_139)) = least_upper_bound(identity,inverse(X_139)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,inverse(X_139)))),bind(Y0,$fot(multiply(least_upper_bound(X_139,identity),inverse(X_139))))]]) ).
cnf(refute_0_306,plain,
multiply(least_upper_bound(X_139,identity),inverse(X_139)) = least_upper_bound(identity,inverse(X_139)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_139)),multiply(least_upper_bound(X_139,identity),inverse(X_139))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) != greatest_lower_bound(least_upper_bound(X_139,identity),multiply(least_upper_bound(X_139,identity),inverse(X_139)))
| multiply(least_upper_bound(X_139,identity),inverse(X_139)) != least_upper_bound(identity,inverse(X_139))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) = greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)),greatest_lower_bound(least_upper_bound(X_139,identity),multiply(least_upper_bound(X_139,identity),inverse(X_139)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_139)))]]) ).
cnf(refute_0_308,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) != greatest_lower_bound(least_upper_bound(X_139,identity),multiply(least_upper_bound(X_139,identity),inverse(X_139)))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) = greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),inverse(X_139)),least_upper_bound(identity,inverse(X_139))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) = greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)),greatest_lower_bound(least_upper_bound(X_139,identity),multiply(least_upper_bound(X_139,identity),inverse(X_139)))) )],[refute_0_183,refute_0_308]) ).
cnf(refute_0_310,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = greatest_lower_bound(X_27,multiply(X_27,X_56)),
inference(subst,[],[refute_0_71:[bind(X_28,$fot(multiply(X_27,X_56)))]]) ).
cnf(refute_0_311,plain,
multiply(X_27,greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_27,multiply(X_27,X_56)),
inference(subst,[],[refute_0_182:[bind(X_35,$fot(X_27)),bind(X_36,$fot(X_56))]]) ).
cnf(refute_0_312,plain,
( multiply(X_27,greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_27,multiply(X_27,X_56))
| greatest_lower_bound(X_27,multiply(X_27,X_56)) = multiply(X_27,greatest_lower_bound(X_56,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_27,greatest_lower_bound(X_56,identity)))),bind(Y0,$fot(greatest_lower_bound(X_27,multiply(X_27,X_56))))]]) ).
cnf(refute_0_313,plain,
greatest_lower_bound(X_27,multiply(X_27,X_56)) = multiply(X_27,greatest_lower_bound(X_56,identity)),
inference(resolve,[$cnf( $equal(multiply(X_27,greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_27,multiply(X_27,X_56))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
( greatest_lower_bound(X_27,multiply(X_27,X_56)) != multiply(X_27,greatest_lower_bound(X_56,identity))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) != greatest_lower_bound(X_27,multiply(X_27,X_56))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(X_56,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))),greatest_lower_bound(X_27,multiply(X_27,X_56))) ),[1],$fot(multiply(X_27,greatest_lower_bound(X_56,identity)))]]) ).
cnf(refute_0_315,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) != greatest_lower_bound(X_27,multiply(X_27,X_56))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(X_56,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_27,X_56)),multiply(X_27,greatest_lower_bound(X_56,identity))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(X_56,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))),greatest_lower_bound(X_27,multiply(X_27,X_56))) )],[refute_0_310,refute_0_315]) ).
cnf(refute_0_317,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)) = greatest_lower_bound(identity,X_56),
inference(subst,[],[refute_0_96:[bind(Y,$fot(X_56)),bind(X_21,$fot(identity))]]) ).
cnf(refute_0_318,plain,
multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))),
introduced(tautology,[refl,[$fot(multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))))]]) ).
cnf(refute_0_319,plain,
( multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) != multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)) != greatest_lower_bound(identity,X_56)
| multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(identity,X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))),multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_56))]]) ).
cnf(refute_0_320,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)) != greatest_lower_bound(identity,X_56)
| multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(identity,X_56)) ),
inference(resolve,[$cnf( $equal(multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))),multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(identity,X_56)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)),greatest_lower_bound(identity,X_56)) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) = greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_35,X_37))),bind(Y,$fot(multiply(X_35,X_36)))]]) ).
cnf(refute_0_323,plain,
multiply(X_35,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_35)),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_324,plain,
( multiply(X_35,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37))
| greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37)) = multiply(X_35,greatest_lower_bound(X_36,X_37)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_35,greatest_lower_bound(X_36,X_37)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37))))]]) ).
cnf(refute_0_325,plain,
greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37)) = multiply(X_35,greatest_lower_bound(X_36,X_37)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37)) != multiply(X_35,greatest_lower_bound(X_36,X_37))
| greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) != greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37))
| greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) = multiply(X_35,greatest_lower_bound(X_36,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)),greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37))) ),[1],$fot(multiply(X_35,greatest_lower_bound(X_36,X_37)))]]) ).
cnf(refute_0_327,plain,
( greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) != greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37))
| greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) = multiply(X_35,greatest_lower_bound(X_36,X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37)),multiply(X_35,greatest_lower_bound(X_36,X_37))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) = multiply(X_35,greatest_lower_bound(X_36,X_37)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)),greatest_lower_bound(multiply(X_35,X_36),multiply(X_35,X_37))) )],[refute_0_322,refute_0_327]) ).
cnf(refute_0_329,plain,
greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) = multiply(X_35,greatest_lower_bound(X_37,X_36)),
inference(subst,[],[refute_0_252:[bind(X,$fot(X_35)),bind(Y,$fot(X_37)),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_330,plain,
( greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) != multiply(X_35,greatest_lower_bound(X_36,X_37))
| greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) != multiply(X_35,greatest_lower_bound(X_37,X_36))
| multiply(X_35,greatest_lower_bound(X_37,X_36)) = multiply(X_35,greatest_lower_bound(X_36,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)),multiply(X_35,greatest_lower_bound(X_36,X_37))) ),[0],$fot(multiply(X_35,greatest_lower_bound(X_37,X_36)))]]) ).
cnf(refute_0_331,plain,
( greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)) != multiply(X_35,greatest_lower_bound(X_36,X_37))
| multiply(X_35,greatest_lower_bound(X_37,X_36)) = multiply(X_35,greatest_lower_bound(X_36,X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)),multiply(X_35,greatest_lower_bound(X_37,X_36))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
multiply(X_35,greatest_lower_bound(X_37,X_36)) = multiply(X_35,greatest_lower_bound(X_36,X_37)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_35,X_37),multiply(X_35,X_36)),multiply(X_35,greatest_lower_bound(X_36,X_37))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( multiply(X_35,greatest_lower_bound(X_37,X_36)) != multiply(X_35,greatest_lower_bound(X_36,X_37))
| multiply(X_35,greatest_lower_bound(X_36,X_37)) = multiply(X_35,greatest_lower_bound(X_37,X_36)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_35,greatest_lower_bound(X_37,X_36)))),bind(Y0,$fot(multiply(X_35,greatest_lower_bound(X_36,X_37))))]]) ).
cnf(refute_0_334,plain,
multiply(X_35,greatest_lower_bound(X_36,X_37)) = multiply(X_35,greatest_lower_bound(X_37,X_36)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(X_37,X_36)),multiply(X_35,greatest_lower_bound(X_36,X_37))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity)) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))),
inference(subst,[],[refute_0_334:[bind(X_35,$fot(X_27)),bind(X_36,$fot(greatest_lower_bound(X_56,identity))),bind(X_37,$fot(identity))]]) ).
cnf(refute_0_336,plain,
( multiply(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(X_35,multiply(X_35,X_36))
| greatest_lower_bound(X_35,multiply(X_35,X_36)) = multiply(X_35,greatest_lower_bound(X_36,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_35,greatest_lower_bound(X_36,identity)))),bind(Y0,$fot(greatest_lower_bound(X_35,multiply(X_35,X_36))))]]) ).
cnf(refute_0_337,plain,
greatest_lower_bound(X_35,multiply(X_35,X_36)) = multiply(X_35,greatest_lower_bound(X_36,identity)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_35,multiply(X_35,X_36))) )],[refute_0_182,refute_0_336]) ).
cnf(refute_0_338,plain,
greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity)),
inference(subst,[],[refute_0_337:[bind(X_35,$fot(X_27)),bind(X_36,$fot(greatest_lower_bound(X_56,identity)))]]) ).
cnf(refute_0_339,plain,
( multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity)) != multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))) != multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity))
| greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))))),bind(Y0,$fot(multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity)))),bind(Z0,$fot(multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))))]]) ).
cnf(refute_0_340,plain,
( multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity)) != multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))),multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))),
inference(resolve,[$cnf( $equal(multiply(X_27,greatest_lower_bound(greatest_lower_bound(X_56,identity),identity)),multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))) )],[refute_0_335,refute_0_340]) ).
cnf(refute_0_342,plain,
greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_56))),
inference(subst,[],[refute_0_132:[bind(X,$fot(multiply(X_27,X_56)))]]) ).
cnf(refute_0_343,plain,
( greatest_lower_bound(X_27,multiply(X_27,X_56)) != multiply(X_27,greatest_lower_bound(X_56,identity))
| greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_56)))
| greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_56)))) ),[1,1],$fot(multiply(X_27,greatest_lower_bound(X_56,identity)))]]) ).
cnf(refute_0_344,plain,
( greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_56)))
| greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_27,X_56)),multiply(X_27,greatest_lower_bound(X_56,identity))) )],[refute_0_313,refute_0_343]) ).
cnf(refute_0_345,plain,
greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,multiply(X_27,X_56)))) )],[refute_0_342,refute_0_344]) ).
cnf(refute_0_346,plain,
greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) = greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_56))),
inference(subst,[],[refute_0_145:[bind(X_45,$fot(X_27)),bind(X_46,$fot(multiply(X_27,X_56))),bind(X_47,$fot(X_26))]]) ).
cnf(refute_0_347,plain,
( greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_56)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_56))) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity)))) ),[0],$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_56))))]]) ).
cnf(refute_0_348,plain,
( greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_56))) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_56)))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_26,multiply(X_27,X_56))) = greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_27,X_56),greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,multiply(X_27,greatest_lower_bound(X_56,identity)))) )],[refute_0_345,refute_0_348]) ).
cnf(refute_0_350,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))),
inference(subst,[],[refute_0_349:[bind(X_26,$fot(X_27))]]) ).
cnf(refute_0_351,plain,
( greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))) != multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) != greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))))),bind(Y0,$fot(greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))))),bind(Z0,$fot(multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))))]]) ).
cnf(refute_0_352,plain,
( greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))) != multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))),greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity)))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,multiply(X_27,greatest_lower_bound(X_56,identity))),multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))) )],[refute_0_341,refute_0_352]) ).
cnf(refute_0_354,plain,
( multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) != multiply(X_27,greatest_lower_bound(identity,X_56))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) != multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(identity,X_56)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))))),bind(Y0,$fot(multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))))),bind(Z0,$fot(multiply(X_27,greatest_lower_bound(identity,X_56))))]]) ).
cnf(refute_0_355,plain,
( multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))) != multiply(X_27,greatest_lower_bound(identity,X_56))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(identity,X_56)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))),multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) = multiply(X_27,greatest_lower_bound(identity,X_56)),
inference(resolve,[$cnf( $equal(multiply(X_27,greatest_lower_bound(identity,greatest_lower_bound(X_56,identity))),multiply(X_27,greatest_lower_bound(identity,X_56))) )],[refute_0_321,refute_0_355]) ).
cnf(refute_0_357,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) != multiply(X_27,greatest_lower_bound(X_56,identity))
| greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) != multiply(X_27,greatest_lower_bound(identity,X_56))
| multiply(X_27,greatest_lower_bound(identity,X_56)) = multiply(X_27,greatest_lower_bound(X_56,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))),multiply(X_27,greatest_lower_bound(X_56,identity))) ),[0],$fot(multiply(X_27,greatest_lower_bound(identity,X_56)))]]) ).
cnf(refute_0_358,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))) != multiply(X_27,greatest_lower_bound(X_56,identity))
| multiply(X_27,greatest_lower_bound(identity,X_56)) = multiply(X_27,greatest_lower_bound(X_56,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))),multiply(X_27,greatest_lower_bound(identity,X_56))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
multiply(X_27,greatest_lower_bound(identity,X_56)) = multiply(X_27,greatest_lower_bound(X_56,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,multiply(X_27,X_56))),multiply(X_27,greatest_lower_bound(X_56,identity))) )],[refute_0_316,refute_0_358]) ).
cnf(refute_0_360,plain,
( multiply(X_27,greatest_lower_bound(identity,X_56)) != multiply(X_27,greatest_lower_bound(X_56,identity))
| multiply(X_27,greatest_lower_bound(X_56,identity)) = multiply(X_27,greatest_lower_bound(identity,X_56)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_27,greatest_lower_bound(identity,X_56)))),bind(Y0,$fot(multiply(X_27,greatest_lower_bound(X_56,identity))))]]) ).
cnf(refute_0_361,plain,
multiply(X_27,greatest_lower_bound(X_56,identity)) = multiply(X_27,greatest_lower_bound(identity,X_56)),
inference(resolve,[$cnf( $equal(multiply(X_27,greatest_lower_bound(identity,X_56)),multiply(X_27,greatest_lower_bound(X_56,identity))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) = multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))),
inference(subst,[],[refute_0_361:[bind(X_27,$fot(least_upper_bound(X_139,identity))),bind(X_56,$fot(inverse(X_139)))]]) ).
cnf(refute_0_363,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) != multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) != greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) = greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)),greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) ),[0],$fot(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))))]]) ).
cnf(refute_0_364,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) != greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) = greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)),multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139)))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) = multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity)),
inference(subst,[],[refute_0_167:[bind(X_95,$fot(X_139))]]) ).
cnf(refute_0_366,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) != greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))
| greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))) != multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) = multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))),multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))))]]) ).
cnf(refute_0_367,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) != greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) = multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139))),multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)) != greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))
| multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) = multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))),greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) = multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(inverse(X_139),identity)),greatest_lower_bound(least_upper_bound(X_139,identity),least_upper_bound(identity,inverse(X_139)))) )],[refute_0_309,refute_0_368]) ).
cnf(refute_0_370,plain,
( multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) != multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity))
| multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity)) = multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity))))]]) ).
cnf(refute_0_371,plain,
multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity)) = multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,identity),greatest_lower_bound(identity,inverse(X_139))),multiply(greatest_lower_bound(identity,inverse(X_139)),least_upper_bound(X_139,identity))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) = multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))),
inference(subst,[],[refute_0_371:[bind(X_139,$fot(a))]]) ).
cnf(refute_0_373,plain,
( multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) != multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a)))
| multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))) != identity
| multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),identity) ),[0],$fot(multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))))]]) ).
cnf(refute_0_374,plain,
( multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))) != identity
| multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))) != identity,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(a,identity)),identity) )],[refute_0_374,refute_0_171]) ).
cnf(refute_0_376,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(least_upper_bound(X_26,Y))),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_377,plain,
greatest_lower_bound(X_26,least_upper_bound(X_26,Y)) = X_26,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_378,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)
| greatest_lower_bound(X_26,least_upper_bound(X_26,Y)) != X_26
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(X_26,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)),greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_379,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(X_26,X_28) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_26) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)) = greatest_lower_bound(X_26,X_28),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_26,Y),X_28)),greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_26,Y)),X_28)) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(subst,[],[refute_0_380:[bind(X_26,$fot(least_upper_bound(X_291,identity))),bind(X_28,$fot(least_upper_bound(identity,inverse(X_291))))]]) ).
cnf(refute_0_382,plain,
multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) = multiply(least_upper_bound(X_95,identity),greatest_lower_bound(identity,inverse(X_95))),
inference(subst,[],[refute_0_371:[bind(X_139,$fot(X_95))]]) ).
cnf(refute_0_383,plain,
( multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) != multiply(least_upper_bound(X_95,identity),greatest_lower_bound(identity,inverse(X_95)))
| multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) != greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))
| multiply(least_upper_bound(X_95,identity),greatest_lower_bound(identity,inverse(X_95))) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)),greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))) ),[0],$fot(multiply(least_upper_bound(X_95,identity),greatest_lower_bound(identity,inverse(X_95))))]]) ).
cnf(refute_0_384,plain,
( multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)) != greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))
| multiply(least_upper_bound(X_95,identity),greatest_lower_bound(identity,inverse(X_95))) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)),multiply(least_upper_bound(X_95,identity),greatest_lower_bound(identity,inverse(X_95)))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
multiply(least_upper_bound(X_95,identity),greatest_lower_bound(identity,inverse(X_95))) = greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_95)),least_upper_bound(X_95,identity)),greatest_lower_bound(least_upper_bound(X_95,identity),least_upper_bound(identity,inverse(X_95)))) )],[refute_0_165,refute_0_384]) ).
cnf(refute_0_386,plain,
multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) = greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(subst,[],[refute_0_385:[bind(X_95,$fot(X_291))]]) ).
cnf(refute_0_387,plain,
( multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) != greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_388,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))),greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) != greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) != multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))),multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))]]) ).
cnf(refute_0_390,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) != greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))),greatest_lower_bound(least_upper_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_381,refute_0_390]) ).
cnf(refute_0_392,plain,
multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) = greatest_lower_bound(least_upper_bound(identity,X_110),multiply(inverse(X_110),least_upper_bound(identity,X_110))),
inference(subst,[],[refute_0_22:[bind(X_42,$fot(least_upper_bound(identity,X_110))),bind(X_43,$fot(inverse(X_110)))]]) ).
cnf(refute_0_393,plain,
multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = least_upper_bound(inverse(X_95),multiply(inverse(X_95),least_upper_bound(X_95,identity))),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(inverse(X_95))),bind(X_76,$fot(least_upper_bound(X_95,identity)))]]) ).
cnf(refute_0_394,plain,
( multiply(inverse(X_95),least_upper_bound(X_95,identity)) != least_upper_bound(identity,inverse(X_95))
| multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) != least_upper_bound(inverse(X_95),multiply(inverse(X_95),least_upper_bound(X_95,identity)))
| multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)),least_upper_bound(inverse(X_95),multiply(inverse(X_95),least_upper_bound(X_95,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_95)))]]) ).
cnf(refute_0_395,plain,
( multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) != least_upper_bound(inverse(X_95),multiply(inverse(X_95),least_upper_bound(X_95,identity)))
| multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(X_95,identity)),least_upper_bound(identity,inverse(X_95))) )],[refute_0_63,refute_0_394]) ).
cnf(refute_0_396,plain,
multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)),least_upper_bound(inverse(X_95),multiply(inverse(X_95),least_upper_bound(X_95,identity)))) )],[refute_0_393,refute_0_395]) ).
cnf(refute_0_397,plain,
least_upper_bound(identity,least_upper_bound(X_95,identity)) = least_upper_bound(identity,X_95),
inference(subst,[],[refute_0_214:[bind(Y,$fot(X_95)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_398,plain,
multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))) = multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))))]]) ).
cnf(refute_0_399,plain,
( multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))) != multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity)))
| least_upper_bound(identity,least_upper_bound(X_95,identity)) != least_upper_bound(identity,X_95)
| multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))) = multiply(inverse(X_95),least_upper_bound(identity,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))),multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_95))]]) ).
cnf(refute_0_400,plain,
( least_upper_bound(identity,least_upper_bound(X_95,identity)) != least_upper_bound(identity,X_95)
| multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))) = multiply(inverse(X_95),least_upper_bound(identity,X_95)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))),multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity)))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))) = multiply(inverse(X_95),least_upper_bound(identity,X_95)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_95,identity)),least_upper_bound(identity,X_95)) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))),
inference(subst,[],[refute_0_296:[bind(X_17,$fot(inverse(X_95))),bind(X_94,$fot(least_upper_bound(X_95,identity)))]]) ).
cnf(refute_0_403,plain,
( multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))) != multiply(inverse(X_95),least_upper_bound(identity,X_95))
| multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) != multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity)))
| multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = multiply(inverse(X_95),least_upper_bound(identity,X_95)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)))),bind(Y0,$fot(multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))))),bind(Z0,$fot(multiply(inverse(X_95),least_upper_bound(identity,X_95))))]]) ).
cnf(refute_0_404,plain,
( multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))) != multiply(inverse(X_95),least_upper_bound(identity,X_95))
| multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = multiply(inverse(X_95),least_upper_bound(identity,X_95)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)),multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity)))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) = multiply(inverse(X_95),least_upper_bound(identity,X_95)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(identity,least_upper_bound(X_95,identity))),multiply(inverse(X_95),least_upper_bound(identity,X_95))) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
( multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) != multiply(inverse(X_95),least_upper_bound(identity,X_95))
| multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) != least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))
| multiply(inverse(X_95),least_upper_bound(identity,X_95)) = least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)),least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))) ),[0],$fot(multiply(inverse(X_95),least_upper_bound(identity,X_95)))]]) ).
cnf(refute_0_407,plain,
( multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) != least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))
| multiply(inverse(X_95),least_upper_bound(identity,X_95)) = least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)),multiply(inverse(X_95),least_upper_bound(identity,X_95))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
least_upper_bound(inverse(X_95),inverse(X_95)) = inverse(X_95),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(inverse(X_95)))]]) ).
cnf(refute_0_409,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))) = least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))))]]) ).
cnf(refute_0_410,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))) != least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95)))
| least_upper_bound(inverse(X_95),inverse(X_95)) != inverse(X_95)
| least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))) = least_upper_bound(identity,inverse(X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))),least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95)))) ),[1,1],$fot(inverse(X_95))]]) ).
cnf(refute_0_411,plain,
( least_upper_bound(inverse(X_95),inverse(X_95)) != inverse(X_95)
| least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))) = least_upper_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))),least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95)))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))) = least_upper_bound(identity,inverse(X_95)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_95),inverse(X_95)),inverse(X_95)) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)) = least_upper_bound(least_upper_bound(X_64,greatest_lower_bound(Y,X_64)),X_66),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_64)),bind(Y,$fot(greatest_lower_bound(Y,X_64))),bind(Z,$fot(X_66))]]) ).
cnf(refute_0_414,plain,
least_upper_bound(X_64,greatest_lower_bound(Y,X_64)) = X_64,
inference(subst,[],[refute_0_203:[bind(X,$fot(X_64))]]) ).
cnf(refute_0_415,plain,
( least_upper_bound(X_64,greatest_lower_bound(Y,X_64)) != X_64
| least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)) != least_upper_bound(least_upper_bound(X_64,greatest_lower_bound(Y,X_64)),X_66)
| least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)) = least_upper_bound(X_64,X_66) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)),least_upper_bound(least_upper_bound(X_64,greatest_lower_bound(Y,X_64)),X_66)) ),[1,0],$fot(X_64)]]) ).
cnf(refute_0_416,plain,
( least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)) != least_upper_bound(least_upper_bound(X_64,greatest_lower_bound(Y,X_64)),X_66)
| least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)) = least_upper_bound(X_64,X_66) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,greatest_lower_bound(Y,X_64)),X_64) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)) = least_upper_bound(X_64,X_66),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(greatest_lower_bound(Y,X_64),X_66)),least_upper_bound(least_upper_bound(X_64,greatest_lower_bound(Y,X_64)),X_66)) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),X_69)) = least_upper_bound(least_upper_bound(X_21,Y),X_69),
inference(subst,[],[refute_0_417:[bind(Y,$fot(least_upper_bound(Y,X_21))),bind(X_64,$fot(least_upper_bound(X_21,Y))),bind(X_66,$fot(X_69))]]) ).
cnf(refute_0_419,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)) != least_upper_bound(Y,X_21)
| least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),X_69)) != least_upper_bound(least_upper_bound(X_21,Y),X_69)
| least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(least_upper_bound(X_21,Y),X_69) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),X_69)),least_upper_bound(least_upper_bound(X_21,Y),X_69)) ),[0,1,0],$fot(least_upper_bound(Y,X_21))]]) ).
cnf(refute_0_420,plain,
( least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),X_69)) != least_upper_bound(least_upper_bound(X_21,Y),X_69)
| least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(least_upper_bound(X_21,Y),X_69) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),least_upper_bound(Y,X_21)) )],[refute_0_238,refute_0_419]) ).
cnf(refute_0_421,plain,
least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(least_upper_bound(X_21,Y),X_69),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),X_69)),least_upper_bound(least_upper_bound(X_21,Y),X_69)) )],[refute_0_418,refute_0_420]) ).
cnf(refute_0_422,plain,
least_upper_bound(X_64,least_upper_bound(X_65,least_upper_bound(Y,X_65))) = least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_64)),bind(Y,$fot(X_65)),bind(Z,$fot(least_upper_bound(Y,X_65)))]]) ).
cnf(refute_0_423,plain,
least_upper_bound(X_65,least_upper_bound(Y,X_65)) = least_upper_bound(X_65,Y),
inference(subst,[],[refute_0_214:[bind(X_15,$fot(X_65))]]) ).
cnf(refute_0_424,plain,
( least_upper_bound(X_64,least_upper_bound(X_65,least_upper_bound(Y,X_65))) != least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65))
| least_upper_bound(X_65,least_upper_bound(Y,X_65)) != least_upper_bound(X_65,Y)
| least_upper_bound(X_64,least_upper_bound(X_65,Y)) = least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(X_65,least_upper_bound(Y,X_65))),least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65))) ),[0,1],$fot(least_upper_bound(X_65,Y))]]) ).
cnf(refute_0_425,plain,
( least_upper_bound(X_64,least_upper_bound(X_65,least_upper_bound(Y,X_65))) != least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65))
| least_upper_bound(X_64,least_upper_bound(X_65,Y)) = least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_65,least_upper_bound(Y,X_65)),least_upper_bound(X_65,Y)) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
least_upper_bound(X_64,least_upper_bound(X_65,Y)) = least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(X_65,least_upper_bound(Y,X_65))),least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65))) )],[refute_0_422,refute_0_425]) ).
cnf(refute_0_427,plain,
least_upper_bound(least_upper_bound(X_64,X_65),Y) = least_upper_bound(X_64,least_upper_bound(X_65,Y)),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_64)),bind(Y,$fot(X_65)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_428,plain,
least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)) = least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)))]]) ).
cnf(refute_0_429,plain,
( least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)) != least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y))
| least_upper_bound(least_upper_bound(X_64,X_65),Y) != least_upper_bound(X_64,least_upper_bound(X_65,Y))
| least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)),least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y))) ),[1,1],$fot(least_upper_bound(X_64,least_upper_bound(X_65,Y)))]]) ).
cnf(refute_0_430,plain,
( least_upper_bound(least_upper_bound(X_64,X_65),Y) != least_upper_bound(X_64,least_upper_bound(X_65,Y))
| least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)),least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_64,X_65),Y),least_upper_bound(X_64,least_upper_bound(X_65,Y))) )],[refute_0_427,refute_0_430]) ).
cnf(refute_0_432,plain,
least_upper_bound(X,least_upper_bound(X_64,X_65)) = least_upper_bound(least_upper_bound(X_64,X_65),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_64,X_65)))]]) ).
cnf(refute_0_433,plain,
least_upper_bound(X_64,least_upper_bound(X_65,X)) = least_upper_bound(least_upper_bound(X_64,X_65),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_64)),bind(Y,$fot(X_65)),bind(Z,$fot(X))]]) ).
cnf(refute_0_434,plain,
( least_upper_bound(X_64,least_upper_bound(X_65,X)) != least_upper_bound(least_upper_bound(X_64,X_65),X)
| least_upper_bound(least_upper_bound(X_64,X_65),X) = least_upper_bound(X_64,least_upper_bound(X_65,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_64,least_upper_bound(X_65,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_64,X_65),X)))]]) ).
cnf(refute_0_435,plain,
least_upper_bound(least_upper_bound(X_64,X_65),X) = least_upper_bound(X_64,least_upper_bound(X_65,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(X_65,X)),least_upper_bound(least_upper_bound(X_64,X_65),X)) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
( least_upper_bound(X,least_upper_bound(X_64,X_65)) != least_upper_bound(least_upper_bound(X_64,X_65),X)
| least_upper_bound(least_upper_bound(X_64,X_65),X) != least_upper_bound(X_64,least_upper_bound(X_65,X))
| least_upper_bound(X,least_upper_bound(X_64,X_65)) = least_upper_bound(X_64,least_upper_bound(X_65,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_64,X_65)),least_upper_bound(X_64,least_upper_bound(X_65,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_64,X_65),X))]]) ).
cnf(refute_0_437,plain,
( least_upper_bound(X,least_upper_bound(X_64,X_65)) != least_upper_bound(least_upper_bound(X_64,X_65),X)
| least_upper_bound(X,least_upper_bound(X_64,X_65)) = least_upper_bound(X_64,least_upper_bound(X_65,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_64,X_65),X),least_upper_bound(X_64,least_upper_bound(X_65,X))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
least_upper_bound(X,least_upper_bound(X_64,X_65)) = least_upper_bound(X_64,least_upper_bound(X_65,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_64,X_65)),least_upper_bound(least_upper_bound(X_64,X_65),X)) )],[refute_0_432,refute_0_437]) ).
cnf(refute_0_439,plain,
( least_upper_bound(X,least_upper_bound(X_64,X_65)) != least_upper_bound(X_64,least_upper_bound(X_65,X))
| least_upper_bound(X_64,least_upper_bound(X_65,X)) = least_upper_bound(X,least_upper_bound(X_64,X_65)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_64,X_65)))),bind(Y0,$fot(least_upper_bound(X_64,least_upper_bound(X_65,X))))]]) ).
cnf(refute_0_440,plain,
least_upper_bound(X_64,least_upper_bound(X_65,X)) = least_upper_bound(X,least_upper_bound(X_64,X_65)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_64,X_65)),least_upper_bound(X_64,least_upper_bound(X_65,X))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) = least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)),
inference(subst,[],[refute_0_440:[bind(X,$fot(X_65)),bind(X_64,$fot(least_upper_bound(X_64,X_65))),bind(X_65,$fot(Y))]]) ).
cnf(refute_0_442,plain,
( least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)) != least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))
| least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) != least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y))
| least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)))),bind(Y0,$fot(least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)))),bind(Z0,$fot(least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))))]]) ).
cnf(refute_0_443,plain,
( least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)) != least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))
| least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)),least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_65,least_upper_bound(least_upper_bound(X_64,X_65),Y)),least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))) )],[refute_0_431,refute_0_443]) ).
cnf(refute_0_445,plain,
( least_upper_bound(X_64,least_upper_bound(X_65,Y)) != least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65))
| least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)) != least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))
| least_upper_bound(X_64,least_upper_bound(X_65,Y)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_64,least_upper_bound(X_65,Y)),least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)))]]) ).
cnf(refute_0_446,plain,
( least_upper_bound(X_64,least_upper_bound(X_65,Y)) != least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65))
| least_upper_bound(X_64,least_upper_bound(X_65,Y)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65)),least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
least_upper_bound(X_64,least_upper_bound(X_65,Y)) = least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(X_65,Y)),least_upper_bound(least_upper_bound(X_64,X_65),least_upper_bound(Y,X_65))) )],[refute_0_426,refute_0_446]) ).
cnf(refute_0_448,plain,
( least_upper_bound(X_64,least_upper_bound(X_65,Y)) != least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))
| least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) = least_upper_bound(X_64,least_upper_bound(X_65,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_64,least_upper_bound(X_65,Y)))),bind(Y0,$fot(least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))))]]) ).
cnf(refute_0_449,plain,
least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y))) = least_upper_bound(X_64,least_upper_bound(X_65,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(X_65,Y)),least_upper_bound(X_65,least_upper_bound(X_64,least_upper_bound(X_65,Y)))) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))) = least_upper_bound(Y,least_upper_bound(X_21,X_69)),
inference(subst,[],[refute_0_449:[bind(Y,$fot(X_69)),bind(X_64,$fot(Y)),bind(X_65,$fot(X_21))]]) ).
cnf(refute_0_451,plain,
least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))) = least_upper_bound(Y,least_upper_bound(X_21,X_69)),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(least_upper_bound(X_21,X_69))),bind(X_17,$fot(Y))]]) ).
cnf(refute_0_452,plain,
least_upper_bound(least_upper_bound(Y,X_21),X_69) = least_upper_bound(Y,least_upper_bound(X_21,X_69)),
inference(subst,[],[refute_0_210:[bind(X,$fot(Y)),bind(Y,$fot(X_21)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_453,plain,
least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)))]]) ).
cnf(refute_0_454,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))
| least_upper_bound(least_upper_bound(Y,X_21),X_69) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_21,X_69)))]]) ).
cnf(refute_0_455,plain,
( least_upper_bound(least_upper_bound(Y,X_21),X_69) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_21),X_69),least_upper_bound(Y,least_upper_bound(X_21,X_69))) )],[refute_0_452,refute_0_455]) ).
cnf(refute_0_457,plain,
( least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69)))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_21,X_69))))]]) ).
cnf(refute_0_458,plain,
( least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69)))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(Y,least_upper_bound(X_21,X_69))),least_upper_bound(Y,least_upper_bound(X_21,X_69))) )],[refute_0_451,refute_0_458]) ).
cnf(refute_0_460,plain,
least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) = least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))))]]) ).
cnf(refute_0_461,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) != least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)))
| least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) = least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))),least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_21,X_69)))]]) ).
cnf(refute_0_462,plain,
( least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) = least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))),least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) = least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(Y,least_upper_bound(X_21,X_69))) )],[refute_0_459,refute_0_462]) ).
cnf(refute_0_464,plain,
( least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) != least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69)))
| least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) = least_upper_bound(Y,least_upper_bound(X_21,X_69)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_21,X_69))))]]) ).
cnf(refute_0_465,plain,
( least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) = least_upper_bound(Y,least_upper_bound(X_21,X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))),least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69)))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) = least_upper_bound(Y,least_upper_bound(X_21,X_69)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(X_21,X_69))),least_upper_bound(Y,least_upper_bound(X_21,X_69))) )],[refute_0_450,refute_0_465]) ).
cnf(refute_0_467,plain,
least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_21)),bind(Z,$fot(least_upper_bound(least_upper_bound(Y,X_21),X_69)))]]) ).
cnf(refute_0_468,plain,
( least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)))
| least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_21,X_69))))]]) ).
cnf(refute_0_469,plain,
( least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69)))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(Y,least_upper_bound(least_upper_bound(Y,X_21),X_69))),least_upper_bound(Y,least_upper_bound(X_21,X_69))) )],[refute_0_466,refute_0_469]) ).
cnf(refute_0_471,plain,
( least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(Y,least_upper_bound(X_21,X_69))
| least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(least_upper_bound(X_21,Y),X_69)
| least_upper_bound(Y,least_upper_bound(X_21,X_69)) = least_upper_bound(least_upper_bound(X_21,Y),X_69) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(least_upper_bound(X_21,Y),X_69)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_21,X_69)))]]) ).
cnf(refute_0_472,plain,
( least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(least_upper_bound(X_21,Y),X_69)
| least_upper_bound(Y,least_upper_bound(X_21,X_69)) = least_upper_bound(least_upper_bound(X_21,Y),X_69) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(Y,least_upper_bound(X_21,X_69))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
least_upper_bound(least_upper_bound(X_21,Y),X_69) = least_upper_bound(X_21,least_upper_bound(Y,X_69)),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_21)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_474,plain,
( least_upper_bound(Y,least_upper_bound(X_21,X_69)) != least_upper_bound(least_upper_bound(X_21,Y),X_69)
| least_upper_bound(least_upper_bound(X_21,Y),X_69) != least_upper_bound(X_21,least_upper_bound(Y,X_69))
| least_upper_bound(Y,least_upper_bound(X_21,X_69)) = least_upper_bound(X_21,least_upper_bound(Y,X_69)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_21,X_69)),least_upper_bound(X_21,least_upper_bound(Y,X_69))) ),[0],$fot(least_upper_bound(least_upper_bound(X_21,Y),X_69))]]) ).
cnf(refute_0_475,plain,
( least_upper_bound(Y,least_upper_bound(X_21,X_69)) != least_upper_bound(least_upper_bound(X_21,Y),X_69)
| least_upper_bound(Y,least_upper_bound(X_21,X_69)) = least_upper_bound(X_21,least_upper_bound(Y,X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),X_69),least_upper_bound(X_21,least_upper_bound(Y,X_69))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
( least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)) != least_upper_bound(least_upper_bound(X_21,Y),X_69)
| least_upper_bound(Y,least_upper_bound(X_21,X_69)) = least_upper_bound(X_21,least_upper_bound(Y,X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_21,X_69)),least_upper_bound(least_upper_bound(X_21,Y),X_69)) )],[refute_0_472,refute_0_475]) ).
cnf(refute_0_477,plain,
least_upper_bound(Y,least_upper_bound(X_21,X_69)) = least_upper_bound(X_21,least_upper_bound(Y,X_69)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),least_upper_bound(least_upper_bound(Y,X_21),X_69)),least_upper_bound(least_upper_bound(X_21,Y),X_69)) )],[refute_0_421,refute_0_476]) ).
cnf(refute_0_478,plain,
( least_upper_bound(Y,least_upper_bound(X_21,X_69)) != least_upper_bound(X_21,least_upper_bound(Y,X_69))
| least_upper_bound(X_21,least_upper_bound(Y,X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_21,X_69)))),bind(Y0,$fot(least_upper_bound(X_21,least_upper_bound(Y,X_69))))]]) ).
cnf(refute_0_479,plain,
least_upper_bound(X_21,least_upper_bound(Y,X_69)) = least_upper_bound(Y,least_upper_bound(X_21,X_69)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_21,X_69)),least_upper_bound(X_21,least_upper_bound(Y,X_69))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) = least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))),
inference(subst,[],[refute_0_479:[bind(Y,$fot(identity)),bind(X_21,$fot(inverse(X_95))),bind(X_69,$fot(inverse(X_95)))]]) ).
cnf(refute_0_481,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))) != least_upper_bound(identity,inverse(X_95))
| least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) != least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95)))
| least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) = least_upper_bound(identity,inverse(X_95)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_95))))]]) ).
cnf(refute_0_482,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))) != least_upper_bound(identity,inverse(X_95))
| least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) = least_upper_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))),least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95)))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) = least_upper_bound(identity,inverse(X_95)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_95),inverse(X_95))),least_upper_bound(identity,inverse(X_95))) )],[refute_0_412,refute_0_482]) ).
cnf(refute_0_484,plain,
( multiply(inverse(X_95),least_upper_bound(identity,X_95)) != least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))
| least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))) != least_upper_bound(identity,inverse(X_95))
| multiply(inverse(X_95),least_upper_bound(identity,X_95)) = least_upper_bound(identity,inverse(X_95)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_95),least_upper_bound(identity,X_95)),least_upper_bound(identity,inverse(X_95))) ),[0],$fot(least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))))]]) ).
cnf(refute_0_485,plain,
( multiply(inverse(X_95),least_upper_bound(identity,X_95)) != least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))
| multiply(inverse(X_95),least_upper_bound(identity,X_95)) = least_upper_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95))),least_upper_bound(identity,inverse(X_95))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
( multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)) != least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))
| multiply(inverse(X_95),least_upper_bound(identity,X_95)) = least_upper_bound(identity,inverse(X_95)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(identity,X_95)),least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))) )],[refute_0_407,refute_0_485]) ).
cnf(refute_0_487,plain,
multiply(inverse(X_95),least_upper_bound(identity,X_95)) = least_upper_bound(identity,inverse(X_95)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(least_upper_bound(X_95,identity),identity)),least_upper_bound(inverse(X_95),least_upper_bound(identity,inverse(X_95)))) )],[refute_0_396,refute_0_486]) ).
cnf(refute_0_488,plain,
multiply(inverse(X_110),least_upper_bound(identity,X_110)) = least_upper_bound(identity,inverse(X_110)),
inference(subst,[],[refute_0_487:[bind(X_95,$fot(X_110))]]) ).
cnf(refute_0_489,plain,
( multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) != greatest_lower_bound(least_upper_bound(identity,X_110),multiply(inverse(X_110),least_upper_bound(identity,X_110)))
| multiply(inverse(X_110),least_upper_bound(identity,X_110)) != least_upper_bound(identity,inverse(X_110))
| multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)),greatest_lower_bound(least_upper_bound(identity,X_110),multiply(inverse(X_110),least_upper_bound(identity,X_110)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_110)))]]) ).
cnf(refute_0_490,plain,
( multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) != greatest_lower_bound(least_upper_bound(identity,X_110),multiply(inverse(X_110),least_upper_bound(identity,X_110)))
| multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_110),least_upper_bound(identity,X_110)),least_upper_bound(identity,inverse(X_110))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)),greatest_lower_bound(least_upper_bound(identity,X_110),multiply(inverse(X_110),least_upper_bound(identity,X_110)))) )],[refute_0_392,refute_0_490]) ).
cnf(refute_0_492,plain,
multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) = multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)),
inference(subst,[],[refute_0_161:[bind(X_27,$fot(least_upper_bound(identity,X_110))),bind(X_88,$fot(inverse(X_110)))]]) ).
cnf(refute_0_493,plain,
( multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) != multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110))
| multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) != greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)),greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)))]]) ).
cnf(refute_0_494,plain,
( multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)) != greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)),multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_110),identity),least_upper_bound(identity,X_110)),greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_491,refute_0_494]) ).
cnf(refute_0_496,plain,
multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = greatest_lower_bound(least_upper_bound(identity,X_273),multiply(least_upper_bound(identity,X_273),inverse(X_273))),
inference(subst,[],[refute_0_182:[bind(X_35,$fot(least_upper_bound(identity,X_273))),bind(X_36,$fot(inverse(X_273)))]]) ).
cnf(refute_0_497,plain,
multiply(multiply(inverse(X_58),X_58),X_59) = multiply(inverse(X_58),multiply(X_58,X_59)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_58))),bind(Y,$fot(X_58)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_498,plain,
multiply(inverse(X_58),X_58) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_58))]]) ).
cnf(refute_0_499,plain,
( multiply(multiply(inverse(X_58),X_58),X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| multiply(inverse(X_58),X_58) != identity
| multiply(identity,X_59) = multiply(inverse(X_58),multiply(X_58,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_58),X_58),X_59),multiply(inverse(X_58),multiply(X_58,X_59))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_500,plain,
( multiply(multiply(inverse(X_58),X_58),X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| multiply(identity,X_59) = multiply(inverse(X_58),multiply(X_58,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),X_58),identity) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
multiply(identity,X_59) = multiply(inverse(X_58),multiply(X_58,X_59)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_58),X_58),X_59),multiply(inverse(X_58),multiply(X_58,X_59))) )],[refute_0_497,refute_0_500]) ).
cnf(refute_0_502,plain,
multiply(identity,X_59) = X_59,
inference(subst,[],[left_identity:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_503,plain,
( multiply(identity,X_59) != X_59
| multiply(identity,X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| X_59 = multiply(inverse(X_58),multiply(X_58,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_59),multiply(inverse(X_58),multiply(X_58,X_59))) ),[0],$fot(X_59)]]) ).
cnf(refute_0_504,plain,
( multiply(identity,X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| X_59 = multiply(inverse(X_58),multiply(X_58,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_59),X_59) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
X_59 = multiply(inverse(X_58),multiply(X_58,X_59)),
inference(resolve,[$cnf( $equal(multiply(identity,X_59),multiply(inverse(X_58),multiply(X_58,X_59))) )],[refute_0_501,refute_0_504]) ).
cnf(refute_0_506,plain,
inverse(X) = multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X))),
inference(subst,[],[refute_0_505:[bind(X_58,$fot(inverse(Y))),bind(X_59,$fot(inverse(X)))]]) ).
cnf(refute_0_507,plain,
( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
| multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).
cnf(refute_0_508,plain,
multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p20x_3,refute_0_507]) ).
cnf(refute_0_509,plain,
( multiply(inverse(Y),inverse(X)) != inverse(multiply(X,Y))
| inverse(X) != multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))
| inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,Y)))]]) ).
cnf(refute_0_510,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( $equal(multiply(inverse(Y),inverse(X)),inverse(multiply(X,Y))) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
inverse(X) = multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),inverse(X)))) )],[refute_0_506,refute_0_510]) ).
cnf(refute_0_512,plain,
inverse(multiply(X_22,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_22)),
inference(subst,[],[p20x_3:[bind(X,$fot(X_22)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_513,plain,
( inverse(multiply(X_22,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_22))
| inverse(inverse(X)) != X
| inverse(multiply(X_22,inverse(X))) = multiply(X,inverse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_22,inverse(X))),multiply(inverse(inverse(X)),inverse(X_22))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_514,plain,
( inverse(multiply(X_22,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_22))
| inverse(multiply(X_22,inverse(X))) = multiply(X,inverse(X_22)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_513]) ).
cnf(refute_0_515,plain,
inverse(multiply(X_22,inverse(X))) = multiply(X,inverse(X_22)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_22,inverse(X))),multiply(inverse(inverse(X)),inverse(X_22))) )],[refute_0_512,refute_0_514]) ).
cnf(refute_0_516,plain,
inverse(multiply(multiply(X,Y),inverse(Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(subst,[],[refute_0_515:[bind(X,$fot(Y)),bind(X_22,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_517,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = inverse(multiply(multiply(X,Y),inverse(Y))),
inference(subst,[],[refute_0_508:[bind(X,$fot(multiply(X,Y))),bind(Y,$fot(inverse(Y)))]]) ).
cnf(refute_0_518,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != inverse(multiply(multiply(X,Y),inverse(Y)))
| inverse(multiply(multiply(X,Y),inverse(Y))) != multiply(Y,inverse(multiply(X,Y)))
| multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))) ),
inference(subst,[],[refute_0_122:[bind(X0,$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_519,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( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),inverse(multiply(multiply(X,Y),inverse(Y)))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X,Y),inverse(Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_516,refute_0_519]) ).
cnf(refute_0_521,plain,
( multiply(inverse(inverse(Y)),inverse(multiply(X,Y))) != multiply(Y,inverse(multiply(X,Y)))
| inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) ),[1],$fot(multiply(Y,inverse(multiply(X,Y))))]]) ).
cnf(refute_0_522,plain,
( inverse(X) != multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))
| inverse(X) = multiply(Y,inverse(multiply(X,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(Y)),inverse(multiply(X,Y))),multiply(Y,inverse(multiply(X,Y)))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
inverse(X) = multiply(Y,inverse(multiply(X,Y))),
inference(resolve,[$cnf( $equal(inverse(X),multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))) )],[refute_0_511,refute_0_522]) ).
cnf(refute_0_524,plain,
inverse(inverse(least_upper_bound(identity,inverse(X_136)))) = multiply(least_upper_bound(identity,X_136),inverse(multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136)))),
inference(subst,[],[refute_0_523:[bind(X,$fot(inverse(least_upper_bound(identity,inverse(X_136))))),bind(Y,$fot(least_upper_bound(identity,X_136)))]]) ).
cnf(refute_0_525,plain,
X_59 = multiply(inverse(least_upper_bound(inverse(X_59),X_86)),multiply(least_upper_bound(inverse(X_59),X_86),X_59)),
inference(subst,[],[refute_0_505:[bind(X_58,$fot(least_upper_bound(inverse(X_59),X_86)))]]) ).
cnf(refute_0_526,plain,
multiply(least_upper_bound(inverse(X_59),X_86),X_59) = least_upper_bound(identity,multiply(X_86,X_59)),
inference(subst,[],[refute_0_189:[bind(X_80,$fot(X_59)),bind(X_82,$fot(X_86))]]) ).
cnf(refute_0_527,plain,
( X_59 != multiply(inverse(least_upper_bound(inverse(X_59),X_86)),multiply(least_upper_bound(inverse(X_59),X_86),X_59))
| multiply(least_upper_bound(inverse(X_59),X_86),X_59) != least_upper_bound(identity,multiply(X_86,X_59))
| X_59 = multiply(inverse(least_upper_bound(inverse(X_59),X_86)),least_upper_bound(identity,multiply(X_86,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(inverse(X_59),X_86)),multiply(least_upper_bound(inverse(X_59),X_86),X_59))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_86,X_59)))]]) ).
cnf(refute_0_528,plain,
( X_59 != multiply(inverse(least_upper_bound(inverse(X_59),X_86)),multiply(least_upper_bound(inverse(X_59),X_86),X_59))
| X_59 = multiply(inverse(least_upper_bound(inverse(X_59),X_86)),least_upper_bound(identity,multiply(X_86,X_59))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_59),X_86),X_59),least_upper_bound(identity,multiply(X_86,X_59))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
X_59 = multiply(inverse(least_upper_bound(inverse(X_59),X_86)),least_upper_bound(identity,multiply(X_86,X_59))),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(inverse(X_59),X_86)),multiply(least_upper_bound(inverse(X_59),X_86),X_59))) )],[refute_0_525,refute_0_528]) ).
cnf(refute_0_530,plain,
X_134 = multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,multiply(identity,X_134))),
inference(subst,[],[refute_0_529:[bind(X_59,$fot(X_134)),bind(X_86,$fot(identity))]]) ).
cnf(refute_0_531,plain,
multiply(identity,X_134) = X_134,
inference(subst,[],[left_identity:[bind(X,$fot(X_134))]]) ).
cnf(refute_0_532,plain,
( X_134 != multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,multiply(identity,X_134)))
| multiply(identity,X_134) != X_134
| X_134 = multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134)) ),
introduced(tautology,[equality,[$cnf( $equal(X_134,multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,multiply(identity,X_134)))) ),[1,1,1],$fot(X_134)]]) ).
cnf(refute_0_533,plain,
( X_134 != multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,multiply(identity,X_134)))
| X_134 = multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_134),X_134) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
X_134 = multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134)),
inference(resolve,[$cnf( $equal(X_134,multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,multiply(identity,X_134)))) )],[refute_0_530,refute_0_533]) ).
cnf(refute_0_535,plain,
inverse(multiply(inverse(X),X_23)) = multiply(inverse(X_23),inverse(inverse(X))),
inference(subst,[],[p20x_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_536,plain,
( inverse(multiply(inverse(X),X_23)) != multiply(inverse(X_23),inverse(inverse(X)))
| inverse(inverse(X)) != X
| inverse(multiply(inverse(X),X_23)) = multiply(inverse(X_23),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_23)),multiply(inverse(X_23),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_537,plain,
( inverse(multiply(inverse(X),X_23)) != multiply(inverse(X_23),inverse(inverse(X)))
| inverse(multiply(inverse(X),X_23)) = multiply(inverse(X_23),X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_536]) ).
cnf(refute_0_538,plain,
inverse(multiply(inverse(X),X_23)) = multiply(inverse(X_23),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_23)),multiply(inverse(X_23),inverse(inverse(X)))) )],[refute_0_535,refute_0_537]) ).
cnf(refute_0_539,plain,
inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) = multiply(inverse(least_upper_bound(X_124,identity)),X),
inference(subst,[],[refute_0_538:[bind(X_23,$fot(least_upper_bound(X_124,identity)))]]) ).
cnf(refute_0_540,plain,
inverse(least_upper_bound(X_99,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))))),
inference(subst,[],[refute_0_523:[bind(X,$fot(least_upper_bound(X_99,identity))),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_99)))))]]) ).
cnf(refute_0_541,plain,
inverse(inverse(X_94)) = multiply(least_upper_bound(X_94,identity),inverse(multiply(inverse(X_94),least_upper_bound(X_94,identity)))),
inference(subst,[],[refute_0_523:[bind(X,$fot(inverse(X_94))),bind(Y,$fot(least_upper_bound(X_94,identity)))]]) ).
cnf(refute_0_542,plain,
( multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(identity,inverse(X_94))
| inverse(inverse(X_94)) != multiply(least_upper_bound(X_94,identity),inverse(multiply(inverse(X_94),least_upper_bound(X_94,identity))))
| inverse(inverse(X_94)) = multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_94)),multiply(least_upper_bound(X_94,identity),inverse(multiply(inverse(X_94),least_upper_bound(X_94,identity))))) ),[1,1,0],$fot(least_upper_bound(identity,inverse(X_94)))]]) ).
cnf(refute_0_543,plain,
( inverse(inverse(X_94)) != multiply(least_upper_bound(X_94,identity),inverse(multiply(inverse(X_94),least_upper_bound(X_94,identity))))
| inverse(inverse(X_94)) = multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),least_upper_bound(identity,inverse(X_94))) )],[refute_0_62,refute_0_542]) ).
cnf(refute_0_544,plain,
inverse(inverse(X_94)) = multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_94)),multiply(least_upper_bound(X_94,identity),inverse(multiply(inverse(X_94),least_upper_bound(X_94,identity))))) )],[refute_0_541,refute_0_543]) ).
cnf(refute_0_545,plain,
inverse(inverse(X_94)) = X_94,
inference(subst,[],[p20x_2:[bind(X,$fot(X_94))]]) ).
cnf(refute_0_546,plain,
( inverse(inverse(X_94)) != X_94
| inverse(inverse(X_94)) != multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94))))
| X_94 = multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_94)),multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94))))) ),[0],$fot(X_94)]]) ).
cnf(refute_0_547,plain,
( inverse(inverse(X_94)) != multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94))))
| X_94 = multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_94)),X_94) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
X_94 = multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_94)),multiply(least_upper_bound(X_94,identity),inverse(least_upper_bound(identity,inverse(X_94))))) )],[refute_0_544,refute_0_547]) ).
cnf(refute_0_549,plain,
X_99 = multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),
inference(subst,[],[refute_0_548:[bind(X_94,$fot(X_99))]]) ).
cnf(refute_0_550,plain,
( X_99 != multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))
| multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = X_99 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_99)),bind(Y0,$fot(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))))]]) ).
cnf(refute_0_551,plain,
multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) = X_99,
inference(resolve,[$cnf( $equal(X_99,multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))) )],[refute_0_549,refute_0_550]) ).
cnf(refute_0_552,plain,
( multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))) != X_99
| inverse(least_upper_bound(X_99,identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))))
| inverse(least_upper_bound(X_99,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))))) ),[1,1,0],$fot(X_99)]]) ).
cnf(refute_0_553,plain,
( inverse(least_upper_bound(X_99,identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))))
| inverse(least_upper_bound(X_99,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99)))),X_99) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
inverse(least_upper_bound(X_99,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(multiply(least_upper_bound(X_99,identity),inverse(least_upper_bound(identity,inverse(X_99))))))) )],[refute_0_540,refute_0_553]) ).
cnf(refute_0_555,plain,
inverse(inverse(X_99)) = X_99,
inference(subst,[],[p20x_2:[bind(X,$fot(X_99))]]) ).
cnf(refute_0_556,plain,
least_upper_bound(identity,inverse(inverse(X_99))) = least_upper_bound(identity,inverse(inverse(X_99))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(inverse(X_99))))]]) ).
cnf(refute_0_557,plain,
( inverse(inverse(X_99)) != X_99
| least_upper_bound(identity,inverse(inverse(X_99))) != least_upper_bound(identity,inverse(inverse(X_99)))
| least_upper_bound(identity,inverse(inverse(X_99))) = least_upper_bound(identity,X_99) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_99))),least_upper_bound(identity,inverse(inverse(X_99)))) ),[1,1],$fot(X_99)]]) ).
cnf(refute_0_558,plain,
( inverse(inverse(X_99)) != X_99
| least_upper_bound(identity,inverse(inverse(X_99))) = least_upper_bound(identity,X_99) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_99))),least_upper_bound(identity,inverse(inverse(X_99)))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
least_upper_bound(identity,inverse(inverse(X_99))) = least_upper_bound(identity,X_99),
inference(resolve,[$cnf( $equal(inverse(inverse(X_99)),X_99) )],[refute_0_555,refute_0_558]) ).
cnf(refute_0_560,plain,
( X != multiply(X,identity)
| multiply(X,identity) = X ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).
cnf(refute_0_561,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_43,refute_0_560]) ).
cnf(refute_0_562,plain,
multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity) = least_upper_bound(identity,inverse(inverse(X_99))),
inference(subst,[],[refute_0_561:[bind(X,$fot(least_upper_bound(identity,inverse(inverse(X_99)))))]]) ).
cnf(refute_0_563,plain,
greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))) = least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),
inference(subst,[],[refute_0_238:[bind(Y,$fot(multiply(X_82,X_80))),bind(X_21,$fot(multiply(X_81,X_80)))]]) ).
cnf(refute_0_564,plain,
multiply(least_upper_bound(X_81,X_82),X_80) = least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_80)),bind(Y,$fot(X_81)),bind(Z,$fot(X_82))]]) ).
cnf(refute_0_565,plain,
( multiply(least_upper_bound(X_81,X_82),X_80) != least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))
| least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80)) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_81,X_82),X_80))),bind(Y0,$fot(least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))))]]) ).
cnf(refute_0_566,plain,
least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80)) = multiply(least_upper_bound(X_81,X_82),X_80),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))) != least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))
| least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80)) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) = least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) ),[0,1],$fot(multiply(least_upper_bound(X_81,X_82),X_80))]]) ).
cnf(refute_0_568,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))) != least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))
| greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) = least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) = least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),least_upper_bound(multiply(X_81,X_80),multiply(X_82,X_80))),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) )],[refute_0_563,refute_0_568]) ).
cnf(refute_0_570,plain,
greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)) = least_upper_bound(X_81,X_82),
inference(subst,[],[refute_0_238:[bind(Y,$fot(X_81)),bind(X_21,$fot(X_82))]]) ).
cnf(refute_0_571,plain,
multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80) = multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80))]]) ).
cnf(refute_0_572,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80) != multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80)
| greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)) != least_upper_bound(X_81,X_82)
| multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80) = multiply(least_upper_bound(X_81,X_82),X_80) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80),multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80)) ),[1,0],$fot(least_upper_bound(X_81,X_82))]]) ).
cnf(refute_0_573,plain,
( greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)) != least_upper_bound(X_81,X_82)
| multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80),multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80)) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80) = multiply(least_upper_bound(X_81,X_82),X_80),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),least_upper_bound(X_81,X_82)) )],[refute_0_570,refute_0_573]) ).
cnf(refute_0_575,plain,
greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) = multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80),
inference(subst,[],[refute_0_110:[bind(X,$fot(X_80)),bind(Y,$fot(least_upper_bound(X_81,X_82))),bind(Z,$fot(least_upper_bound(X_82,X_81)))]]) ).
cnf(refute_0_576,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) != multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80)
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80))),bind(Z0,$fot(multiply(least_upper_bound(X_81,X_82),X_80)))]]) ).
cnf(refute_0_577,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)),multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80)) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) = multiply(least_upper_bound(X_81,X_82),X_80),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_81,X_82),least_upper_bound(X_82,X_81)),X_80),multiply(least_upper_bound(X_81,X_82),X_80)) )],[refute_0_574,refute_0_577]) ).
cnf(refute_0_579,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_580,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_579]) ).
cnf(refute_0_581,plain,
least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) = multiply(least_upper_bound(X_82,X_81),X_80),
inference(subst,[],[refute_0_580:[bind(X,$fot(X_80)),bind(Y,$fot(X_82)),bind(Z,$fot(X_81))]]) ).
cnf(refute_0_582,plain,
greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) = greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))))]]) ).
cnf(refute_0_583,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) != greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)))
| least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) != multiply(least_upper_bound(X_82,X_81),X_80)
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) = greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))),greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)))) ),[1,1],$fot(multiply(least_upper_bound(X_82,X_81),X_80))]]) ).
cnf(refute_0_584,plain,
( least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) != multiply(least_upper_bound(X_82,X_81),X_80)
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) = greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))),greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)))) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) = greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_82,X_81),X_80)) )],[refute_0_581,refute_0_584]) ).
cnf(refute_0_586,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) != greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80))
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)))),bind(Z0,$fot(multiply(least_upper_bound(X_81,X_82),X_80)))]]) ).
cnf(refute_0_587,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))),greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) = multiply(least_upper_bound(X_81,X_82),X_80),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) )],[refute_0_578,refute_0_587]) ).
cnf(refute_0_589,plain,
greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) = greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))),
inference(subst,[],[refute_0_18:[bind(X_27,$fot(multiply(least_upper_bound(X_81,X_82),X_80))),bind(X_28,$fot(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))))]]) ).
cnf(refute_0_590,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) != greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)))
| greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))))),bind(Z0,$fot(multiply(least_upper_bound(X_81,X_82),X_80)))]]) ).
cnf(refute_0_591,plain,
( greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)),greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) = multiply(least_upper_bound(X_81,X_82),X_80),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))),multiply(least_upper_bound(X_81,X_82),X_80)) )],[refute_0_588,refute_0_591]) ).
cnf(refute_0_593,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) != multiply(least_upper_bound(X_81,X_82),X_80)
| greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) != least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))
| multiply(least_upper_bound(X_81,X_82),X_80) = least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) ),[0],$fot(multiply(least_upper_bound(X_81,X_82),X_80))]]) ).
cnf(refute_0_594,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) != least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))
| multiply(least_upper_bound(X_81,X_82),X_80) = least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
( multiply(least_upper_bound(X_81,X_82),X_80) != least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))
| least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)) != multiply(least_upper_bound(X_82,X_81),X_80)
| multiply(least_upper_bound(X_81,X_82),X_80) = multiply(least_upper_bound(X_82,X_81),X_80) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) ),[0],$fot(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)))]]) ).
cnf(refute_0_596,plain,
( multiply(least_upper_bound(X_81,X_82),X_80) != least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))
| multiply(least_upper_bound(X_81,X_82),X_80) = multiply(least_upper_bound(X_82,X_81),X_80) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_82,X_81),X_80)) )],[refute_0_581,refute_0_595]) ).
cnf(refute_0_597,plain,
( greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)) != least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))
| multiply(least_upper_bound(X_81,X_82),X_80) = multiply(least_upper_bound(X_82,X_81),X_80) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,X_82),X_80),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) )],[refute_0_594,refute_0_596]) ).
cnf(refute_0_598,plain,
multiply(least_upper_bound(X_81,X_82),X_80) = multiply(least_upper_bound(X_82,X_81),X_80),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80)),multiply(least_upper_bound(X_81,X_82),X_80)),least_upper_bound(multiply(X_82,X_80),multiply(X_81,X_80))) )],[refute_0_569,refute_0_597]) ).
cnf(refute_0_599,plain,
( multiply(least_upper_bound(X_81,X_82),X_80) != multiply(least_upper_bound(X_82,X_81),X_80)
| multiply(least_upper_bound(X_82,X_81),X_80) = multiply(least_upper_bound(X_81,X_82),X_80) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_81,X_82),X_80))),bind(Y0,$fot(multiply(least_upper_bound(X_82,X_81),X_80)))]]) ).
cnf(refute_0_600,plain,
multiply(least_upper_bound(X_82,X_81),X_80) = multiply(least_upper_bound(X_81,X_82),X_80),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,X_82),X_80),multiply(least_upper_bound(X_82,X_81),X_80)) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity) = multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity),
inference(subst,[],[refute_0_600:[bind(X_80,$fot(identity)),bind(X_81,$fot(identity)),bind(X_82,$fot(inverse(inverse(X_99))))]]) ).
cnf(refute_0_602,plain,
( multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity) != least_upper_bound(identity,inverse(inverse(X_99)))
| multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity) != multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity)
| multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity) = least_upper_bound(identity,inverse(inverse(X_99))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(inverse(X_99)))))]]) ).
cnf(refute_0_603,plain,
( multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity) != least_upper_bound(identity,inverse(inverse(X_99)))
| multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity) = least_upper_bound(identity,inverse(inverse(X_99))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity),multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity)) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity) = least_upper_bound(identity,inverse(inverse(X_99))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(inverse(X_99))),identity),least_upper_bound(identity,inverse(inverse(X_99)))) )],[refute_0_562,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(least_upper_bound(X_81,identity),X_80) = least_upper_bound(multiply(X_81,X_80),multiply(identity,X_80)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_80)),bind(Y,$fot(X_81)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_606,plain,
multiply(identity,X_80) = X_80,
inference(subst,[],[left_identity:[bind(X,$fot(X_80))]]) ).
cnf(refute_0_607,plain,
( multiply(identity,X_80) != X_80
| multiply(least_upper_bound(X_81,identity),X_80) != least_upper_bound(multiply(X_81,X_80),multiply(identity,X_80))
| multiply(least_upper_bound(X_81,identity),X_80) = least_upper_bound(multiply(X_81,X_80),X_80) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_81,identity),X_80),least_upper_bound(multiply(X_81,X_80),multiply(identity,X_80))) ),[1,1],$fot(X_80)]]) ).
cnf(refute_0_608,plain,
( multiply(least_upper_bound(X_81,identity),X_80) != least_upper_bound(multiply(X_81,X_80),multiply(identity,X_80))
| multiply(least_upper_bound(X_81,identity),X_80) = least_upper_bound(multiply(X_81,X_80),X_80) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_80),X_80) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
multiply(least_upper_bound(X_81,identity),X_80) = least_upper_bound(multiply(X_81,X_80),X_80),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,identity),X_80),least_upper_bound(multiply(X_81,X_80),multiply(identity,X_80))) )],[refute_0_605,refute_0_608]) ).
cnf(refute_0_610,plain,
least_upper_bound(multiply(X_81,X_80),X_80) = least_upper_bound(X_80,multiply(X_81,X_80)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_80)),bind(Y,$fot(multiply(X_81,X_80)))]]) ).
cnf(refute_0_611,plain,
( multiply(least_upper_bound(X_81,identity),X_80) != least_upper_bound(multiply(X_81,X_80),X_80)
| least_upper_bound(multiply(X_81,X_80),X_80) != least_upper_bound(X_80,multiply(X_81,X_80))
| multiply(least_upper_bound(X_81,identity),X_80) = least_upper_bound(X_80,multiply(X_81,X_80)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_81,identity),X_80),least_upper_bound(X_80,multiply(X_81,X_80))) ),[0],$fot(least_upper_bound(multiply(X_81,X_80),X_80))]]) ).
cnf(refute_0_612,plain,
( multiply(least_upper_bound(X_81,identity),X_80) != least_upper_bound(multiply(X_81,X_80),X_80)
| multiply(least_upper_bound(X_81,identity),X_80) = least_upper_bound(X_80,multiply(X_81,X_80)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_81,X_80),X_80),least_upper_bound(X_80,multiply(X_81,X_80))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
multiply(least_upper_bound(X_81,identity),X_80) = least_upper_bound(X_80,multiply(X_81,X_80)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,identity),X_80),least_upper_bound(multiply(X_81,X_80),X_80)) )],[refute_0_609,refute_0_612]) ).
cnf(refute_0_614,plain,
( multiply(least_upper_bound(X_81,identity),X_80) != least_upper_bound(X_80,multiply(X_81,X_80))
| least_upper_bound(X_80,multiply(X_81,X_80)) = multiply(least_upper_bound(X_81,identity),X_80) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_81,identity),X_80))),bind(Y0,$fot(least_upper_bound(X_80,multiply(X_81,X_80))))]]) ).
cnf(refute_0_615,plain,
least_upper_bound(X_80,multiply(X_81,X_80)) = multiply(least_upper_bound(X_81,identity),X_80),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,identity),X_80),least_upper_bound(X_80,multiply(X_81,X_80))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) = multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity),
inference(subst,[],[refute_0_615:[bind(X_80,$fot(identity)),bind(X_81,$fot(inverse(inverse(X_99))))]]) ).
cnf(refute_0_617,plain,
( multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity) != least_upper_bound(identity,inverse(inverse(X_99)))
| least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) != multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity)
| least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) = least_upper_bound(identity,inverse(inverse(X_99))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(inverse(X_99)))))]]) ).
cnf(refute_0_618,plain,
( multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity) != least_upper_bound(identity,inverse(inverse(X_99)))
| least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) = least_upper_bound(identity,inverse(inverse(X_99))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)),multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity)) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) = least_upper_bound(identity,inverse(inverse(X_99))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X_99)),identity),identity),least_upper_bound(identity,inverse(inverse(X_99)))) )],[refute_0_604,refute_0_618]) ).
cnf(refute_0_620,plain,
( least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) != least_upper_bound(identity,inverse(inverse(X_99)))
| least_upper_bound(identity,inverse(inverse(X_99))) != least_upper_bound(identity,X_99)
| least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) = least_upper_bound(identity,X_99) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(inverse(X_99))))),bind(Z0,$fot(least_upper_bound(identity,X_99)))]]) ).
cnf(refute_0_621,plain,
( least_upper_bound(identity,inverse(inverse(X_99))) != least_upper_bound(identity,X_99)
| least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) = least_upper_bound(identity,X_99) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)),least_upper_bound(identity,inverse(inverse(X_99)))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) = least_upper_bound(identity,X_99),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(inverse(X_99))),least_upper_bound(identity,X_99)) )],[refute_0_559,refute_0_621]) ).
cnf(refute_0_623,plain,
inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))) = inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))))]]) ).
cnf(refute_0_624,plain,
( inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))) != inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)))
| least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) != least_upper_bound(identity,X_99)
| inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))) = inverse(least_upper_bound(identity,X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))),inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)))) ),[1,0],$fot(least_upper_bound(identity,X_99))]]) ).
cnf(refute_0_625,plain,
( least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)) != least_upper_bound(identity,X_99)
| inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))) = inverse(least_upper_bound(identity,X_99)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))),inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)))) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))) = inverse(least_upper_bound(identity,X_99)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)),least_upper_bound(identity,X_99)) )],[refute_0_622,refute_0_625]) ).
cnf(refute_0_627,plain,
inverse(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X))))) = multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X),
inference(subst,[],[refute_0_538:[bind(X_23,$fot(least_upper_bound(X_79,inverse(inverse(X)))))]]) ).
cnf(refute_0_628,plain,
multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_75)),bind(Y,$fot(X_76)),bind(Z,$fot(inverse(X_75)))]]) ).
cnf(refute_0_629,plain,
multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).
cnf(refute_0_630,plain,
inverse(inverse(X_1)) = X_1,
inference(subst,[],[p20x_2:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_631,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| inverse(inverse(X_1)) != X_1
| multiply(X_1,inverse(X_1)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_632,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| multiply(X_1,inverse(X_1)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
multiply(X_1,inverse(X_1)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_629,refute_0_632]) ).
cnf(refute_0_634,plain,
multiply(X_75,inverse(X_75)) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(X_75))]]) ).
cnf(refute_0_635,plain,
( multiply(X_75,inverse(X_75)) != identity
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_636,plain,
( multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_75,inverse(X_75)),identity) )],[refute_0_634,refute_0_635]) ).
cnf(refute_0_637,plain,
multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(multiply(X_75,X_76),identity),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(multiply(X_75,X_76),multiply(X_75,inverse(X_75)))) )],[refute_0_628,refute_0_636]) ).
cnf(refute_0_638,plain,
least_upper_bound(multiply(X_75,X_76),identity) = least_upper_bound(identity,multiply(X_75,X_76)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_75,X_76)))]]) ).
cnf(refute_0_639,plain,
( multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),identity)
| least_upper_bound(multiply(X_75,X_76),identity) != least_upper_bound(identity,multiply(X_75,X_76))
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(identity,multiply(X_75,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(identity,multiply(X_75,X_76))) ),[0],$fot(least_upper_bound(multiply(X_75,X_76),identity))]]) ).
cnf(refute_0_640,plain,
( multiply(X_75,least_upper_bound(X_76,inverse(X_75))) != least_upper_bound(multiply(X_75,X_76),identity)
| multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(identity,multiply(X_75,X_76)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_75,X_76),identity),least_upper_bound(identity,multiply(X_75,X_76))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
multiply(X_75,least_upper_bound(X_76,inverse(X_75))) = least_upper_bound(identity,multiply(X_75,X_76)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,inverse(X_75))),least_upper_bound(multiply(X_75,X_76),identity)) )],[refute_0_637,refute_0_640]) ).
cnf(refute_0_642,plain,
multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X)))) = least_upper_bound(identity,multiply(inverse(X),X_79)),
inference(subst,[],[refute_0_641:[bind(X_75,$fot(inverse(X))),bind(X_76,$fot(X_79))]]) ).
cnf(refute_0_643,plain,
( multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X)))) != least_upper_bound(identity,multiply(inverse(X),X_79))
| inverse(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X))))) != multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)
| inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X))))),multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)) ),[0,0],$fot(least_upper_bound(identity,multiply(inverse(X),X_79)))]]) ).
cnf(refute_0_644,plain,
( inverse(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X))))) != multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)
| inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) )],[refute_0_642,refute_0_643]) ).
cnf(refute_0_645,plain,
inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X))))),multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)) )],[refute_0_627,refute_0_644]) ).
cnf(refute_0_646,plain,
least_upper_bound(X_79,inverse(inverse(X))) = least_upper_bound(X_79,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_79,inverse(inverse(X))))]]) ).
cnf(refute_0_647,plain,
( inverse(inverse(X)) != X
| least_upper_bound(X_79,inverse(inverse(X))) != least_upper_bound(X_79,inverse(inverse(X)))
| least_upper_bound(X_79,inverse(inverse(X))) = least_upper_bound(X_79,X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_79,inverse(inverse(X))),least_upper_bound(X_79,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_648,plain,
( inverse(inverse(X)) != X
| least_upper_bound(X_79,inverse(inverse(X))) = least_upper_bound(X_79,X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,inverse(inverse(X))),least_upper_bound(X_79,inverse(inverse(X)))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
least_upper_bound(X_79,inverse(inverse(X))) = least_upper_bound(X_79,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_648]) ).
cnf(refute_0_650,plain,
inverse(least_upper_bound(X_79,inverse(inverse(X)))) = inverse(least_upper_bound(X_79,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_79,inverse(inverse(X)))))]]) ).
cnf(refute_0_651,plain,
( inverse(least_upper_bound(X_79,inverse(inverse(X)))) != inverse(least_upper_bound(X_79,inverse(inverse(X))))
| least_upper_bound(X_79,inverse(inverse(X))) != least_upper_bound(X_79,X)
| inverse(least_upper_bound(X_79,inverse(inverse(X)))) = inverse(least_upper_bound(X_79,X)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_79,inverse(inverse(X)))),inverse(least_upper_bound(X_79,inverse(inverse(X))))) ),[1,0],$fot(least_upper_bound(X_79,X))]]) ).
cnf(refute_0_652,plain,
( least_upper_bound(X_79,inverse(inverse(X))) != least_upper_bound(X_79,X)
| inverse(least_upper_bound(X_79,inverse(inverse(X)))) = inverse(least_upper_bound(X_79,X)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_79,inverse(inverse(X)))),inverse(least_upper_bound(X_79,inverse(inverse(X))))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
inverse(least_upper_bound(X_79,inverse(inverse(X)))) = inverse(least_upper_bound(X_79,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,inverse(inverse(X))),least_upper_bound(X_79,X)) )],[refute_0_649,refute_0_652]) ).
cnf(refute_0_654,plain,
multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) = multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X))]]) ).
cnf(refute_0_655,plain,
( multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) != multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)
| inverse(least_upper_bound(X_79,inverse(inverse(X)))) != inverse(least_upper_bound(X_79,X))
| multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) = multiply(inverse(least_upper_bound(X_79,X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X),multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)) ),[1,0],$fot(inverse(least_upper_bound(X_79,X)))]]) ).
cnf(refute_0_656,plain,
( inverse(least_upper_bound(X_79,inverse(inverse(X)))) != inverse(least_upper_bound(X_79,X))
| multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) = multiply(inverse(least_upper_bound(X_79,X)),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X),multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) = multiply(inverse(least_upper_bound(X_79,X)),X),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_79,inverse(inverse(X)))),inverse(least_upper_bound(X_79,X))) )],[refute_0_653,refute_0_656]) ).
cnf(refute_0_658,plain,
( multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X) != multiply(inverse(least_upper_bound(X_79,X)),X)
| inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) != multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)
| inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(inverse(least_upper_bound(X_79,X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X),X_79))),multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)) ),[1],$fot(multiply(inverse(least_upper_bound(X_79,X)),X))]]) ).
cnf(refute_0_659,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) != multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)
| inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(inverse(least_upper_bound(X_79,X)),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X),multiply(inverse(least_upper_bound(X_79,X)),X)) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(inverse(least_upper_bound(X_79,X)),X),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X),X_79))),multiply(inverse(least_upper_bound(X_79,inverse(inverse(X)))),X)) )],[refute_0_645,refute_0_659]) ).
cnf(refute_0_661,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) != multiply(inverse(least_upper_bound(X_79,X)),X)
| multiply(inverse(least_upper_bound(X_79,X)),X) = inverse(least_upper_bound(identity,multiply(inverse(X),X_79))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(X),X_79))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_79,X)),X)))]]) ).
cnf(refute_0_662,plain,
multiply(inverse(least_upper_bound(X_79,X)),X) = inverse(least_upper_bound(identity,multiply(inverse(X),X_79))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X),X_79))),multiply(inverse(least_upper_bound(X_79,X)),X)) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))),
inference(subst,[],[refute_0_662:[bind(X,$fot(inverse(X_99))),bind(X_79,$fot(identity))]]) ).
cnf(refute_0_664,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) != inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)))
| inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))) != inverse(least_upper_bound(identity,X_99))
| multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(least_upper_bound(identity,X_99)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_99))))]]) ).
cnf(refute_0_665,plain,
( inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))) != inverse(least_upper_bound(identity,X_99))
| multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(least_upper_bound(identity,X_99)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)),inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity)))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(least_upper_bound(identity,X_99)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(inverse(X_99)),identity))),inverse(least_upper_bound(identity,X_99))) )],[refute_0_626,refute_0_665]) ).
cnf(refute_0_667,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) != inverse(least_upper_bound(identity,X_99))
| inverse(least_upper_bound(X_99,identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))
| inverse(least_upper_bound(X_99,identity)) = inverse(least_upper_bound(identity,X_99)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))) ),[1],$fot(inverse(least_upper_bound(identity,X_99)))]]) ).
cnf(refute_0_668,plain,
( inverse(least_upper_bound(X_99,identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))
| inverse(least_upper_bound(X_99,identity)) = inverse(least_upper_bound(identity,X_99)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)),inverse(least_upper_bound(identity,X_99))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
inverse(least_upper_bound(X_99,identity)) = inverse(least_upper_bound(identity,X_99)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))) )],[refute_0_554,refute_0_668]) ).
cnf(refute_0_670,plain,
inverse(least_upper_bound(X_124,identity)) = inverse(least_upper_bound(identity,X_124)),
inference(subst,[],[refute_0_669:[bind(X_99,$fot(X_124))]]) ).
cnf(refute_0_671,plain,
( inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) != multiply(inverse(least_upper_bound(X_124,identity)),X)
| inverse(least_upper_bound(X_124,identity)) != inverse(least_upper_bound(identity,X_124))
| inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) = multiply(inverse(least_upper_bound(identity,X_124)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),least_upper_bound(X_124,identity))),multiply(inverse(least_upper_bound(X_124,identity)),X)) ),[1,0],$fot(inverse(least_upper_bound(identity,X_124)))]]) ).
cnf(refute_0_672,plain,
( inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) != multiply(inverse(least_upper_bound(X_124,identity)),X)
| inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) = multiply(inverse(least_upper_bound(identity,X_124)),X) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_124,identity)),inverse(least_upper_bound(identity,X_124))) )],[refute_0_670,refute_0_671]) ).
cnf(refute_0_673,plain,
inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) = multiply(inverse(least_upper_bound(identity,X_124)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),least_upper_bound(X_124,identity))),multiply(inverse(least_upper_bound(X_124,identity)),X)) )],[refute_0_539,refute_0_672]) ).
cnf(refute_0_674,plain,
( inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) != multiply(inverse(least_upper_bound(X_124,identity)),X)
| inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) != multiply(inverse(least_upper_bound(identity,X_124)),X)
| multiply(inverse(least_upper_bound(X_124,identity)),X) = multiply(inverse(least_upper_bound(identity,X_124)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),least_upper_bound(X_124,identity))),multiply(inverse(least_upper_bound(identity,X_124)),X)) ),[0],$fot(multiply(inverse(least_upper_bound(X_124,identity)),X))]]) ).
cnf(refute_0_675,plain,
( inverse(multiply(inverse(X),least_upper_bound(X_124,identity))) != multiply(inverse(least_upper_bound(identity,X_124)),X)
| multiply(inverse(least_upper_bound(X_124,identity)),X) = multiply(inverse(least_upper_bound(identity,X_124)),X) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),least_upper_bound(X_124,identity))),multiply(inverse(least_upper_bound(X_124,identity)),X)) )],[refute_0_539,refute_0_674]) ).
cnf(refute_0_676,plain,
multiply(inverse(least_upper_bound(X_124,identity)),X) = multiply(inverse(least_upper_bound(identity,X_124)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),least_upper_bound(X_124,identity))),multiply(inverse(least_upper_bound(identity,X_124)),X)) )],[refute_0_673,refute_0_675]) ).
cnf(refute_0_677,plain,
multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134)) = multiply(inverse(least_upper_bound(identity,inverse(X_134))),least_upper_bound(identity,X_134)),
inference(subst,[],[refute_0_676:[bind(X,$fot(least_upper_bound(identity,X_134))),bind(X_124,$fot(inverse(X_134)))]]) ).
cnf(refute_0_678,plain,
( X_134 != multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134))
| multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134)) != multiply(inverse(least_upper_bound(identity,inverse(X_134))),least_upper_bound(identity,X_134))
| X_134 = multiply(inverse(least_upper_bound(identity,inverse(X_134))),least_upper_bound(identity,X_134)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_134,multiply(inverse(least_upper_bound(identity,inverse(X_134))),least_upper_bound(identity,X_134))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134)))]]) ).
cnf(refute_0_679,plain,
( X_134 != multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134))
| X_134 = multiply(inverse(least_upper_bound(identity,inverse(X_134))),least_upper_bound(identity,X_134)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134)),multiply(inverse(least_upper_bound(identity,inverse(X_134))),least_upper_bound(identity,X_134))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
X_134 = multiply(inverse(least_upper_bound(identity,inverse(X_134))),least_upper_bound(identity,X_134)),
inference(resolve,[$cnf( $equal(X_134,multiply(inverse(least_upper_bound(inverse(X_134),identity)),least_upper_bound(identity,X_134))) )],[refute_0_534,refute_0_679]) ).
cnf(refute_0_681,plain,
X_136 = multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136)),
inference(subst,[],[refute_0_680:[bind(X_134,$fot(X_136))]]) ).
cnf(refute_0_682,plain,
( X_136 != multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136))
| multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136)) = X_136 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_136)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136))))]]) ).
cnf(refute_0_683,plain,
multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136)) = X_136,
inference(resolve,[$cnf( $equal(X_136,multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
( multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136)) != X_136
| inverse(inverse(least_upper_bound(identity,inverse(X_136)))) != multiply(least_upper_bound(identity,X_136),inverse(multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136))))
| inverse(inverse(least_upper_bound(identity,inverse(X_136)))) = multiply(least_upper_bound(identity,X_136),inverse(X_136)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_136)))),multiply(least_upper_bound(identity,X_136),inverse(multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136))))) ),[1,1,0],$fot(X_136)]]) ).
cnf(refute_0_685,plain,
( inverse(inverse(least_upper_bound(identity,inverse(X_136)))) != multiply(least_upper_bound(identity,X_136),inverse(multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136))))
| inverse(inverse(least_upper_bound(identity,inverse(X_136)))) = multiply(least_upper_bound(identity,X_136),inverse(X_136)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136)),X_136) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
inverse(inverse(least_upper_bound(identity,inverse(X_136)))) = multiply(least_upper_bound(identity,X_136),inverse(X_136)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_136)))),multiply(least_upper_bound(identity,X_136),inverse(multiply(inverse(least_upper_bound(identity,inverse(X_136))),least_upper_bound(identity,X_136))))) )],[refute_0_524,refute_0_685]) ).
cnf(refute_0_687,plain,
inverse(inverse(least_upper_bound(identity,inverse(X_136)))) = least_upper_bound(identity,inverse(X_136)),
inference(subst,[],[p20x_2:[bind(X,$fot(least_upper_bound(identity,inverse(X_136))))]]) ).
cnf(refute_0_688,plain,
( inverse(inverse(least_upper_bound(identity,inverse(X_136)))) != multiply(least_upper_bound(identity,X_136),inverse(X_136))
| inverse(inverse(least_upper_bound(identity,inverse(X_136)))) != least_upper_bound(identity,inverse(X_136))
| least_upper_bound(identity,inverse(X_136)) = multiply(least_upper_bound(identity,X_136),inverse(X_136)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_136)))),multiply(least_upper_bound(identity,X_136),inverse(X_136))) ),[0],$fot(least_upper_bound(identity,inverse(X_136)))]]) ).
cnf(refute_0_689,plain,
( inverse(inverse(least_upper_bound(identity,inverse(X_136)))) != multiply(least_upper_bound(identity,X_136),inverse(X_136))
| least_upper_bound(identity,inverse(X_136)) = multiply(least_upper_bound(identity,X_136),inverse(X_136)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_136)))),least_upper_bound(identity,inverse(X_136))) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
least_upper_bound(identity,inverse(X_136)) = multiply(least_upper_bound(identity,X_136),inverse(X_136)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,inverse(X_136)))),multiply(least_upper_bound(identity,X_136),inverse(X_136))) )],[refute_0_686,refute_0_689]) ).
cnf(refute_0_691,plain,
least_upper_bound(identity,inverse(X_273)) = multiply(least_upper_bound(identity,X_273),inverse(X_273)),
inference(subst,[],[refute_0_690:[bind(X_136,$fot(X_273))]]) ).
cnf(refute_0_692,plain,
( least_upper_bound(identity,inverse(X_273)) != multiply(least_upper_bound(identity,X_273),inverse(X_273))
| multiply(least_upper_bound(identity,X_273),inverse(X_273)) = least_upper_bound(identity,inverse(X_273)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,inverse(X_273)))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_273),inverse(X_273))))]]) ).
cnf(refute_0_693,plain,
multiply(least_upper_bound(identity,X_273),inverse(X_273)) = least_upper_bound(identity,inverse(X_273)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_273)),multiply(least_upper_bound(identity,X_273),inverse(X_273))) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) != greatest_lower_bound(least_upper_bound(identity,X_273),multiply(least_upper_bound(identity,X_273),inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),inverse(X_273)) != least_upper_bound(identity,inverse(X_273))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)),greatest_lower_bound(least_upper_bound(identity,X_273),multiply(least_upper_bound(identity,X_273),inverse(X_273)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_273)))]]) ).
cnf(refute_0_695,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) != greatest_lower_bound(least_upper_bound(identity,X_273),multiply(least_upper_bound(identity,X_273),inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),inverse(X_273)),least_upper_bound(identity,inverse(X_273))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)),greatest_lower_bound(least_upper_bound(identity,X_273),multiply(least_upper_bound(identity,X_273),inverse(X_273)))) )],[refute_0_496,refute_0_695]) ).
cnf(refute_0_697,plain,
inverse(multiply(inverse(X_60),multiply(X_60,X_61))) = multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))),
inference(subst,[],[p20x_3:[bind(X,$fot(inverse(X_60))),bind(Y,$fot(multiply(X_60,X_61)))]]) ).
cnf(refute_0_698,plain,
X_61 = multiply(inverse(X_60),multiply(X_60,X_61)),
inference(subst,[],[refute_0_505:[bind(X_58,$fot(X_60)),bind(X_59,$fot(X_61))]]) ).
cnf(refute_0_699,plain,
( X_61 != multiply(inverse(X_60),multiply(X_60,X_61))
| multiply(inverse(X_60),multiply(X_60,X_61)) = X_61 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_61)),bind(Y0,$fot(multiply(inverse(X_60),multiply(X_60,X_61))))]]) ).
cnf(refute_0_700,plain,
multiply(inverse(X_60),multiply(X_60,X_61)) = X_61,
inference(resolve,[$cnf( $equal(X_61,multiply(inverse(X_60),multiply(X_60,X_61))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
( multiply(inverse(X_60),multiply(X_60,X_61)) != X_61
| inverse(multiply(inverse(X_60),multiply(X_60,X_61))) != multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))
| inverse(X_61) = multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_60),multiply(X_60,X_61))),multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))) ),[0,0],$fot(X_61)]]) ).
cnf(refute_0_702,plain,
( inverse(multiply(inverse(X_60),multiply(X_60,X_61))) != multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))
| inverse(X_61) = multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),multiply(X_60,X_61)),X_61) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
inverse(X_61) = multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_60),multiply(X_60,X_61))),multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))) )],[refute_0_697,refute_0_702]) ).
cnf(refute_0_704,plain,
inverse(multiply(inverse(X_60),multiply(X_60,X_61))) = multiply(inverse(multiply(X_60,X_61)),X_60),
inference(subst,[],[refute_0_538:[bind(X,$fot(X_60)),bind(X_23,$fot(multiply(X_60,X_61)))]]) ).
cnf(refute_0_705,plain,
multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) = inverse(multiply(inverse(X_60),multiply(X_60,X_61))),
inference(subst,[],[refute_0_508:[bind(X,$fot(inverse(X_60))),bind(Y,$fot(multiply(X_60,X_61)))]]) ).
cnf(refute_0_706,plain,
( multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) != inverse(multiply(inverse(X_60),multiply(X_60,X_61)))
| inverse(multiply(inverse(X_60),multiply(X_60,X_61))) != multiply(inverse(multiply(X_60,X_61)),X_60)
| multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) = multiply(inverse(multiply(X_60,X_61)),X_60) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))))),bind(Y0,$fot(inverse(multiply(inverse(X_60),multiply(X_60,X_61))))),bind(Z0,$fot(multiply(inverse(multiply(X_60,X_61)),X_60)))]]) ).
cnf(refute_0_707,plain,
( inverse(multiply(inverse(X_60),multiply(X_60,X_61))) != multiply(inverse(multiply(X_60,X_61)),X_60)
| multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) = multiply(inverse(multiply(X_60,X_61)),X_60) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))),inverse(multiply(inverse(X_60),multiply(X_60,X_61)))) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) = multiply(inverse(multiply(X_60,X_61)),X_60),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_60),multiply(X_60,X_61))),multiply(inverse(multiply(X_60,X_61)),X_60)) )],[refute_0_704,refute_0_707]) ).
cnf(refute_0_709,plain,
( multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))) != multiply(inverse(multiply(X_60,X_61)),X_60)
| inverse(X_61) != multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))
| inverse(X_61) = multiply(inverse(multiply(X_60,X_61)),X_60) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_61),multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))) ),[1],$fot(multiply(inverse(multiply(X_60,X_61)),X_60))]]) ).
cnf(refute_0_710,plain,
( inverse(X_61) != multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))
| inverse(X_61) = multiply(inverse(multiply(X_60,X_61)),X_60) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60))),multiply(inverse(multiply(X_60,X_61)),X_60)) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
inverse(X_61) = multiply(inverse(multiply(X_60,X_61)),X_60),
inference(resolve,[$cnf( $equal(inverse(X_61),multiply(inverse(multiply(X_60,X_61)),inverse(inverse(X_60)))) )],[refute_0_703,refute_0_710]) ).
cnf(refute_0_712,plain,
inverse(inverse(least_upper_bound(X_84,X_224))) = multiply(inverse(multiply(X_224,inverse(least_upper_bound(X_84,X_224)))),X_224),
inference(subst,[],[refute_0_711:[bind(X_60,$fot(X_224)),bind(X_61,$fot(inverse(least_upper_bound(X_84,X_224))))]]) ).
cnf(refute_0_713,plain,
inverse(multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X))) = multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))),
inference(subst,[],[refute_0_515:[bind(X_22,$fot(least_upper_bound(X_84,inverse(inverse(X)))))]]) ).
cnf(refute_0_714,plain,
multiply(least_upper_bound(X_81,inverse(X_80)),X_80) = least_upper_bound(multiply(X_81,X_80),multiply(inverse(X_80),X_80)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_80)),bind(Y,$fot(X_81)),bind(Z,$fot(inverse(X_80)))]]) ).
cnf(refute_0_715,plain,
( multiply(inverse(X_80),X_80) != identity
| multiply(least_upper_bound(X_81,inverse(X_80)),X_80) != least_upper_bound(multiply(X_81,X_80),multiply(inverse(X_80),X_80))
| multiply(least_upper_bound(X_81,inverse(X_80)),X_80) = least_upper_bound(multiply(X_81,X_80),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_80)),X_80),least_upper_bound(multiply(X_81,X_80),multiply(inverse(X_80),X_80))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_716,plain,
( multiply(least_upper_bound(X_81,inverse(X_80)),X_80) != least_upper_bound(multiply(X_81,X_80),multiply(inverse(X_80),X_80))
| multiply(least_upper_bound(X_81,inverse(X_80)),X_80) = least_upper_bound(multiply(X_81,X_80),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),X_80),identity) )],[refute_0_186,refute_0_715]) ).
cnf(refute_0_717,plain,
multiply(least_upper_bound(X_81,inverse(X_80)),X_80) = least_upper_bound(multiply(X_81,X_80),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_80)),X_80),least_upper_bound(multiply(X_81,X_80),multiply(inverse(X_80),X_80))) )],[refute_0_714,refute_0_716]) ).
cnf(refute_0_718,plain,
least_upper_bound(multiply(X_81,X_80),identity) = least_upper_bound(identity,multiply(X_81,X_80)),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_81,X_80)))]]) ).
cnf(refute_0_719,plain,
( multiply(least_upper_bound(X_81,inverse(X_80)),X_80) != least_upper_bound(multiply(X_81,X_80),identity)
| least_upper_bound(multiply(X_81,X_80),identity) != least_upper_bound(identity,multiply(X_81,X_80))
| multiply(least_upper_bound(X_81,inverse(X_80)),X_80) = least_upper_bound(identity,multiply(X_81,X_80)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_81,inverse(X_80)),X_80),least_upper_bound(identity,multiply(X_81,X_80))) ),[0],$fot(least_upper_bound(multiply(X_81,X_80),identity))]]) ).
cnf(refute_0_720,plain,
( multiply(least_upper_bound(X_81,inverse(X_80)),X_80) != least_upper_bound(multiply(X_81,X_80),identity)
| multiply(least_upper_bound(X_81,inverse(X_80)),X_80) = least_upper_bound(identity,multiply(X_81,X_80)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_81,X_80),identity),least_upper_bound(identity,multiply(X_81,X_80))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
multiply(least_upper_bound(X_81,inverse(X_80)),X_80) = least_upper_bound(identity,multiply(X_81,X_80)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_80)),X_80),least_upper_bound(multiply(X_81,X_80),identity)) )],[refute_0_717,refute_0_720]) ).
cnf(refute_0_722,plain,
multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X)) = least_upper_bound(identity,multiply(X_84,inverse(X))),
inference(subst,[],[refute_0_721:[bind(X_80,$fot(inverse(X))),bind(X_81,$fot(X_84))]]) ).
cnf(refute_0_723,plain,
( multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X)) != least_upper_bound(identity,multiply(X_84,inverse(X)))
| inverse(multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X))) != multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))
| inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) = multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X))),multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))) ),[0,0],$fot(least_upper_bound(identity,multiply(X_84,inverse(X))))]]) ).
cnf(refute_0_724,plain,
( inverse(multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X))) != multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))
| inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) = multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X)),least_upper_bound(identity,multiply(X_84,inverse(X)))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) = multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_84,inverse(inverse(X))),inverse(X))),multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))) )],[refute_0_713,refute_0_724]) ).
cnf(refute_0_726,plain,
least_upper_bound(X_84,inverse(inverse(X))) = least_upper_bound(X_84,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_84,inverse(inverse(X))))]]) ).
cnf(refute_0_727,plain,
( inverse(inverse(X)) != X
| least_upper_bound(X_84,inverse(inverse(X))) != least_upper_bound(X_84,inverse(inverse(X)))
| least_upper_bound(X_84,inverse(inverse(X))) = least_upper_bound(X_84,X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_84,inverse(inverse(X))),least_upper_bound(X_84,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_728,plain,
( inverse(inverse(X)) != X
| least_upper_bound(X_84,inverse(inverse(X))) = least_upper_bound(X_84,X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,inverse(inverse(X))),least_upper_bound(X_84,inverse(inverse(X)))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
least_upper_bound(X_84,inverse(inverse(X))) = least_upper_bound(X_84,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_728]) ).
cnf(refute_0_730,plain,
inverse(least_upper_bound(X_84,inverse(inverse(X)))) = inverse(least_upper_bound(X_84,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_84,inverse(inverse(X)))))]]) ).
cnf(refute_0_731,plain,
( inverse(least_upper_bound(X_84,inverse(inverse(X)))) != inverse(least_upper_bound(X_84,inverse(inverse(X))))
| least_upper_bound(X_84,inverse(inverse(X))) != least_upper_bound(X_84,X)
| inverse(least_upper_bound(X_84,inverse(inverse(X)))) = inverse(least_upper_bound(X_84,X)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_84,inverse(inverse(X)))),inverse(least_upper_bound(X_84,inverse(inverse(X))))) ),[1,0],$fot(least_upper_bound(X_84,X))]]) ).
cnf(refute_0_732,plain,
( least_upper_bound(X_84,inverse(inverse(X))) != least_upper_bound(X_84,X)
| inverse(least_upper_bound(X_84,inverse(inverse(X)))) = inverse(least_upper_bound(X_84,X)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_84,inverse(inverse(X)))),inverse(least_upper_bound(X_84,inverse(inverse(X))))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
inverse(least_upper_bound(X_84,inverse(inverse(X)))) = inverse(least_upper_bound(X_84,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,inverse(inverse(X))),least_upper_bound(X_84,X)) )],[refute_0_729,refute_0_732]) ).
cnf(refute_0_734,plain,
multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) = multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))),
introduced(tautology,[refl,[$fot(multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))))]]) ).
cnf(refute_0_735,plain,
( multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) != multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))
| inverse(least_upper_bound(X_84,inverse(inverse(X)))) != inverse(least_upper_bound(X_84,X))
| multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) = multiply(X,inverse(least_upper_bound(X_84,X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))),multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))) ),[1,1],$fot(inverse(least_upper_bound(X_84,X)))]]) ).
cnf(refute_0_736,plain,
( inverse(least_upper_bound(X_84,inverse(inverse(X)))) != inverse(least_upper_bound(X_84,X))
| multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) = multiply(X,inverse(least_upper_bound(X_84,X))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))),multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) = multiply(X,inverse(least_upper_bound(X_84,X))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_84,inverse(inverse(X)))),inverse(least_upper_bound(X_84,X))) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
( multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))) != multiply(X,inverse(least_upper_bound(X_84,X)))
| inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) != multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))
| inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) = multiply(X,inverse(least_upper_bound(X_84,X))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))),multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))) ),[1],$fot(multiply(X,inverse(least_upper_bound(X_84,X))))]]) ).
cnf(refute_0_739,plain,
( inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) != multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))
| inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) = multiply(X,inverse(least_upper_bound(X_84,X))) ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X))))),multiply(X,inverse(least_upper_bound(X_84,X)))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))) = multiply(X,inverse(least_upper_bound(X_84,X))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_84,inverse(X)))),multiply(X,inverse(least_upper_bound(X_84,inverse(inverse(X)))))) )],[refute_0_725,refute_0_739]) ).
cnf(refute_0_741,plain,
inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224)))) = multiply(X_224,inverse(least_upper_bound(X_84,X_224))),
inference(subst,[],[refute_0_740:[bind(X,$fot(X_224))]]) ).
cnf(refute_0_742,plain,
( inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224)))) != multiply(X_224,inverse(least_upper_bound(X_84,X_224)))
| multiply(X_224,inverse(least_upper_bound(X_84,X_224))) = inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224)))))),bind(Y0,$fot(multiply(X_224,inverse(least_upper_bound(X_84,X_224)))))]]) ).
cnf(refute_0_743,plain,
multiply(X_224,inverse(least_upper_bound(X_84,X_224))) = inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224)))),multiply(X_224,inverse(least_upper_bound(X_84,X_224)))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
( multiply(X_224,inverse(least_upper_bound(X_84,X_224))) != inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))
| inverse(inverse(least_upper_bound(X_84,X_224))) != multiply(inverse(multiply(X_224,inverse(least_upper_bound(X_84,X_224)))),X_224)
| inverse(inverse(least_upper_bound(X_84,X_224))) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(X_84,X_224))),multiply(inverse(multiply(X_224,inverse(least_upper_bound(X_84,X_224)))),X_224)) ),[1,0,0],$fot(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224)))))]]) ).
cnf(refute_0_745,plain,
( inverse(inverse(least_upper_bound(X_84,X_224))) != multiply(inverse(multiply(X_224,inverse(least_upper_bound(X_84,X_224)))),X_224)
| inverse(inverse(least_upper_bound(X_84,X_224))) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) ),
inference(resolve,[$cnf( $equal(multiply(X_224,inverse(least_upper_bound(X_84,X_224))),inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
inverse(inverse(least_upper_bound(X_84,X_224))) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_84,X_224))),multiply(inverse(multiply(X_224,inverse(least_upper_bound(X_84,X_224)))),X_224)) )],[refute_0_712,refute_0_745]) ).
cnf(refute_0_747,plain,
inverse(inverse(least_upper_bound(X_84,X_224))) = least_upper_bound(X_84,X_224),
inference(subst,[],[p20x_2:[bind(X,$fot(least_upper_bound(X_84,X_224)))]]) ).
cnf(refute_0_748,plain,
( inverse(inverse(least_upper_bound(X_84,X_224))) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)
| inverse(inverse(least_upper_bound(X_84,X_224))) != least_upper_bound(X_84,X_224)
| least_upper_bound(X_84,X_224) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(X_84,X_224))),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)) ),[0],$fot(least_upper_bound(X_84,X_224))]]) ).
cnf(refute_0_749,plain,
( inverse(inverse(least_upper_bound(X_84,X_224))) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)
| least_upper_bound(X_84,X_224) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_84,X_224))),least_upper_bound(X_84,X_224)) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))) = least_upper_bound(identity,multiply(X_84,inverse(X_224))),
inference(subst,[],[p20x_2:[bind(X,$fot(least_upper_bound(identity,multiply(X_84,inverse(X_224)))))]]) ).
cnf(refute_0_751,plain,
multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) = multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224))]]) ).
cnf(refute_0_752,plain,
( multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)
| inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))) != least_upper_bound(identity,multiply(X_84,inverse(X_224)))
| multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)) ),[1,0],$fot(least_upper_bound(identity,multiply(X_84,inverse(X_224))))]]) ).
cnf(refute_0_753,plain,
( inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))) != least_upper_bound(identity,multiply(X_84,inverse(X_224)))
| multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),least_upper_bound(identity,multiply(X_84,inverse(X_224)))) )],[refute_0_750,refute_0_753]) ).
cnf(refute_0_755,plain,
( multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224) != multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224)
| least_upper_bound(X_84,X_224) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)
| least_upper_bound(X_84,X_224) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_84,X_224),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)) ),[1],$fot(multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224))]]) ).
cnf(refute_0_756,plain,
( least_upper_bound(X_84,X_224) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)
| least_upper_bound(X_84,X_224) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224),multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224)) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
( inverse(inverse(least_upper_bound(X_84,X_224))) != multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)
| least_upper_bound(X_84,X_224) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,X_224),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)) )],[refute_0_749,refute_0_756]) ).
cnf(refute_0_758,plain,
least_upper_bound(X_84,X_224) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_84,X_224))),multiply(inverse(inverse(least_upper_bound(identity,multiply(X_84,inverse(X_224))))),X_224)) )],[refute_0_746,refute_0_757]) ).
cnf(refute_0_759,plain,
least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))),greatest_lower_bound(identity,inverse(X_40))),
inference(subst,[],[refute_0_758:[bind(X_224,$fot(greatest_lower_bound(identity,inverse(X_40)))),bind(X_84,$fot(greatest_lower_bound(X_40,identity)))]]) ).
cnf(refute_0_760,plain,
inverse(inverse(X_40)) = multiply(greatest_lower_bound(X_40,identity),inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,identity)))),
inference(subst,[],[refute_0_523:[bind(X,$fot(inverse(X_40))),bind(Y,$fot(greatest_lower_bound(X_40,identity)))]]) ).
cnf(refute_0_761,plain,
multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(multiply(inverse(X_36),X_36),multiply(inverse(X_36),X_37)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_36))),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_762,plain,
multiply(inverse(X_36),X_36) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_763,plain,
( multiply(inverse(X_36),X_36) != identity
| multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(multiply(inverse(X_36),X_36),multiply(inverse(X_36),X_37))
| multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(identity,multiply(inverse(X_36),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(multiply(inverse(X_36),X_36),multiply(inverse(X_36),X_37))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_764,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(multiply(inverse(X_36),X_36),multiply(inverse(X_36),X_37))
| multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(identity,multiply(inverse(X_36),X_37)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),X_36),identity) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(identity,multiply(inverse(X_36),X_37)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(multiply(inverse(X_36),X_36),multiply(inverse(X_36),X_37))) )],[refute_0_761,refute_0_764]) ).
cnf(refute_0_766,plain,
multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) = greatest_lower_bound(identity,multiply(inverse(X_40),identity)),
inference(subst,[],[refute_0_765:[bind(X_36,$fot(X_40)),bind(X_37,$fot(identity))]]) ).
cnf(refute_0_767,plain,
inverse(X_40) = multiply(inverse(X_40),identity),
inference(subst,[],[refute_0_43:[bind(X,$fot(inverse(X_40)))]]) ).
cnf(refute_0_768,plain,
( inverse(X_40) != multiply(inverse(X_40),identity)
| multiply(inverse(X_40),identity) = inverse(X_40) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_40))),bind(Y0,$fot(multiply(inverse(X_40),identity)))]]) ).
cnf(refute_0_769,plain,
multiply(inverse(X_40),identity) = inverse(X_40),
inference(resolve,[$cnf( $equal(inverse(X_40),multiply(inverse(X_40),identity)) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
( multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) != greatest_lower_bound(identity,multiply(inverse(X_40),identity))
| multiply(inverse(X_40),identity) != inverse(X_40)
| multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) = greatest_lower_bound(identity,inverse(X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_40),greatest_lower_bound(X_40,identity)),greatest_lower_bound(identity,multiply(inverse(X_40),identity))) ),[1,1],$fot(inverse(X_40))]]) ).
cnf(refute_0_771,plain,
( multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) != greatest_lower_bound(identity,multiply(inverse(X_40),identity))
| multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) = greatest_lower_bound(identity,inverse(X_40)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),identity),inverse(X_40)) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) = greatest_lower_bound(identity,inverse(X_40)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),greatest_lower_bound(X_40,identity)),greatest_lower_bound(identity,multiply(inverse(X_40),identity))) )],[refute_0_766,refute_0_771]) ).
cnf(refute_0_773,plain,
( multiply(inverse(X_40),greatest_lower_bound(X_40,identity)) != greatest_lower_bound(identity,inverse(X_40))
| inverse(inverse(X_40)) != multiply(greatest_lower_bound(X_40,identity),inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,identity))))
| inverse(inverse(X_40)) = multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_40)),multiply(greatest_lower_bound(X_40,identity),inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,identity))))) ),[1,1,0],$fot(greatest_lower_bound(identity,inverse(X_40)))]]) ).
cnf(refute_0_774,plain,
( inverse(inverse(X_40)) != multiply(greatest_lower_bound(X_40,identity),inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,identity))))
| inverse(inverse(X_40)) = multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),greatest_lower_bound(X_40,identity)),greatest_lower_bound(identity,inverse(X_40))) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
inverse(inverse(X_40)) = multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_40)),multiply(greatest_lower_bound(X_40,identity),inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,identity))))) )],[refute_0_760,refute_0_774]) ).
cnf(refute_0_776,plain,
inverse(inverse(X_40)) = X_40,
inference(subst,[],[p20x_2:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_777,plain,
( inverse(inverse(X_40)) != X_40
| inverse(inverse(X_40)) != multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))
| X_40 = multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_40)),multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))) ),[0],$fot(X_40)]]) ).
cnf(refute_0_778,plain,
( inverse(inverse(X_40)) != multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))
| X_40 = multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_40)),X_40) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
X_40 = multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_40)),multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))) )],[refute_0_775,refute_0_778]) ).
cnf(refute_0_780,plain,
( X_40 != multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))
| multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))) = X_40 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_40)),bind(Y0,$fot(multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))))]]) ).
cnf(refute_0_781,plain,
multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))) = X_40,
inference(resolve,[$cnf( $equal(X_40,multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))) )],[refute_0_779,refute_0_780]) ).
cnf(refute_0_782,plain,
( multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))) != X_40
| least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))),greatest_lower_bound(identity,inverse(X_40)))
| least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) = multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))),greatest_lower_bound(identity,inverse(X_40)))) ),[1,0,1],$fot(X_40)]]) ).
cnf(refute_0_783,plain,
( least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))),greatest_lower_bound(identity,inverse(X_40)))
| least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) = multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40)))),X_40) )],[refute_0_781,refute_0_782]) ).
cnf(refute_0_784,plain,
least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) = multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_40,identity),inverse(greatest_lower_bound(identity,inverse(X_40))))),greatest_lower_bound(identity,inverse(X_40)))) )],[refute_0_759,refute_0_783]) ).
cnf(refute_0_785,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106))),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(greatest_lower_bound(X_106,identity))),bind(X_76,$fot(inverse(X_106)))]]) ).
cnf(refute_0_786,plain,
multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) = greatest_lower_bound(inverse(X_88),multiply(X_88,inverse(X_88))),
inference(subst,[],[refute_0_22:[bind(X_42,$fot(inverse(X_88))),bind(X_43,$fot(X_88))]]) ).
cnf(refute_0_787,plain,
multiply(X_88,inverse(X_88)) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(X_88))]]) ).
cnf(refute_0_788,plain,
( multiply(X_88,inverse(X_88)) != identity
| multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) != greatest_lower_bound(inverse(X_88),multiply(X_88,inverse(X_88)))
| multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) = greatest_lower_bound(inverse(X_88),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),inverse(X_88)),greatest_lower_bound(inverse(X_88),multiply(X_88,inverse(X_88)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_789,plain,
( multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) != greatest_lower_bound(inverse(X_88),multiply(X_88,inverse(X_88)))
| multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) = greatest_lower_bound(inverse(X_88),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_88,inverse(X_88)),identity) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) = greatest_lower_bound(inverse(X_88),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),inverse(X_88)),greatest_lower_bound(inverse(X_88),multiply(X_88,inverse(X_88)))) )],[refute_0_786,refute_0_789]) ).
cnf(refute_0_791,plain,
multiply(inverse(X_36),greatest_lower_bound(X_36,multiply(X_36,X_56))) = greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))),
inference(subst,[],[refute_0_765:[bind(X_37,$fot(multiply(X_36,X_56)))]]) ).
cnf(refute_0_792,plain,
multiply(X_36,greatest_lower_bound(X_56,identity)) = greatest_lower_bound(X_36,multiply(X_36,X_56)),
inference(subst,[],[refute_0_182:[bind(X_35,$fot(X_36)),bind(X_36,$fot(X_56))]]) ).
cnf(refute_0_793,plain,
( multiply(X_36,greatest_lower_bound(X_56,identity)) != greatest_lower_bound(X_36,multiply(X_36,X_56))
| greatest_lower_bound(X_36,multiply(X_36,X_56)) = multiply(X_36,greatest_lower_bound(X_56,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_36,greatest_lower_bound(X_56,identity)))),bind(Y0,$fot(greatest_lower_bound(X_36,multiply(X_36,X_56))))]]) ).
cnf(refute_0_794,plain,
greatest_lower_bound(X_36,multiply(X_36,X_56)) = multiply(X_36,greatest_lower_bound(X_56,identity)),
inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_56,identity)),greatest_lower_bound(X_36,multiply(X_36,X_56))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_36,multiply(X_36,X_56))) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| greatest_lower_bound(X_36,multiply(X_36,X_56)) != multiply(X_36,greatest_lower_bound(X_56,identity))
| multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) = greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_36,multiply(X_36,X_56))),greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))) ),[0,1],$fot(multiply(X_36,greatest_lower_bound(X_56,identity)))]]) ).
cnf(refute_0_796,plain,
( multiply(inverse(X_36),greatest_lower_bound(X_36,multiply(X_36,X_56))) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) = greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,multiply(X_36,X_56)),multiply(X_36,greatest_lower_bound(X_56,identity))) )],[refute_0_794,refute_0_795]) ).
cnf(refute_0_797,plain,
multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) = greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),greatest_lower_bound(X_36,multiply(X_36,X_56))),greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))) )],[refute_0_791,refute_0_796]) ).
cnf(refute_0_798,plain,
( X_59 != multiply(inverse(X_58),multiply(X_58,X_59))
| multiply(inverse(X_58),multiply(X_58,X_59)) = X_59 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_59)),bind(Y0,$fot(multiply(inverse(X_58),multiply(X_58,X_59))))]]) ).
cnf(refute_0_799,plain,
multiply(inverse(X_58),multiply(X_58,X_59)) = X_59,
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(X_58),multiply(X_58,X_59))) )],[refute_0_505,refute_0_798]) ).
cnf(refute_0_800,plain,
multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) = greatest_lower_bound(X_56,identity),
inference(subst,[],[refute_0_799:[bind(X_58,$fot(X_36)),bind(X_59,$fot(greatest_lower_bound(X_56,identity)))]]) ).
cnf(refute_0_801,plain,
( multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) != greatest_lower_bound(X_56,identity)
| multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| greatest_lower_bound(X_56,identity) = greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))),greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))) ),[0],$fot(greatest_lower_bound(X_56,identity))]]) ).
cnf(refute_0_802,plain,
( multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| greatest_lower_bound(X_56,identity) = greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))),greatest_lower_bound(X_56,identity)) )],[refute_0_800,refute_0_801]) ).
cnf(refute_0_803,plain,
multiply(inverse(X_36),multiply(X_36,X_56)) = X_56,
inference(subst,[],[refute_0_799:[bind(X_58,$fot(X_36)),bind(X_59,$fot(X_56))]]) ).
cnf(refute_0_804,plain,
greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) = greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))))]]) ).
cnf(refute_0_805,plain,
( multiply(inverse(X_36),multiply(X_36,X_56)) != X_56
| greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) = greatest_lower_bound(identity,X_56) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))),greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))) ),[1,1],$fot(X_56)]]) ).
cnf(refute_0_806,plain,
( multiply(inverse(X_36),multiply(X_36,X_56)) != X_56
| greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) = greatest_lower_bound(identity,X_56) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))),greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) = greatest_lower_bound(identity,X_56),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),multiply(X_36,X_56)),X_56) )],[refute_0_803,refute_0_806]) ).
cnf(refute_0_808,plain,
( greatest_lower_bound(X_56,identity) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))) != greatest_lower_bound(identity,X_56)
| greatest_lower_bound(X_56,identity) = greatest_lower_bound(identity,X_56) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_56,identity),greatest_lower_bound(identity,X_56)) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))))]]) ).
cnf(refute_0_809,plain,
( greatest_lower_bound(X_56,identity) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| greatest_lower_bound(X_56,identity) = greatest_lower_bound(identity,X_56) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56))),greatest_lower_bound(identity,X_56)) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
( multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))) != greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))
| greatest_lower_bound(X_56,identity) = greatest_lower_bound(identity,X_56) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_56,identity),greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))) )],[refute_0_802,refute_0_809]) ).
cnf(refute_0_811,plain,
greatest_lower_bound(X_56,identity) = greatest_lower_bound(identity,X_56),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),multiply(X_36,greatest_lower_bound(X_56,identity))),greatest_lower_bound(identity,multiply(inverse(X_36),multiply(X_36,X_56)))) )],[refute_0_797,refute_0_810]) ).
cnf(refute_0_812,plain,
greatest_lower_bound(inverse(X_88),identity) = greatest_lower_bound(identity,inverse(X_88)),
inference(subst,[],[refute_0_811:[bind(X_56,$fot(inverse(X_88)))]]) ).
cnf(refute_0_813,plain,
( multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) != greatest_lower_bound(inverse(X_88),identity)
| greatest_lower_bound(inverse(X_88),identity) != greatest_lower_bound(identity,inverse(X_88))
| multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) = greatest_lower_bound(identity,inverse(X_88)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_88,identity),inverse(X_88)),greatest_lower_bound(identity,inverse(X_88))) ),[0],$fot(greatest_lower_bound(inverse(X_88),identity))]]) ).
cnf(refute_0_814,plain,
( multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) != greatest_lower_bound(inverse(X_88),identity)
| multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) = greatest_lower_bound(identity,inverse(X_88)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_88),identity),greatest_lower_bound(identity,inverse(X_88))) )],[refute_0_812,refute_0_813]) ).
cnf(refute_0_815,plain,
multiply(greatest_lower_bound(X_88,identity),inverse(X_88)) = greatest_lower_bound(identity,inverse(X_88)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),inverse(X_88)),greatest_lower_bound(inverse(X_88),identity)) )],[refute_0_790,refute_0_814]) ).
cnf(refute_0_816,plain,
multiply(greatest_lower_bound(X_106,identity),inverse(X_106)) = greatest_lower_bound(identity,inverse(X_106)),
inference(subst,[],[refute_0_815:[bind(X_88,$fot(X_106))]]) ).
cnf(refute_0_817,plain,
( multiply(greatest_lower_bound(X_106,identity),inverse(X_106)) != greatest_lower_bound(identity,inverse(X_106))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_106)))]]) ).
cnf(refute_0_818,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),inverse(X_106)),greatest_lower_bound(identity,inverse(X_106))) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) )],[refute_0_785,refute_0_818]) ).
cnf(refute_0_820,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) = multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),
inference(subst,[],[refute_0_296:[bind(X_17,$fot(greatest_lower_bound(X_106,identity))),bind(X_94,$fot(inverse(X_106)))]]) ).
cnf(refute_0_821,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))) ),[0],$fot(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))))]]) ).
cnf(refute_0_822,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106)))) )],[refute_0_820,refute_0_821]) ).
cnf(refute_0_823,plain,
multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) = least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(inverse(X_106),identity)),least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))) )],[refute_0_819,refute_0_822]) ).
cnf(refute_0_824,plain,
( multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) != least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))
| least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) = multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))))]]) ).
cnf(refute_0_825,plain,
least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106))) = multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),least_upper_bound(identity,inverse(X_106))),least_upper_bound(greatest_lower_bound(X_106,identity),greatest_lower_bound(identity,inverse(X_106)))) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) = multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))),
inference(subst,[],[refute_0_825:[bind(X_106,$fot(X_40))]]) ).
cnf(refute_0_827,plain,
( least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) != multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40)))
| least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) != multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40)))
| multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))) = multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))),multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40)))) ),[0],$fot(multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))))]]) ).
cnf(refute_0_828,plain,
( least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))) != multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40)))
| multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))) = multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))),multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40)))) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))) = multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_40,identity),greatest_lower_bound(identity,inverse(X_40))),multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40)))) )],[refute_0_784,refute_0_828]) ).
cnf(refute_0_830,plain,
( multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))) != multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40)))
| multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))) = multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40)))))]]) ).
cnf(refute_0_831,plain,
multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40))) = multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_40,identity),least_upper_bound(identity,inverse(X_40))),multiply(least_upper_bound(identity,X_40),greatest_lower_bound(identity,inverse(X_40)))) )],[refute_0_829,refute_0_830]) ).
cnf(refute_0_832,plain,
multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) = multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),
inference(subst,[],[refute_0_831:[bind(X_40,$fot(X_273))]]) ).
cnf(refute_0_833,plain,
multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) = least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(identity,X_208))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(greatest_lower_bound(identity,X_208)))]]) ).
cnf(refute_0_834,plain,
multiply(Z,greatest_lower_bound(identity,X_208)) = multiply(Z,greatest_lower_bound(X_208,identity)),
inference(subst,[],[refute_0_359:[bind(X_27,$fot(Z)),bind(X_56,$fot(X_208))]]) ).
cnf(refute_0_835,plain,
( multiply(Z,greatest_lower_bound(identity,X_208)) != multiply(Z,greatest_lower_bound(X_208,identity))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) != least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(identity,X_208)))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) = least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)),least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(identity,X_208)))) ),[1,1],$fot(multiply(Z,greatest_lower_bound(X_208,identity)))]]) ).
cnf(refute_0_836,plain,
( multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) != least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(identity,X_208)))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) = least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))) ),
inference(resolve,[$cnf( $equal(multiply(Z,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) = least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)),least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(identity,X_208)))) )],[refute_0_833,refute_0_836]) ).
cnf(refute_0_838,plain,
multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_230,X_229)),multiply(Z,greatest_lower_bound(X_230,X_229))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(greatest_lower_bound(X_230,X_229)))]]) ).
cnf(refute_0_839,plain,
multiply(Y,greatest_lower_bound(X_230,X_229)) = multiply(Y,greatest_lower_bound(X_229,X_230)),
inference(subst,[],[refute_0_332:[bind(X_35,$fot(Y)),bind(X_36,$fot(X_229)),bind(X_37,$fot(X_230))]]) ).
cnf(refute_0_840,plain,
( multiply(Y,greatest_lower_bound(X_230,X_229)) != multiply(Y,greatest_lower_bound(X_229,X_230))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) != least_upper_bound(multiply(Y,greatest_lower_bound(X_230,X_229)),multiply(Z,greatest_lower_bound(X_230,X_229)))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)),least_upper_bound(multiply(Y,greatest_lower_bound(X_230,X_229)),multiply(Z,greatest_lower_bound(X_230,X_229)))) ),[1,0],$fot(multiply(Y,greatest_lower_bound(X_229,X_230)))]]) ).
cnf(refute_0_841,plain,
( multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) != least_upper_bound(multiply(Y,greatest_lower_bound(X_230,X_229)),multiply(Z,greatest_lower_bound(X_230,X_229)))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229))) ),
inference(resolve,[$cnf( $equal(multiply(Y,greatest_lower_bound(X_230,X_229)),multiply(Y,greatest_lower_bound(X_229,X_230))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)),least_upper_bound(multiply(Y,greatest_lower_bound(X_230,X_229)),multiply(Z,greatest_lower_bound(X_230,X_229)))) )],[refute_0_838,refute_0_841]) ).
cnf(refute_0_843,plain,
( multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) != least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229)))
| least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229))) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)))),bind(Y0,$fot(least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229)))))]]) ).
cnf(refute_0_844,plain,
least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229))) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_230,X_229)),least_upper_bound(multiply(Y,greatest_lower_bound(X_229,X_230)),multiply(Z,greatest_lower_bound(X_230,X_229)))) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity)),
inference(subst,[],[refute_0_844:[bind(X_229,$fot(identity)),bind(X_230,$fot(X_208))]]) ).
cnf(refute_0_846,plain,
( multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) != least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity)))
| least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))) != multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)),multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity))) ),[0],$fot(least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))))]]) ).
cnf(refute_0_847,plain,
( multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) != least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity)))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity))),multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity))) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)),least_upper_bound(multiply(Y,greatest_lower_bound(identity,X_208)),multiply(Z,greatest_lower_bound(X_208,identity)))) )],[refute_0_837,refute_0_847]) ).
cnf(refute_0_849,plain,
( multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) != multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity))
| multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity)) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)))),bind(Y0,$fot(multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity))))]]) ).
cnf(refute_0_850,plain,
multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity)) = multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),greatest_lower_bound(identity,X_208)),multiply(least_upper_bound(Y,Z),greatest_lower_bound(X_208,identity))) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))),
inference(subst,[],[refute_0_850:[bind(Y,$fot(identity)),bind(Z,$fot(X_273)),bind(X_208,$fot(inverse(X_273)))]]) ).
cnf(refute_0_852,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) != multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) != multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)))),bind(Y0,$fot(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))))]]) ).
cnf(refute_0_853,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))) != multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)),multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273)))) )],[refute_0_851,refute_0_852]) ).
cnf(refute_0_854,plain,
multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) = multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(identity,inverse(X_273))),multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))) )],[refute_0_832,refute_0_853]) ).
cnf(refute_0_855,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) != multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))
| multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) != greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))
| multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)),greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))) ),[0],$fot(multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))))]]) ).
cnf(refute_0_856,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) != greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))
| multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)),multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273)))) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
( multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) != greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))
| greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) = multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))))]]) ).
cnf(refute_0_858,plain,
greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) = multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)),greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_495,refute_0_857]) ).
cnf(refute_0_859,plain,
greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))) = multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)),
inference(subst,[],[refute_0_858:[bind(X_110,$fot(X_273))]]) ).
cnf(refute_0_860,plain,
( multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) != greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))
| greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))) != multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))
| multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))))]]) ).
cnf(refute_0_861,plain,
( multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) != greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))
| multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273))),multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
( multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)) != greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))
| multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))) )],[refute_0_856,refute_0_861]) ).
cnf(refute_0_863,plain,
multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) = multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_273),greatest_lower_bound(inverse(X_273),identity)),greatest_lower_bound(least_upper_bound(identity,X_273),least_upper_bound(identity,inverse(X_273)))) )],[refute_0_696,refute_0_862]) ).
cnf(refute_0_864,plain,
( multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) != multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))
| multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) = multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))))]]) ).
cnf(refute_0_865,plain,
multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273)) = multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_273,identity),least_upper_bound(identity,inverse(X_273))),multiply(greatest_lower_bound(identity,inverse(X_273)),least_upper_bound(identity,X_273))) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) = multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))),
inference(subst,[],[refute_0_865:[bind(X_273,$fot(X_110))]]) ).
cnf(refute_0_867,plain,
( multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) != multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110)))
| multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) != greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)),greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))) ),[0],$fot(multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))))]]) ).
cnf(refute_0_868,plain,
( multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)) != greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)),multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_866,refute_0_867]) ).
cnf(refute_0_869,plain,
multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))) = greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_110)),least_upper_bound(identity,X_110)),greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_495,refute_0_868]) ).
cnf(refute_0_870,plain,
( multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))) != greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))
| greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) = multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))))]]) ).
cnf(refute_0_871,plain,
greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110))) = multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_110,identity),least_upper_bound(identity,inverse(X_110))),greatest_lower_bound(least_upper_bound(identity,X_110),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(subst,[],[refute_0_871:[bind(X_110,$fot(X_291))]]) ).
cnf(refute_0_873,plain,
greatest_lower_bound(X_27,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) = greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)),
inference(subst,[],[refute_0_71:[bind(X_28,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_874,plain,
least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))) = greatest_lower_bound(X_31,Y),
inference(subst,[],[refute_0_203:[bind(X,$fot(greatest_lower_bound(X_31,Y)))]]) ).
cnf(refute_0_875,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_31,Y)) = greatest_lower_bound(Y,X_31),
inference(subst,[],[refute_0_96:[bind(Y,$fot(X_31)),bind(X_21,$fot(Y))]]) ).
cnf(refute_0_876,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_31,Y)) != greatest_lower_bound(Y,X_31)
| least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))) != greatest_lower_bound(X_31,Y)
| least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,X_31)) = greatest_lower_bound(X_31,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))),greatest_lower_bound(X_31,Y)) ),[0,1],$fot(greatest_lower_bound(Y,X_31))]]) ).
cnf(refute_0_877,plain,
( least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))) != greatest_lower_bound(X_31,Y)
| least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,X_31)) = greatest_lower_bound(X_31,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_31,Y)),greatest_lower_bound(Y,X_31)) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,X_31)) = greatest_lower_bound(X_31,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_31,Y),greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))),greatest_lower_bound(X_31,Y)) )],[refute_0_874,refute_0_877]) ).
cnf(refute_0_879,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),
inference(subst,[],[refute_0_878:[bind(Y,$fot(least_upper_bound(X_286,X_287))),bind(X_31,$fot(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)))]]) ).
cnf(refute_0_880,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48))) = greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X)),
inference(subst,[],[refute_0_132:[bind(X_26,$fot(least_upper_bound(X_48,X_49))),bind(X_27,$fot(least_upper_bound(X_49,X_48)))]]) ).
cnf(refute_0_881,plain,
greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)) = least_upper_bound(X_48,X_49),
inference(subst,[],[refute_0_238:[bind(Y,$fot(X_48)),bind(X_21,$fot(X_49))]]) ).
cnf(refute_0_882,plain,
( greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48))) != greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X))
| greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)) != least_upper_bound(X_48,X_49)
| greatest_lower_bound(X,least_upper_bound(X_48,X_49)) = greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48))),greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X))) ),[0,1],$fot(least_upper_bound(X_48,X_49))]]) ).
cnf(refute_0_883,plain,
( greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48))) != greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X))
| greatest_lower_bound(X,least_upper_bound(X_48,X_49)) = greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)),least_upper_bound(X_48,X_49)) )],[refute_0_881,refute_0_882]) ).
cnf(refute_0_884,plain,
greatest_lower_bound(X,least_upper_bound(X_48,X_49)) = greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48))),greatest_lower_bound(least_upper_bound(X_48,X_49),greatest_lower_bound(least_upper_bound(X_49,X_48),X))) )],[refute_0_880,refute_0_883]) ).
cnf(refute_0_885,plain,
greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),
inference(subst,[],[refute_0_884:[bind(X,$fot(X_285)),bind(X_48,$fot(X_286)),bind(X_49,$fot(X_287))]]) ).
cnf(refute_0_886,plain,
( greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) != greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))
| greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))))]]) ).
cnf(refute_0_887,plain,
greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
( greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) != greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))) ),[0,1],$fot(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)))]]) ).
cnf(refute_0_889,plain,
( least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))) )],[refute_0_879,refute_0_889]) ).
cnf(refute_0_891,plain,
least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))) = greatest_lower_bound(X_47,X_45),
inference(subst,[],[refute_0_203:[bind(X,$fot(greatest_lower_bound(X_47,X_45)))]]) ).
cnf(refute_0_892,plain,
greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47)) = greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45)),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_45)),bind(X_26,$fot(Y)),bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_893,plain,
( greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47)) != greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))
| greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45)) = greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))))]]) ).
cnf(refute_0_894,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45)) = greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47)),greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))) )],[refute_0_892,refute_0_893]) ).
cnf(refute_0_895,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45)) != greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47))
| least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))) != greatest_lower_bound(X_47,X_45)
| least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47))) = greatest_lower_bound(X_47,X_45) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))),greatest_lower_bound(X_47,X_45)) ),[0,1],$fot(greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47)))]]) ).
cnf(refute_0_896,plain,
( least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))) != greatest_lower_bound(X_47,X_45)
| least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47))) = greatest_lower_bound(X_47,X_45) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45)),greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47))) )],[refute_0_894,refute_0_895]) ).
cnf(refute_0_897,plain,
least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(X_45,greatest_lower_bound(Y,X_47))) = greatest_lower_bound(X_47,X_45),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,X_45),greatest_lower_bound(Y,greatest_lower_bound(X_47,X_45))),greatest_lower_bound(X_47,X_45)) )],[refute_0_891,refute_0_896]) ).
cnf(refute_0_898,plain,
least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),
inference(subst,[],[refute_0_897:[bind(Y,$fot(least_upper_bound(X_287,X_286))),bind(X_45,$fot(least_upper_bound(X_286,X_287))),bind(X_47,$fot(X_285))]]) ).
cnf(refute_0_899,plain,
least_upper_bound(X_79,X) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,multiply(inverse(X),least_upper_bound(X_79,X)))),
inference(subst,[],[refute_0_529:[bind(X_59,$fot(least_upper_bound(X_79,X))),bind(X_86,$fot(inverse(X)))]]) ).
cnf(refute_0_900,plain,
( multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X)))) != least_upper_bound(identity,multiply(inverse(X),X_79))
| inverse(inverse(X)) != X
| multiply(inverse(X),least_upper_bound(X_79,X)) = least_upper_bound(identity,multiply(inverse(X),X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) ),[0,1,1],$fot(X)]]) ).
cnf(refute_0_901,plain,
( multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X)))) != least_upper_bound(identity,multiply(inverse(X),X_79))
| multiply(inverse(X),least_upper_bound(X_79,X)) = least_upper_bound(identity,multiply(inverse(X),X_79)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_900]) ).
cnf(refute_0_902,plain,
multiply(inverse(X),least_upper_bound(X_79,X)) = least_upper_bound(identity,multiply(inverse(X),X_79)),
inference(resolve,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_79,inverse(inverse(X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) )],[refute_0_642,refute_0_901]) ).
cnf(refute_0_903,plain,
( multiply(inverse(X),least_upper_bound(X_79,X)) != least_upper_bound(identity,multiply(inverse(X),X_79))
| least_upper_bound(X_79,X) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,multiply(inverse(X),least_upper_bound(X_79,X))))
| least_upper_bound(X_79,X) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_79,X),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,multiply(inverse(X),least_upper_bound(X_79,X))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(inverse(X),X_79)))]]) ).
cnf(refute_0_904,plain,
( least_upper_bound(X_79,X) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,multiply(inverse(X),least_upper_bound(X_79,X))))
| least_upper_bound(X_79,X) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_79,X)),least_upper_bound(identity,multiply(inverse(X),X_79))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
least_upper_bound(X_79,X) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,X),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,multiply(inverse(X),least_upper_bound(X_79,X))))) )],[refute_0_899,refute_0_904]) ).
cnf(refute_0_906,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(identity,multiply(inverse(X),X_79)),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(multiply(inverse(X),X_79))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_907,plain,
multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))))]]) ).
cnf(refute_0_908,plain,
( multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))) != least_upper_bound(identity,multiply(inverse(X),X_79))
| multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X),X_79)))]]) ).
cnf(refute_0_909,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))) != least_upper_bound(identity,multiply(inverse(X),X_79))
| multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))),least_upper_bound(identity,multiply(inverse(X),X_79))) )],[refute_0_906,refute_0_909]) ).
cnf(refute_0_911,plain,
inverse(least_upper_bound(X_130,X_131)) = multiply(inverse(least_upper_bound(X_131,X_130)),inverse(multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130))))),
inference(subst,[],[refute_0_523:[bind(X,$fot(least_upper_bound(X_130,X_131))),bind(Y,$fot(inverse(least_upper_bound(X_131,X_130))))]]) ).
cnf(refute_0_912,plain,
multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(multiply(inverse(X_37),X_36),multiply(inverse(X_37),X_37)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_37))),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_913,plain,
multiply(inverse(X_37),X_37) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_914,plain,
( multiply(inverse(X_37),X_37) != identity
| multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(multiply(inverse(X_37),X_36),multiply(inverse(X_37),X_37))
| multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(multiply(inverse(X_37),X_36),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(multiply(inverse(X_37),X_36),multiply(inverse(X_37),X_37))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_915,plain,
( multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(multiply(inverse(X_37),X_36),multiply(inverse(X_37),X_37))
| multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(multiply(inverse(X_37),X_36),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),X_37),identity) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(multiply(inverse(X_37),X_36),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(multiply(inverse(X_37),X_36),multiply(inverse(X_37),X_37))) )],[refute_0_912,refute_0_915]) ).
cnf(refute_0_917,plain,
greatest_lower_bound(multiply(inverse(X_37),X_36),identity) = greatest_lower_bound(identity,multiply(inverse(X_37),X_36)),
inference(subst,[],[refute_0_18:[bind(X_27,$fot(identity)),bind(X_28,$fot(multiply(inverse(X_37),X_36)))]]) ).
cnf(refute_0_918,plain,
( multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(multiply(inverse(X_37),X_36),identity)
| greatest_lower_bound(multiply(inverse(X_37),X_36),identity) != greatest_lower_bound(identity,multiply(inverse(X_37),X_36))
| multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(identity,multiply(inverse(X_37),X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_37),X_36),identity))]]) ).
cnf(refute_0_919,plain,
( multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(multiply(inverse(X_37),X_36),identity)
| multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(identity,multiply(inverse(X_37),X_36)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_37),X_36),identity),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(identity,multiply(inverse(X_37),X_36)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(multiply(inverse(X_37),X_36),identity)) )],[refute_0_916,refute_0_919]) ).
cnf(refute_0_921,plain,
multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)),
inference(subst,[],[refute_0_920:[bind(X_36,$fot(identity)),bind(X_37,$fot(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))]]) ).
cnf(refute_0_922,plain,
multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)) = greatest_lower_bound(multiply(X_43,inverse(X_43)),multiply(X_44,inverse(X_43))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_43))),bind(Y,$fot(X_43)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_923,plain,
multiply(X_43,inverse(X_43)) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(X_43))]]) ).
cnf(refute_0_924,plain,
( multiply(X_43,inverse(X_43)) != identity
| multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)) != greatest_lower_bound(multiply(X_43,inverse(X_43)),multiply(X_44,inverse(X_43)))
| multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)) = greatest_lower_bound(identity,multiply(X_44,inverse(X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)),greatest_lower_bound(multiply(X_43,inverse(X_43)),multiply(X_44,inverse(X_43)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_925,plain,
( multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)) != greatest_lower_bound(multiply(X_43,inverse(X_43)),multiply(X_44,inverse(X_43)))
| multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)) = greatest_lower_bound(identity,multiply(X_44,inverse(X_43))) ),
inference(resolve,[$cnf( $equal(multiply(X_43,inverse(X_43)),identity) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)) = greatest_lower_bound(identity,multiply(X_44,inverse(X_43))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,X_44),inverse(X_43)),greatest_lower_bound(multiply(X_43,inverse(X_43)),multiply(X_44,inverse(X_43)))) )],[refute_0_922,refute_0_925]) ).
cnf(refute_0_927,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),inverse(least_upper_bound(Y,X_21))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))),
inference(subst,[],[refute_0_926:[bind(X_43,$fot(least_upper_bound(Y,X_21))),bind(X_44,$fot(least_upper_bound(X_21,Y)))]]) ).
cnf(refute_0_928,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),inverse(least_upper_bound(Y,X_21))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))
| greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)) != least_upper_bound(Y,X_21)
| multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),inverse(least_upper_bound(Y,X_21))),greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))) ),[0,0],$fot(least_upper_bound(Y,X_21))]]) ).
cnf(refute_0_929,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),inverse(least_upper_bound(Y,X_21))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))
| multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),least_upper_bound(Y,X_21)) )],[refute_0_238,refute_0_928]) ).
cnf(refute_0_930,plain,
multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),inverse(least_upper_bound(Y,X_21))),greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))) )],[refute_0_927,refute_0_929]) ).
cnf(refute_0_931,plain,
multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(least_upper_bound(Y,X_21)))]]) ).
cnf(refute_0_932,plain,
( multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))
| multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))) != identity
| identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))),greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_933,plain,
( multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))
| identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))),identity) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,X_21),inverse(least_upper_bound(Y,X_21))),greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))) )],[refute_0_930,refute_0_933]) ).
cnf(refute_0_935,plain,
identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),
inference(subst,[],[refute_0_934:[bind(Y,$fot(X_122)),bind(X_21,$fot(X_123))]]) ).
cnf(refute_0_936,plain,
( identity != greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))))]]) ).
cnf(refute_0_937,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
( multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) != greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) != identity
| multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) = greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_939,plain,
( multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) != greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))
| multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) = greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) = greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))) )],[refute_0_921,refute_0_939]) ).
cnf(refute_0_941,plain,
inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) = multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))),
inference(subst,[],[refute_0_515:[bind(X,$fot(least_upper_bound(X_122,X_123))),bind(X_22,$fot(least_upper_bound(X_123,X_122)))]]) ).
cnf(refute_0_942,plain,
multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) = inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))))]]) ).
cnf(refute_0_943,plain,
( multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) != inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))
| inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) != multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))
| multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) = multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))),bind(Z0,$fot(multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))))]]) ).
cnf(refute_0_944,plain,
( inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) != multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))
| multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) = multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) )],[refute_0_942,refute_0_943]) ).
cnf(refute_0_945,plain,
multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) = multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) )],[refute_0_941,refute_0_944]) ).
cnf(refute_0_946,plain,
( multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) != multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))
| multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) != greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))
| multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) = greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))) ),[0],$fot(multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))))]]) ).
cnf(refute_0_947,plain,
( multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) != greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))
| multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) = greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) )],[refute_0_945,refute_0_946]) ).
cnf(refute_0_948,plain,
( identity != greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))))]]) ).
cnf(refute_0_949,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21)))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(X_21,Y),inverse(least_upper_bound(Y,X_21))))) )],[refute_0_934,refute_0_948]) ).
cnf(refute_0_950,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) = identity,
inference(subst,[],[refute_0_949:[bind(Y,$fot(X_123)),bind(X_21,$fot(X_122))]]) ).
cnf(refute_0_951,plain,
greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))))]]) ).
cnf(refute_0_952,plain,
( greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) != greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))
| inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) != multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))
| greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))) ),[1,1],$fot(multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))))]]) ).
cnf(refute_0_953,plain,
( inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))) != multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))
| greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))),
inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) )],[refute_0_941,refute_0_953]) ).
cnf(refute_0_955,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) != identity
| greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))))
| greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_956,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))) != identity
| greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))))) )],[refute_0_954,refute_0_955]) ).
cnf(refute_0_957,plain,
greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))),identity) )],[refute_0_950,refute_0_956]) ).
cnf(refute_0_958,plain,
multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),
inference(subst,[],[refute_0_561:[bind(X,$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))))]]) ).
cnf(refute_0_959,plain,
multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity) = multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity),
inference(subst,[],[refute_0_161:[bind(X_27,$fot(identity)),bind(X_88,$fot(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))))]]) ).
cnf(refute_0_960,plain,
( multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity) != greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))
| multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity) != multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity)
| multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))))]]) ).
cnf(refute_0_961,plain,
( multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity) != greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))
| multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity),multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity)) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity),greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))) )],[refute_0_958,refute_0_961]) ).
cnf(refute_0_963,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) = multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity),
inference(subst,[],[refute_0_119:[bind(X_42,$fot(identity)),bind(X_43,$fot(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))))]]) ).
cnf(refute_0_964,plain,
( multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity) != greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) != multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity)
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))))]]) ).
cnf(refute_0_965,plain,
( multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity) != greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)),multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity)) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),identity),greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))) )],[refute_0_962,refute_0_965]) ).
cnf(refute_0_967,plain,
( greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) != greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))
| greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) != identity
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_968,plain,
( greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))) != identity
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)),greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))))) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123))))),identity) )],[refute_0_957,refute_0_968]) ).
cnf(refute_0_970,plain,
( multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) != greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))
| greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)) != identity
| multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)))]]) ).
cnf(refute_0_971,plain,
( multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) != greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))
| multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity)),identity) )],[refute_0_969,refute_0_970]) ).
cnf(refute_0_972,plain,
( multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity) != greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))
| multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))),greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))) )],[refute_0_947,refute_0_971]) ).
cnf(refute_0_973,plain,
multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity),greatest_lower_bound(identity,multiply(inverse(multiply(least_upper_bound(X_123,X_122),inverse(least_upper_bound(X_122,X_123)))),identity))) )],[refute_0_940,refute_0_972]) ).
cnf(refute_0_974,plain,
multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130))) = identity,
inference(subst,[],[refute_0_973:[bind(X_122,$fot(X_130)),bind(X_123,$fot(X_131))]]) ).
cnf(refute_0_975,plain,
( multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130))) != identity
| inverse(least_upper_bound(X_130,X_131)) != multiply(inverse(least_upper_bound(X_131,X_130)),inverse(multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130)))))
| inverse(least_upper_bound(X_130,X_131)) = multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_130,X_131)),multiply(inverse(least_upper_bound(X_131,X_130)),inverse(multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130)))))) ),[1,1,0],$fot(identity)]]) ).
cnf(refute_0_976,plain,
( inverse(least_upper_bound(X_130,X_131)) != multiply(inverse(least_upper_bound(X_131,X_130)),inverse(multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130)))))
| inverse(least_upper_bound(X_130,X_131)) = multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130))),identity) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
inverse(least_upper_bound(X_130,X_131)) = multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_130,X_131)),multiply(inverse(least_upper_bound(X_131,X_130)),inverse(multiply(least_upper_bound(X_130,X_131),inverse(least_upper_bound(X_131,X_130)))))) )],[refute_0_911,refute_0_976]) ).
cnf(refute_0_978,plain,
multiply(identity,least_upper_bound(X_131,X_130)) = least_upper_bound(X_131,X_130),
inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_131,X_130)))]]) ).
cnf(refute_0_979,plain,
inverse(multiply(identity,least_upper_bound(X_131,X_130))) = inverse(multiply(identity,least_upper_bound(X_131,X_130))),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,least_upper_bound(X_131,X_130))))]]) ).
cnf(refute_0_980,plain,
( multiply(identity,least_upper_bound(X_131,X_130)) != least_upper_bound(X_131,X_130)
| inverse(multiply(identity,least_upper_bound(X_131,X_130))) != inverse(multiply(identity,least_upper_bound(X_131,X_130)))
| inverse(multiply(identity,least_upper_bound(X_131,X_130))) = inverse(least_upper_bound(X_131,X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_131,X_130))),inverse(multiply(identity,least_upper_bound(X_131,X_130)))) ),[1,0],$fot(least_upper_bound(X_131,X_130))]]) ).
cnf(refute_0_981,plain,
( multiply(identity,least_upper_bound(X_131,X_130)) != least_upper_bound(X_131,X_130)
| inverse(multiply(identity,least_upper_bound(X_131,X_130))) = inverse(least_upper_bound(X_131,X_130)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_131,X_130))),inverse(multiply(identity,least_upper_bound(X_131,X_130)))) )],[refute_0_979,refute_0_980]) ).
cnf(refute_0_982,plain,
inverse(multiply(identity,least_upper_bound(X_131,X_130))) = inverse(least_upper_bound(X_131,X_130)),
inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_131,X_130)),least_upper_bound(X_131,X_130)) )],[refute_0_978,refute_0_981]) ).
cnf(refute_0_983,plain,
multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) = inverse(multiply(identity,least_upper_bound(X_131,X_130))),
inference(subst,[],[refute_0_508:[bind(X,$fot(identity)),bind(Y,$fot(least_upper_bound(X_131,X_130)))]]) ).
cnf(refute_0_984,plain,
( multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) != inverse(multiply(identity,least_upper_bound(X_131,X_130)))
| inverse(multiply(identity,least_upper_bound(X_131,X_130))) != inverse(least_upper_bound(X_131,X_130))
| multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) = inverse(least_upper_bound(X_131,X_130)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)))),bind(Y0,$fot(inverse(multiply(identity,least_upper_bound(X_131,X_130))))),bind(Z0,$fot(inverse(least_upper_bound(X_131,X_130))))]]) ).
cnf(refute_0_985,plain,
( inverse(multiply(identity,least_upper_bound(X_131,X_130))) != inverse(least_upper_bound(X_131,X_130))
| multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) = inverse(least_upper_bound(X_131,X_130)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)),inverse(multiply(identity,least_upper_bound(X_131,X_130)))) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) = inverse(least_upper_bound(X_131,X_130)),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_131,X_130))),inverse(least_upper_bound(X_131,X_130))) )],[refute_0_982,refute_0_985]) ).
cnf(refute_0_987,plain,
( multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)) != inverse(least_upper_bound(X_131,X_130))
| inverse(least_upper_bound(X_130,X_131)) != multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity))
| inverse(least_upper_bound(X_130,X_131)) = inverse(least_upper_bound(X_131,X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_130,X_131)),multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity))) ),[1],$fot(inverse(least_upper_bound(X_131,X_130)))]]) ).
cnf(refute_0_988,plain,
( inverse(least_upper_bound(X_130,X_131)) != multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity))
| inverse(least_upper_bound(X_130,X_131)) = inverse(least_upper_bound(X_131,X_130)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity)),inverse(least_upper_bound(X_131,X_130))) )],[refute_0_986,refute_0_987]) ).
cnf(refute_0_989,plain,
inverse(least_upper_bound(X_130,X_131)) = inverse(least_upper_bound(X_131,X_130)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_130,X_131)),multiply(inverse(least_upper_bound(X_131,X_130)),inverse(identity))) )],[refute_0_977,refute_0_988]) ).
cnf(refute_0_990,plain,
( inverse(least_upper_bound(X_130,X_131)) != inverse(least_upper_bound(X_131,X_130))
| inverse(least_upper_bound(X_131,X_130)) = inverse(least_upper_bound(X_130,X_131)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_130,X_131)))),bind(Y0,$fot(inverse(least_upper_bound(X_131,X_130))))]]) ).
cnf(refute_0_991,plain,
inverse(least_upper_bound(X_131,X_130)) = inverse(least_upper_bound(X_130,X_131)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_130,X_131)),inverse(least_upper_bound(X_131,X_130))) )],[refute_0_989,refute_0_990]) ).
cnf(refute_0_992,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))) = inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),
inference(subst,[],[refute_0_991:[bind(X_130,$fot(inverse(X))),bind(X_131,$fot(inverse(least_upper_bound(X_79,X))))]]) ).
cnf(refute_0_993,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))))]]) ).
cnf(refute_0_994,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))
| inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))) != inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))) ),[1,0],$fot(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))))]]) ).
cnf(refute_0_995,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))) != inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X))))) )],[refute_0_992,refute_0_995]) ).
cnf(refute_0_997,plain,
( multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))))]]) ).
cnf(refute_0_998,plain,
( multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))) )],[refute_0_996,refute_0_997]) ).
cnf(refute_0_999,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))) )],[refute_0_910,refute_0_998]) ).
cnf(refute_0_1000,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))
| least_upper_bound(X_79,X) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))
| least_upper_bound(X_79,X) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_79,X),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))) ),[1],$fot(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))))]]) ).
cnf(refute_0_1001,plain,
( least_upper_bound(X_79,X) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))
| least_upper_bound(X_79,X) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79)))),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))) )],[refute_0_999,refute_0_1000]) ).
cnf(refute_0_1002,plain,
least_upper_bound(X_79,X) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,X),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_79,X)),inverse(X))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X),X_79))))) )],[refute_0_905,refute_0_1001]) ).
cnf(refute_0_1003,plain,
least_upper_bound(multiply(X,identity),X_79) = least_upper_bound(multiply(X,identity),X_79),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X,identity),X_79))]]) ).
cnf(refute_0_1004,plain,
( multiply(X,identity) != X
| least_upper_bound(multiply(X,identity),X_79) != least_upper_bound(multiply(X,identity),X_79)
| least_upper_bound(multiply(X,identity),X_79) = least_upper_bound(X,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X,identity),X_79),least_upper_bound(multiply(X,identity),X_79)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_1005,plain,
( multiply(X,identity) != X
| least_upper_bound(multiply(X,identity),X_79) = least_upper_bound(X,X_79) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,identity),X_79),least_upper_bound(multiply(X,identity),X_79)) )],[refute_0_1003,refute_0_1004]) ).
cnf(refute_0_1006,plain,
least_upper_bound(multiply(X,identity),X_79) = least_upper_bound(X,X_79),
inference(resolve,[$cnf( $equal(multiply(X,identity),X) )],[refute_0_561,refute_0_1005]) ).
cnf(refute_0_1007,plain,
multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))) = least_upper_bound(multiply(X_75,X_76),multiply(X_75,multiply(inverse(X_75),X_59))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_75)),bind(Y,$fot(X_76)),bind(Z,$fot(multiply(inverse(X_75),X_59)))]]) ).
cnf(refute_0_1008,plain,
multiply(multiply(X_57,inverse(X_57)),X_59) = multiply(X_57,multiply(inverse(X_57),X_59)),
inference(subst,[],[associativity:[bind(X,$fot(X_57)),bind(Y,$fot(inverse(X_57))),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_1009,plain,
multiply(X_57,inverse(X_57)) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(X_57))]]) ).
cnf(refute_0_1010,plain,
( multiply(X_57,inverse(X_57)) != identity
| multiply(multiply(X_57,inverse(X_57)),X_59) != multiply(X_57,multiply(inverse(X_57),X_59))
| multiply(identity,X_59) = multiply(X_57,multiply(inverse(X_57),X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_57,inverse(X_57)),X_59),multiply(X_57,multiply(inverse(X_57),X_59))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_1011,plain,
( multiply(multiply(X_57,inverse(X_57)),X_59) != multiply(X_57,multiply(inverse(X_57),X_59))
| multiply(identity,X_59) = multiply(X_57,multiply(inverse(X_57),X_59)) ),
inference(resolve,[$cnf( $equal(multiply(X_57,inverse(X_57)),identity) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
multiply(identity,X_59) = multiply(X_57,multiply(inverse(X_57),X_59)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_57,inverse(X_57)),X_59),multiply(X_57,multiply(inverse(X_57),X_59))) )],[refute_0_1008,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( multiply(identity,X_59) != X_59
| multiply(identity,X_59) != multiply(X_57,multiply(inverse(X_57),X_59))
| X_59 = multiply(X_57,multiply(inverse(X_57),X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_59),multiply(X_57,multiply(inverse(X_57),X_59))) ),[0],$fot(X_59)]]) ).
cnf(refute_0_1014,plain,
( multiply(identity,X_59) != multiply(X_57,multiply(inverse(X_57),X_59))
| X_59 = multiply(X_57,multiply(inverse(X_57),X_59)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_59),X_59) )],[refute_0_502,refute_0_1013]) ).
cnf(refute_0_1015,plain,
X_59 = multiply(X_57,multiply(inverse(X_57),X_59)),
inference(resolve,[$cnf( $equal(multiply(identity,X_59),multiply(X_57,multiply(inverse(X_57),X_59))) )],[refute_0_1012,refute_0_1014]) ).
cnf(refute_0_1016,plain,
X_59 = multiply(X_75,multiply(inverse(X_75),X_59)),
inference(subst,[],[refute_0_1015:[bind(X_57,$fot(X_75))]]) ).
cnf(refute_0_1017,plain,
( X_59 != multiply(X_75,multiply(inverse(X_75),X_59))
| multiply(X_75,multiply(inverse(X_75),X_59)) = X_59 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_59)),bind(Y0,$fot(multiply(X_75,multiply(inverse(X_75),X_59))))]]) ).
cnf(refute_0_1018,plain,
multiply(X_75,multiply(inverse(X_75),X_59)) = X_59,
inference(resolve,[$cnf( $equal(X_59,multiply(X_75,multiply(inverse(X_75),X_59))) )],[refute_0_1016,refute_0_1017]) ).
cnf(refute_0_1019,plain,
( multiply(X_75,multiply(inverse(X_75),X_59)) != X_59
| multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,multiply(inverse(X_75),X_59)))
| multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))) = least_upper_bound(multiply(X_75,X_76),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))),least_upper_bound(multiply(X_75,X_76),multiply(X_75,multiply(inverse(X_75),X_59)))) ),[1,1],$fot(X_59)]]) ).
cnf(refute_0_1020,plain,
( multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))) != least_upper_bound(multiply(X_75,X_76),multiply(X_75,multiply(inverse(X_75),X_59)))
| multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))) = least_upper_bound(multiply(X_75,X_76),X_59) ),
inference(resolve,[$cnf( $equal(multiply(X_75,multiply(inverse(X_75),X_59)),X_59) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))) = least_upper_bound(multiply(X_75,X_76),X_59),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(X_76,multiply(inverse(X_75),X_59))),least_upper_bound(multiply(X_75,X_76),multiply(X_75,multiply(inverse(X_75),X_59)))) )],[refute_0_1007,refute_0_1020]) ).
cnf(refute_0_1022,plain,
multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(multiply(X,identity),X_79),
inference(subst,[],[refute_0_1021:[bind(X_59,$fot(X_79)),bind(X_75,$fot(X)),bind(X_76,$fot(identity))]]) ).
cnf(refute_0_1023,plain,
( multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) != least_upper_bound(multiply(X,identity),X_79)
| least_upper_bound(multiply(X,identity),X_79) != least_upper_bound(X,X_79)
| multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(X,X_79) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))))),bind(Y0,$fot(least_upper_bound(multiply(X,identity),X_79))),bind(Z0,$fot(least_upper_bound(X,X_79)))]]) ).
cnf(refute_0_1024,plain,
( least_upper_bound(multiply(X,identity),X_79) != least_upper_bound(X,X_79)
| multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(X,X_79) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))),least_upper_bound(multiply(X,identity),X_79)) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(X,X_79),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,identity),X_79),least_upper_bound(X,X_79)) )],[refute_0_1006,refute_0_1024]) ).
cnf(refute_0_1026,plain,
X_59 = multiply(inverse(least_upper_bound(X_84,inverse(X_59))),multiply(least_upper_bound(X_84,inverse(X_59)),X_59)),
inference(subst,[],[refute_0_505:[bind(X_58,$fot(least_upper_bound(X_84,inverse(X_59))))]]) ).
cnf(refute_0_1027,plain,
multiply(least_upper_bound(X_84,inverse(X_59)),X_59) = least_upper_bound(identity,multiply(X_84,X_59)),
inference(subst,[],[refute_0_721:[bind(X_80,$fot(X_59)),bind(X_81,$fot(X_84))]]) ).
cnf(refute_0_1028,plain,
( X_59 != multiply(inverse(least_upper_bound(X_84,inverse(X_59))),multiply(least_upper_bound(X_84,inverse(X_59)),X_59))
| multiply(least_upper_bound(X_84,inverse(X_59)),X_59) != least_upper_bound(identity,multiply(X_84,X_59))
| X_59 = multiply(inverse(least_upper_bound(X_84,inverse(X_59))),least_upper_bound(identity,multiply(X_84,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(X_84,inverse(X_59))),multiply(least_upper_bound(X_84,inverse(X_59)),X_59))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_84,X_59)))]]) ).
cnf(refute_0_1029,plain,
( X_59 != multiply(inverse(least_upper_bound(X_84,inverse(X_59))),multiply(least_upper_bound(X_84,inverse(X_59)),X_59))
| X_59 = multiply(inverse(least_upper_bound(X_84,inverse(X_59))),least_upper_bound(identity,multiply(X_84,X_59))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X_59)),X_59),least_upper_bound(identity,multiply(X_84,X_59))) )],[refute_0_1027,refute_0_1028]) ).
cnf(refute_0_1030,plain,
X_59 = multiply(inverse(least_upper_bound(X_84,inverse(X_59))),least_upper_bound(identity,multiply(X_84,X_59))),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(X_84,inverse(X_59))),multiply(least_upper_bound(X_84,inverse(X_59)),X_59))) )],[refute_0_1026,refute_0_1029]) ).
cnf(refute_0_1031,plain,
X_59 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_153,X_59)),X_59))),
inference(subst,[],[refute_0_1030:[bind(X_84,$fot(inverse(least_upper_bound(X_153,X_59))))]]) ).
cnf(refute_0_1032,plain,
inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))) = multiply(inverse(least_upper_bound(X_153,X_59)),X_59),
inference(subst,[],[refute_0_660:[bind(X,$fot(X_59)),bind(X_79,$fot(X_153))]]) ).
cnf(refute_0_1033,plain,
( inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))) != multiply(inverse(least_upper_bound(X_153,X_59)),X_59)
| multiply(inverse(least_upper_bound(X_153,X_59)),X_59) = inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_153,X_59)),X_59)))]]) ).
cnf(refute_0_1034,plain,
multiply(inverse(least_upper_bound(X_153,X_59)),X_59) = inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))),multiply(inverse(least_upper_bound(X_153,X_59)),X_59)) )],[refute_0_1032,refute_0_1033]) ).
cnf(refute_0_1035,plain,
( X_59 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_153,X_59)),X_59)))
| multiply(inverse(least_upper_bound(X_153,X_59)),X_59) != inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))
| X_59 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_153,X_59)),X_59)))) ),[1,1,1],$fot(inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))]]) ).
cnf(refute_0_1036,plain,
( X_59 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_153,X_59)),X_59)))
| X_59 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_153,X_59)),X_59),inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))) )],[refute_0_1034,refute_0_1035]) ).
cnf(refute_0_1037,plain,
X_59 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_153,X_59)),X_59)))) )],[refute_0_1031,refute_0_1036]) ).
cnf(refute_0_1038,plain,
multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity) = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))))]]) ).
cnf(refute_0_1039,plain,
multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))),
inference(subst,[],[refute_0_487:[bind(X_95,$fot(least_upper_bound(identity,X_16)))]]) ).
cnf(refute_0_1040,plain,
least_upper_bound(identity,least_upper_bound(identity,X_16)) = least_upper_bound(identity,X_16),
inference(subst,[],[refute_0_221:[bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1041,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| least_upper_bound(identity,least_upper_bound(identity,X_16)) != least_upper_bound(identity,X_16)
| multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) ),[0,1],$fot(least_upper_bound(identity,X_16))]]) ).
cnf(refute_0_1042,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) )],[refute_0_1040,refute_0_1041]) ).
cnf(refute_0_1043,plain,
multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,least_upper_bound(identity,X_16))),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) )],[refute_0_1039,refute_0_1042]) ).
cnf(refute_0_1044,plain,
multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(identity,X_16)))]]) ).
cnf(refute_0_1045,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) != identity
| multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1046,plain,
( multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)) != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)),identity) )],[refute_0_1044,refute_0_1045]) ).
cnf(refute_0_1047,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_16)),least_upper_bound(identity,X_16)),least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) )],[refute_0_1043,refute_0_1046]) ).
cnf(refute_0_1048,plain,
( identity != least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))
| least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))))]]) ).
cnf(refute_0_1049,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X_16))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,X_16)))) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))) = identity,
inference(subst,[],[refute_0_1049:[bind(X_16,$fot(multiply(inverse(X_59),X_153)))]]) ).
cnf(refute_0_1051,plain,
multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))))]]) ).
cnf(refute_0_1052,plain,
( multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) != multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))
| least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))) != identity
| multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1053,plain,
( least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))) != identity
| multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))) )],[refute_0_1051,refute_0_1052]) ).
cnf(refute_0_1054,plain,
multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))),identity) )],[refute_0_1050,refute_0_1053]) ).
cnf(refute_0_1055,plain,
inverse(least_upper_bound(X_123,X_122)) = multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))))),
inference(subst,[],[refute_0_1030:[bind(X_59,$fot(inverse(least_upper_bound(X_123,X_122)))),bind(X_84,$fot(least_upper_bound(X_122,X_123)))]]) ).
cnf(refute_0_1056,plain,
( multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))) != identity
| inverse(least_upper_bound(X_123,X_122)) != multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))))
| inverse(least_upper_bound(X_123,X_122)) = multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_123,X_122)),multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_1057,plain,
( inverse(least_upper_bound(X_123,X_122)) != multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))))
| inverse(least_upper_bound(X_123,X_122)) = multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122))),identity) )],[refute_0_973,refute_0_1056]) ).
cnf(refute_0_1058,plain,
inverse(least_upper_bound(X_123,X_122)) = multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_123,X_122)),multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,multiply(least_upper_bound(X_122,X_123),inverse(least_upper_bound(X_123,X_122)))))) )],[refute_0_1055,refute_0_1057]) ).
cnf(refute_0_1059,plain,
multiply(inverse(least_upper_bound(X_122,X_123)),identity) = inverse(least_upper_bound(X_122,X_123)),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(least_upper_bound(X_122,X_123))))]]) ).
cnf(refute_0_1060,plain,
least_upper_bound(identity,identity) = identity,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1061,plain,
multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_1062,plain,
( multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity))
| least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1063,plain,
( least_upper_bound(identity,identity) != identity
| multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity))) )],[refute_0_1061,refute_0_1062]) ).
cnf(refute_0_1064,plain,
multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_1060,refute_0_1063]) ).
cnf(refute_0_1065,plain,
least_upper_bound(X_122,least_upper_bound(X_123,X_122)) = least_upper_bound(X_122,X_123),
inference(subst,[],[refute_0_214:[bind(Y,$fot(X_123)),bind(X_15,$fot(X_122))]]) ).
cnf(refute_0_1066,plain,
least_upper_bound(X_123,least_upper_bound(X_123,X_122)) = least_upper_bound(X_123,X_122),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(X_122)),bind(X_17,$fot(X_123))]]) ).
cnf(refute_0_1067,plain,
inverse(inverse(least_upper_bound(X_123,X_122))) = least_upper_bound(X_123,X_122),
inference(subst,[],[p20x_2:[bind(X,$fot(least_upper_bound(X_123,X_122)))]]) ).
cnf(refute_0_1068,plain,
least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))))]]) ).
cnf(refute_0_1069,plain,
( inverse(inverse(least_upper_bound(X_123,X_122))) != least_upper_bound(X_123,X_122)
| least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) != least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))
| least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_123,least_upper_bound(X_123,X_122)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))),least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) ),[1,1],$fot(least_upper_bound(X_123,X_122))]]) ).
cnf(refute_0_1070,plain,
( inverse(inverse(least_upper_bound(X_123,X_122))) != least_upper_bound(X_123,X_122)
| least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_123,least_upper_bound(X_123,X_122)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))),least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) )],[refute_0_1068,refute_0_1069]) ).
cnf(refute_0_1071,plain,
least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_123,least_upper_bound(X_123,X_122)),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_123,X_122))),least_upper_bound(X_123,X_122)) )],[refute_0_1067,refute_0_1070]) ).
cnf(refute_0_1072,plain,
( least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) != least_upper_bound(X_123,least_upper_bound(X_123,X_122))
| least_upper_bound(X_123,least_upper_bound(X_123,X_122)) != least_upper_bound(X_123,X_122)
| least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_123,X_122) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))))),bind(Y0,$fot(least_upper_bound(X_123,least_upper_bound(X_123,X_122)))),bind(Z0,$fot(least_upper_bound(X_123,X_122)))]]) ).
cnf(refute_0_1073,plain,
( least_upper_bound(X_123,least_upper_bound(X_123,X_122)) != least_upper_bound(X_123,X_122)
| least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_123,X_122) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))),least_upper_bound(X_123,least_upper_bound(X_123,X_122))) )],[refute_0_1071,refute_0_1072]) ).
cnf(refute_0_1074,plain,
least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_123,X_122),
inference(resolve,[$cnf( $equal(least_upper_bound(X_123,least_upper_bound(X_123,X_122)),least_upper_bound(X_123,X_122)) )],[refute_0_1066,refute_0_1073]) ).
cnf(refute_0_1075,plain,
least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) = least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))))]]) ).
cnf(refute_0_1076,plain,
( least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) != least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))))
| least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) != least_upper_bound(X_123,X_122)
| least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) = least_upper_bound(X_122,least_upper_bound(X_123,X_122)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))))) ),[1,1],$fot(least_upper_bound(X_123,X_122))]]) ).
cnf(refute_0_1077,plain,
( least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))) != least_upper_bound(X_123,X_122)
| least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) = least_upper_bound(X_122,least_upper_bound(X_123,X_122)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))))) )],[refute_0_1075,refute_0_1076]) ).
cnf(refute_0_1078,plain,
least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) = least_upper_bound(X_122,least_upper_bound(X_123,X_122)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))),least_upper_bound(X_123,X_122)) )],[refute_0_1074,refute_0_1077]) ).
cnf(refute_0_1079,plain,
( least_upper_bound(X_122,least_upper_bound(X_123,X_122)) != least_upper_bound(X_122,X_123)
| least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) != least_upper_bound(X_122,least_upper_bound(X_123,X_122))
| least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) = least_upper_bound(X_122,X_123) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))))),bind(Y0,$fot(least_upper_bound(X_122,least_upper_bound(X_123,X_122)))),bind(Z0,$fot(least_upper_bound(X_122,X_123)))]]) ).
cnf(refute_0_1080,plain,
( least_upper_bound(X_122,least_upper_bound(X_123,X_122)) != least_upper_bound(X_122,X_123)
| least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) = least_upper_bound(X_122,X_123) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(X_122,least_upper_bound(X_123,X_122))) )],[refute_0_1078,refute_0_1079]) ).
cnf(refute_0_1081,plain,
least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) = least_upper_bound(X_122,X_123),
inference(resolve,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_123,X_122)),least_upper_bound(X_122,X_123)) )],[refute_0_1065,refute_0_1080]) ).
cnf(refute_0_1082,plain,
least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_122)),bind(Y,$fot(X_123)),bind(Z,$fot(inverse(inverse(least_upper_bound(X_123,X_122)))))]]) ).
cnf(refute_0_1083,plain,
( least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) != least_upper_bound(X_122,X_123)
| least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))) != least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))))
| least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_122,X_123) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))))),bind(Y0,$fot(least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))))),bind(Z0,$fot(least_upper_bound(X_122,X_123)))]]) ).
cnf(refute_0_1084,plain,
( least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))) != least_upper_bound(X_122,X_123)
| least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_122,X_123) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))),least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122)))))) )],[refute_0_1082,refute_0_1083]) ).
cnf(refute_0_1085,plain,
least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))) = least_upper_bound(X_122,X_123),
inference(resolve,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_123,inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(X_122,X_123)) )],[refute_0_1081,refute_0_1084]) ).
cnf(refute_0_1086,plain,
inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))) = inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))))]]) ).
cnf(refute_0_1087,plain,
( inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))) != inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))))
| least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))) != least_upper_bound(X_122,X_123)
| inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))) = inverse(least_upper_bound(X_122,X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))))) ),[1,0],$fot(least_upper_bound(X_122,X_123))]]) ).
cnf(refute_0_1088,plain,
( least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))) != least_upper_bound(X_122,X_123)
| inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))) = inverse(least_upper_bound(X_122,X_123)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))))) )],[refute_0_1086,refute_0_1087]) ).
cnf(refute_0_1089,plain,
inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))) = inverse(least_upper_bound(X_122,X_123)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122)))),least_upper_bound(X_122,X_123)) )],[refute_0_1085,refute_0_1088]) ).
cnf(refute_0_1090,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_1091,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))) != inverse(least_upper_bound(X_122,X_123))
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity))) ),[1,0],$fot(inverse(least_upper_bound(X_122,X_123)))]]) ).
cnf(refute_0_1092,plain,
( inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))) != inverse(least_upper_bound(X_122,X_123))
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity))) )],[refute_0_1090,refute_0_1091]) ).
cnf(refute_0_1093,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),inverse(least_upper_bound(X_122,X_123))) )],[refute_0_1089,refute_0_1092]) ).
cnf(refute_0_1094,plain,
( multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_122,X_123)),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity))
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),identity) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_122,X_123)),identity)))]]) ).
cnf(refute_0_1095,plain,
( multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_122,X_123)),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity))) )],[refute_0_1093,refute_0_1094]) ).
cnf(refute_0_1096,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = multiply(inverse(least_upper_bound(X_122,X_123)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_122,X_123)),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_122,X_123)),identity)) )],[refute_0_1064,refute_0_1095]) ).
cnf(refute_0_1097,plain,
( multiply(inverse(least_upper_bound(X_122,X_123)),identity) != inverse(least_upper_bound(X_122,X_123))
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) != multiply(inverse(least_upper_bound(X_122,X_123)),identity)
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(X_122,X_123)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_122,X_123)),identity))),bind(Z0,$fot(inverse(least_upper_bound(X_122,X_123))))]]) ).
cnf(refute_0_1098,plain,
( multiply(inverse(least_upper_bound(X_122,X_123)),identity) != inverse(least_upper_bound(X_122,X_123))
| multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(X_122,X_123)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)),multiply(inverse(least_upper_bound(X_122,X_123)),identity)) )],[refute_0_1096,refute_0_1097]) ).
cnf(refute_0_1099,plain,
multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) = inverse(least_upper_bound(X_122,X_123)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_122,X_123)),identity),inverse(least_upper_bound(X_122,X_123))) )],[refute_0_1059,refute_0_1098]) ).
cnf(refute_0_1100,plain,
( multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)) != inverse(least_upper_bound(X_122,X_123))
| inverse(least_upper_bound(X_123,X_122)) != multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_123,X_122)) = inverse(least_upper_bound(X_122,X_123)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_123,X_122)),multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity))) ),[1],$fot(inverse(least_upper_bound(X_122,X_123)))]]) ).
cnf(refute_0_1101,plain,
( inverse(least_upper_bound(X_123,X_122)) != multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity))
| inverse(least_upper_bound(X_123,X_122)) = inverse(least_upper_bound(X_122,X_123)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity)),inverse(least_upper_bound(X_122,X_123))) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
inverse(least_upper_bound(X_123,X_122)) = inverse(least_upper_bound(X_122,X_123)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_123,X_122)),multiply(inverse(least_upper_bound(least_upper_bound(X_122,X_123),inverse(inverse(least_upper_bound(X_123,X_122))))),least_upper_bound(identity,identity))) )],[refute_0_1058,refute_0_1101]) ).
cnf(refute_0_1103,plain,
( inverse(least_upper_bound(X_123,X_122)) != inverse(least_upper_bound(X_122,X_123))
| inverse(least_upper_bound(X_122,X_123)) = inverse(least_upper_bound(X_123,X_122)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(least_upper_bound(X_123,X_122)))),bind(Y0,$fot(inverse(least_upper_bound(X_122,X_123))))]]) ).
cnf(refute_0_1104,plain,
inverse(least_upper_bound(X_122,X_123)) = inverse(least_upper_bound(X_123,X_122)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_123,X_122)),inverse(least_upper_bound(X_122,X_123))) )],[refute_0_1102,refute_0_1103]) ).
cnf(refute_0_1105,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))) = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),
inference(subst,[],[refute_0_1104:[bind(X_122,$fot(inverse(least_upper_bound(X_153,X_59)))),bind(X_123,$fot(inverse(X_59)))]]) ).
cnf(refute_0_1106,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))))]]) ).
cnf(refute_0_1107,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))
| inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))) != inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))) ),[1,0],$fot(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))))]]) ).
cnf(refute_0_1108,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))) != inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))) )],[refute_0_1106,refute_0_1107]) ).
cnf(refute_0_1109,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))) )],[refute_0_1105,refute_0_1108]) ).
cnf(refute_0_1110,plain,
( multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) != multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity)
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) != multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity)))]]) ).
cnf(refute_0_1111,plain,
( multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) != multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity)
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))) )],[refute_0_1109,refute_0_1110]) ).
cnf(refute_0_1112,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity)) )],[refute_0_1054,refute_0_1111]) ).
cnf(refute_0_1113,plain,
( multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity) != inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) != multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity)
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity))),bind(Z0,$fot(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))))]]) ).
cnf(refute_0_1114,plain,
( multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity) != inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity)) )],[refute_0_1112,refute_0_1113]) ).
cnf(refute_0_1115,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),identity),inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))) )],[refute_0_1038,refute_0_1114]) ).
cnf(refute_0_1116,plain,
( X_59 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))) != inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))
| X_59 = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_59,inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))))]]) ).
cnf(refute_0_1117,plain,
( X_59 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))
| X_59 = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153))))),inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))) )],[refute_0_1115,refute_0_1116]) ).
cnf(refute_0_1118,plain,
X_59 = inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_153,X_59)),inverse(X_59))),least_upper_bound(identity,inverse(least_upper_bound(identity,multiply(inverse(X_59),X_153)))))) )],[refute_0_1037,refute_0_1117]) ).
cnf(refute_0_1119,plain,
( X_59 != inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))
| inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))) = X_59 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_59)),bind(Y0,$fot(inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))))]]) ).
cnf(refute_0_1120,plain,
inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59)))) = X_59,
inference(resolve,[$cnf( $equal(X_59,inverse(least_upper_bound(inverse(X_59),inverse(least_upper_bound(X_153,X_59))))) )],[refute_0_1118,refute_0_1119]) ).
cnf(refute_0_1121,plain,
inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))) = X,
inference(subst,[],[refute_0_1120:[bind(X_153,$fot(X_79)),bind(X_59,$fot(X))]]) ).
cnf(refute_0_1122,plain,
multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))))]]) ).
cnf(refute_0_1123,plain,
( multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))
| inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))) != X
| multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_1124,plain,
( inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))) != X
| multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))) )],[refute_0_1122,refute_0_1123]) ).
cnf(refute_0_1125,plain,
multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) = multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),X) )],[refute_0_1121,refute_0_1124]) ).
cnf(refute_0_1126,plain,
( multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) != least_upper_bound(X,X_79)
| multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) != multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79)))
| multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(X,X_79) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))))),bind(Y0,$fot(multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))))),bind(Z0,$fot(least_upper_bound(X,X_79)))]]) ).
cnf(refute_0_1127,plain,
( multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))) != least_upper_bound(X,X_79)
| multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(X,X_79) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79)))) )],[refute_0_1125,refute_0_1126]) ).
cnf(refute_0_1128,plain,
multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) = least_upper_bound(X,X_79),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(identity,multiply(inverse(X),X_79))),least_upper_bound(X,X_79)) )],[refute_0_1025,refute_0_1127]) ).
cnf(refute_0_1129,plain,
( multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))) != least_upper_bound(X,X_79)
| least_upper_bound(X_79,X) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))
| least_upper_bound(X_79,X) = least_upper_bound(X,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_79,X),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))) ),[1],$fot(least_upper_bound(X,X_79))]]) ).
cnf(refute_0_1130,plain,
( least_upper_bound(X_79,X) != multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))
| least_upper_bound(X_79,X) = least_upper_bound(X,X_79) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79))),least_upper_bound(X,X_79)) )],[refute_0_1128,refute_0_1129]) ).
cnf(refute_0_1131,plain,
least_upper_bound(X_79,X) = least_upper_bound(X,X_79),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,X),multiply(inverse(least_upper_bound(inverse(X),inverse(least_upper_bound(X_79,X)))),least_upper_bound(identity,multiply(inverse(X),X_79)))) )],[refute_0_1002,refute_0_1130]) ).
cnf(refute_0_1132,plain,
( least_upper_bound(X_79,X) != least_upper_bound(X,X_79)
| least_upper_bound(X,X_79) = least_upper_bound(X_79,X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_79,X))),bind(Y0,$fot(least_upper_bound(X,X_79)))]]) ).
cnf(refute_0_1133,plain,
least_upper_bound(X,X_79) = least_upper_bound(X_79,X),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,X),least_upper_bound(X,X_79)) )],[refute_0_1131,refute_0_1132]) ).
cnf(refute_0_1134,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))),
inference(subst,[],[refute_0_1133:[bind(X,$fot(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)))),bind(X_79,$fot(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))))]]) ).
cnf(refute_0_1135,plain,
( least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) != greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)))
| least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))))),bind(Z0,$fot(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))))]]) ).
cnf(refute_0_1136,plain,
( least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) != greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))),least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)))) )],[refute_0_1134,refute_0_1135]) ).
cnf(refute_0_1137,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) )],[refute_0_898,refute_0_1136]) ).
cnf(refute_0_1138,plain,
least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_280,X_279),inverse(X_224))),X_224),
inference(subst,[],[refute_0_758:[bind(X_84,$fot(greatest_lower_bound(X_280,X_279)))]]) ).
cnf(refute_0_1139,plain,
multiply(greatest_lower_bound(X_280,X_279),inverse(X_224)) = multiply(greatest_lower_bound(X_279,X_280),inverse(X_224)),
inference(subst,[],[refute_0_114:[bind(X_42,$fot(inverse(X_224))),bind(X_43,$fot(X_279)),bind(X_44,$fot(X_280))]]) ).
cnf(refute_0_1140,plain,
( multiply(greatest_lower_bound(X_280,X_279),inverse(X_224)) != multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))
| least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_280,X_279),inverse(X_224))),X_224)
| least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_280,X_279),X_224),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_280,X_279),inverse(X_224))),X_224)) ),[1,0,1],$fot(multiply(greatest_lower_bound(X_279,X_280),inverse(X_224)))]]) ).
cnf(refute_0_1141,plain,
( least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_280,X_279),inverse(X_224))),X_224)
| least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_280,X_279),inverse(X_224)),multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))) )],[refute_0_1139,refute_0_1140]) ).
cnf(refute_0_1142,plain,
least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_280,X_279),X_224),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_280,X_279),inverse(X_224))),X_224)) )],[refute_0_1138,refute_0_1141]) ).
cnf(refute_0_1143,plain,
( least_upper_bound(X_84,X_224) != multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224)
| multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224) = least_upper_bound(X_84,X_224) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_84,X_224))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224)))]]) ).
cnf(refute_0_1144,plain,
multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224) = least_upper_bound(X_84,X_224),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,X_224),multiply(least_upper_bound(identity,multiply(X_84,inverse(X_224))),X_224)) )],[refute_0_758,refute_0_1143]) ).
cnf(refute_0_1145,plain,
multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224) = least_upper_bound(greatest_lower_bound(X_279,X_280),X_224),
inference(subst,[],[refute_0_1144:[bind(X_84,$fot(greatest_lower_bound(X_279,X_280)))]]) ).
cnf(refute_0_1146,plain,
( multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224) != least_upper_bound(greatest_lower_bound(X_279,X_280),X_224)
| least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224)
| least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) = least_upper_bound(greatest_lower_bound(X_279,X_280),X_224) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_280,X_279),X_224),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224)) ),[1],$fot(least_upper_bound(greatest_lower_bound(X_279,X_280),X_224))]]) ).
cnf(refute_0_1147,plain,
( least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224)
| least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) = least_upper_bound(greatest_lower_bound(X_279,X_280),X_224) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224),least_upper_bound(greatest_lower_bound(X_279,X_280),X_224)) )],[refute_0_1145,refute_0_1146]) ).
cnf(refute_0_1148,plain,
least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) = least_upper_bound(greatest_lower_bound(X_279,X_280),X_224),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_280,X_279),X_224),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(X_279,X_280),inverse(X_224))),X_224)) )],[refute_0_1142,refute_0_1147]) ).
cnf(refute_0_1149,plain,
( least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) != least_upper_bound(greatest_lower_bound(X_279,X_280),X_224)
| least_upper_bound(greatest_lower_bound(X_279,X_280),X_224) = least_upper_bound(greatest_lower_bound(X_280,X_279),X_224) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_280,X_279),X_224))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_279,X_280),X_224)))]]) ).
cnf(refute_0_1150,plain,
least_upper_bound(greatest_lower_bound(X_279,X_280),X_224) = least_upper_bound(greatest_lower_bound(X_280,X_279),X_224),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_280,X_279),X_224),least_upper_bound(greatest_lower_bound(X_279,X_280),X_224)) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))),
inference(subst,[],[refute_0_1150:[bind(X_224,$fot(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)))),bind(X_279,$fot(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))),bind(X_280,$fot(least_upper_bound(X_286,X_287)))]]) ).
cnf(refute_0_1152,plain,
( least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)))
| least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))))),bind(Z0,$fot(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))))]]) ).
cnf(refute_0_1153,plain,
( least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))),least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)))) )],[refute_0_1151,refute_0_1152]) ).
cnf(refute_0_1154,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) = greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X_286,X_287),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) )],[refute_0_1137,refute_0_1153]) ).
cnf(refute_0_1155,plain,
( least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))
| least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))
| greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))) ),[0],$fot(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)))]]) ).
cnf(refute_0_1156,plain,
( least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))
| greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) )],[refute_0_1154,refute_0_1155]) ).
cnf(refute_0_1157,plain,
greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),
inference(subst,[],[refute_0_71:[bind(X_27,$fot(least_upper_bound(X_287,X_286))),bind(X_28,$fot(X_285))]]) ).
cnf(refute_0_1158,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_31,X)),Z),
inference(subst,[],[associativity_of_glb:[bind(Y,$fot(greatest_lower_bound(X_31,X)))]]) ).
cnf(refute_0_1159,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,X)) = greatest_lower_bound(X,X_31),
inference(subst,[],[refute_0_96:[bind(Y,$fot(X_31)),bind(X_21,$fot(X))]]) ).
cnf(refute_0_1160,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,X)) != greatest_lower_bound(X,X_31)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_31,X)),Z)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,X_31),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_31,X)),Z)) ),[1,0],$fot(greatest_lower_bound(X,X_31))]]) ).
cnf(refute_0_1161,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_31,X)),Z)
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,X_31),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,X)),greatest_lower_bound(X,X_31)) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(greatest_lower_bound(X,X_31),Z),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(X_31,X)),Z)) )],[refute_0_1158,refute_0_1161]) ).
cnf(refute_0_1163,plain,
greatest_lower_bound(greatest_lower_bound(X_31,X),Z) = greatest_lower_bound(X_31,greatest_lower_bound(X,Z)),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_31)),bind(Y,$fot(X))]]) ).
cnf(refute_0_1164,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)))]]) ).
cnf(refute_0_1165,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) != greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z))
| greatest_lower_bound(greatest_lower_bound(X_31,X),Z) != greatest_lower_bound(X_31,greatest_lower_bound(X,Z))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z))) ),[1,1],$fot(greatest_lower_bound(X_31,greatest_lower_bound(X,Z)))]]) ).
cnf(refute_0_1166,plain,
( greatest_lower_bound(greatest_lower_bound(X_31,X),Z) != greatest_lower_bound(X_31,greatest_lower_bound(X,Z))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z))) )],[refute_0_1164,refute_0_1165]) ).
cnf(refute_0_1167,plain,
greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) = greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_31,X),Z),greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) )],[refute_0_1163,refute_0_1166]) ).
cnf(refute_0_1168,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) != greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z)))
| greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,X_31),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) = greatest_lower_bound(greatest_lower_bound(X,X_31),Z) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),greatest_lower_bound(greatest_lower_bound(X,X_31),Z)) ),[0],$fot(greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))))]]) ).
cnf(refute_0_1169,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,X_31),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) = greatest_lower_bound(greatest_lower_bound(X,X_31),Z) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z)))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
greatest_lower_bound(greatest_lower_bound(X,X_31),Z) = greatest_lower_bound(X,greatest_lower_bound(X_31,Z)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_31))]]) ).
cnf(refute_0_1171,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) != greatest_lower_bound(greatest_lower_bound(X,X_31),Z)
| greatest_lower_bound(greatest_lower_bound(X,X_31),Z) != greatest_lower_bound(X,greatest_lower_bound(X_31,Z))
| greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) = greatest_lower_bound(X,greatest_lower_bound(X_31,Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))),greatest_lower_bound(X,greatest_lower_bound(X_31,Z))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,X_31),Z))]]) ).
cnf(refute_0_1172,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) != greatest_lower_bound(greatest_lower_bound(X,X_31),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) = greatest_lower_bound(X,greatest_lower_bound(X_31,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,X_31),Z),greatest_lower_bound(X,greatest_lower_bound(X_31,Z))) )],[refute_0_1170,refute_0_1171]) ).
cnf(refute_0_1173,plain,
( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)) != greatest_lower_bound(greatest_lower_bound(X,X_31),Z)
| greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) = greatest_lower_bound(X,greatest_lower_bound(X_31,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))),greatest_lower_bound(greatest_lower_bound(X,X_31),Z)) )],[refute_0_1169,refute_0_1172]) ).
cnf(refute_0_1174,plain,
greatest_lower_bound(X,greatest_lower_bound(X_31,greatest_lower_bound(X,Z))) = greatest_lower_bound(X,greatest_lower_bound(X_31,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(X_31,X),Z)),greatest_lower_bound(greatest_lower_bound(X,X_31),Z)) )],[refute_0_1162,refute_0_1173]) ).
cnf(refute_0_1175,plain,
greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)))) = greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))),
inference(subst,[],[refute_0_1174:[bind(X,$fot(least_upper_bound(Y,X_21))),bind(Z,$fot(least_upper_bound(X_21,Y))),bind(X_31,$fot(X_258))]]) ).
cnf(refute_0_1176,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)))) != greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)) != least_upper_bound(Y,X_21)
| greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) = greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)))),greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))) ),[0,1,1],$fot(least_upper_bound(Y,X_21))]]) ).
cnf(refute_0_1177,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)))) != greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) = greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),least_upper_bound(Y,X_21)) )],[refute_0_238,refute_0_1176]) ).
cnf(refute_0_1178,plain,
greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) = greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)))),greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))) )],[refute_0_1175,refute_0_1177]) ).
cnf(refute_0_1179,plain,
greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) = greatest_lower_bound(least_upper_bound(Y,X_21),X_258),
inference(subst,[],[refute_0_96:[bind(Y,$fot(X_258)),bind(X_21,$fot(least_upper_bound(Y,X_21)))]]) ).
cnf(refute_0_1180,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) != greatest_lower_bound(least_upper_bound(Y,X_21),X_258)
| greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) != greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_21),X_258) = greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))),greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(Y,X_21),X_258))]]) ).
cnf(refute_0_1181,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) != greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_21),X_258) = greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))),greatest_lower_bound(least_upper_bound(Y,X_21),X_258)) )],[refute_0_1179,refute_0_1180]) ).
cnf(refute_0_1182,plain,
greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))) = greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48))),
inference(subst,[],[refute_0_132:[bind(X,$fot(least_upper_bound(X_49,X_48))),bind(X_27,$fot(least_upper_bound(X_48,X_49)))]]) ).
cnf(refute_0_1183,plain,
( greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)) != least_upper_bound(X_48,X_49)
| greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))) != greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)))
| greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))) = greatest_lower_bound(X_26,least_upper_bound(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))),greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)))) ),[1,1],$fot(least_upper_bound(X_48,X_49))]]) ).
cnf(refute_0_1184,plain,
( greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))) != greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)))
| greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))) = greatest_lower_bound(X_26,least_upper_bound(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)),least_upper_bound(X_48,X_49)) )],[refute_0_881,refute_0_1183]) ).
cnf(refute_0_1185,plain,
greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))) = greatest_lower_bound(X_26,least_upper_bound(X_48,X_49)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_49,X_48),greatest_lower_bound(X_26,least_upper_bound(X_48,X_49))),greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_48,X_49),least_upper_bound(X_49,X_48)))) )],[refute_0_1182,refute_0_1184]) ).
cnf(refute_0_1186,plain,
greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) = greatest_lower_bound(X_258,least_upper_bound(X_21,Y)),
inference(subst,[],[refute_0_1185:[bind(X_26,$fot(X_258)),bind(X_48,$fot(X_21)),bind(X_49,$fot(Y))]]) ).
cnf(refute_0_1187,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),X_258) != greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) != greatest_lower_bound(X_258,least_upper_bound(X_21,Y))
| greatest_lower_bound(least_upper_bound(Y,X_21),X_258) = greatest_lower_bound(X_258,least_upper_bound(X_21,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(Y,X_21),X_258),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) ),[0],$fot(greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))))]]) ).
cnf(refute_0_1188,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),X_258) != greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_21),X_258) = greatest_lower_bound(X_258,least_upper_bound(X_21,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) )],[refute_0_1186,refute_0_1187]) ).
cnf(refute_0_1189,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))) != greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))
| greatest_lower_bound(least_upper_bound(Y,X_21),X_258) = greatest_lower_bound(X_258,least_upper_bound(X_21,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),X_258),greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))) )],[refute_0_1181,refute_0_1188]) ).
cnf(refute_0_1190,plain,
greatest_lower_bound(least_upper_bound(Y,X_21),X_258) = greatest_lower_bound(X_258,least_upper_bound(X_21,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(Y,X_21))),greatest_lower_bound(least_upper_bound(Y,X_21),greatest_lower_bound(X_258,least_upper_bound(X_21,Y)))) )],[refute_0_1178,refute_0_1189]) ).
cnf(refute_0_1191,plain,
( greatest_lower_bound(least_upper_bound(Y,X_21),X_258) != greatest_lower_bound(X_258,least_upper_bound(X_21,Y))
| greatest_lower_bound(X_258,least_upper_bound(X_21,Y)) = greatest_lower_bound(least_upper_bound(Y,X_21),X_258) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(Y,X_21),X_258))),bind(Y0,$fot(greatest_lower_bound(X_258,least_upper_bound(X_21,Y))))]]) ).
cnf(refute_0_1192,plain,
greatest_lower_bound(X_258,least_upper_bound(X_21,Y)) = greatest_lower_bound(least_upper_bound(Y,X_21),X_258),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),X_258),greatest_lower_bound(X_258,least_upper_bound(X_21,Y))) )],[refute_0_1190,refute_0_1191]) ).
cnf(refute_0_1193,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),
inference(subst,[],[refute_0_1192:[bind(Y,$fot(X_287)),bind(X_21,$fot(X_286)),bind(X_258,$fot(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)))]]) ).
cnf(refute_0_1194,plain,
( greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) != greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))
| greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) != greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)))]]) ).
cnf(refute_0_1195,plain,
( greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) != greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285))) )],[refute_0_1193,refute_0_1194]) ).
cnf(refute_0_1196,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_287,X_286),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) )],[refute_0_1157,refute_0_1195]) ).
cnf(refute_0_1197,plain,
( greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))
| greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)) != greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)
| greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)))]]) ).
cnf(refute_0_1198,plain,
( greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))
| greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(least_upper_bound(X_287,X_286),X_285)) )],[refute_0_1196,refute_0_1197]) ).
cnf(refute_0_1199,plain,
( least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))
| greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))) )],[refute_0_1156,refute_0_1198]) ).
cnf(refute_0_1200,plain,
greatest_lower_bound(X_285,least_upper_bound(X_286,X_287)) = greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287)),greatest_lower_bound(X_285,least_upper_bound(X_286,X_287))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(X_287,X_286),X_285),least_upper_bound(X_286,X_287))) )],[refute_0_890,refute_0_1199]) ).
cnf(refute_0_1201,plain,
greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) = greatest_lower_bound(least_upper_bound(X_290,X_289),X_27),
inference(subst,[],[refute_0_1200:[bind(X_285,$fot(X_27)),bind(X_286,$fot(X_289)),bind(X_287,$fot(X_290))]]) ).
cnf(refute_0_1202,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) != greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))
| greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) != greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)
| greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) = greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))),greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) ),[0,1],$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),X_27))]]) ).
cnf(refute_0_1203,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) != greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))
| greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) = greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)),greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) )],[refute_0_1201,refute_0_1202]) ).
cnf(refute_0_1204,plain,
greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) = greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))),greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) )],[refute_0_873,refute_0_1203]) ).
cnf(refute_0_1205,plain,
greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) = greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)),
inference(subst,[],[refute_0_96:[bind(Y,$fot(least_upper_bound(X_290,X_289))),bind(X_21,$fot(X_27))]]) ).
cnf(refute_0_1206,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) != greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))
| greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) != greatest_lower_bound(X_27,least_upper_bound(X_290,X_289))
| greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)) = greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)),greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) ),[0],$fot(greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)))]]) ).
cnf(refute_0_1207,plain,
( greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) != greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))
| greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)) = greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)),greatest_lower_bound(X_27,least_upper_bound(X_290,X_289))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)) = greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)),greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) )],[refute_0_1204,refute_0_1207]) ).
cnf(refute_0_1209,plain,
( greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)) != greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))
| greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) = greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)))),bind(Y0,$fot(greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))))]]) ).
cnf(refute_0_1210,plain,
greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) = greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,least_upper_bound(X_290,X_289)),greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))) )],[refute_0_1208,refute_0_1209]) ).
cnf(refute_0_1211,plain,
greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)) = greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291))),
inference(subst,[],[refute_0_1210:[bind(X_27,$fot(least_upper_bound(identity,X_291))),bind(X_289,$fot(inverse(X_291))),bind(X_290,$fot(identity))]]) ).
cnf(refute_0_1212,plain,
( greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291))) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)) != greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1213,plain,
( greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291))) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)),greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1211,refute_0_1212]) ).
cnf(refute_0_1214,plain,
greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(identity,inverse(X_291))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_872,refute_0_1213]) ).
cnf(refute_0_1215,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) = greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(inverse(X_35),X_113))),
inference(subst,[],[refute_0_182:[bind(X_36,$fot(least_upper_bound(inverse(X_35),X_113)))]]) ).
cnf(refute_0_1216,plain,
multiply(X_75,least_upper_bound(inverse(X_75),X_77)) = least_upper_bound(multiply(X_75,inverse(X_75)),multiply(X_75,X_77)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_75)),bind(Y,$fot(inverse(X_75))),bind(Z,$fot(X_77))]]) ).
cnf(refute_0_1217,plain,
( multiply(X_75,inverse(X_75)) != identity
| multiply(X_75,least_upper_bound(inverse(X_75),X_77)) != least_upper_bound(multiply(X_75,inverse(X_75)),multiply(X_75,X_77))
| multiply(X_75,least_upper_bound(inverse(X_75),X_77)) = least_upper_bound(identity,multiply(X_75,X_77)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(inverse(X_75),X_77)),least_upper_bound(multiply(X_75,inverse(X_75)),multiply(X_75,X_77))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1218,plain,
( multiply(X_75,least_upper_bound(inverse(X_75),X_77)) != least_upper_bound(multiply(X_75,inverse(X_75)),multiply(X_75,X_77))
| multiply(X_75,least_upper_bound(inverse(X_75),X_77)) = least_upper_bound(identity,multiply(X_75,X_77)) ),
inference(resolve,[$cnf( $equal(multiply(X_75,inverse(X_75)),identity) )],[refute_0_634,refute_0_1217]) ).
cnf(refute_0_1219,plain,
multiply(X_75,least_upper_bound(inverse(X_75),X_77)) = least_upper_bound(identity,multiply(X_75,X_77)),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(inverse(X_75),X_77)),least_upper_bound(multiply(X_75,inverse(X_75)),multiply(X_75,X_77))) )],[refute_0_1216,refute_0_1218]) ).
cnf(refute_0_1220,plain,
multiply(X_35,least_upper_bound(inverse(X_35),X_113)) = least_upper_bound(identity,multiply(X_35,X_113)),
inference(subst,[],[refute_0_1219:[bind(X_75,$fot(X_35)),bind(X_77,$fot(X_113))]]) ).
cnf(refute_0_1221,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) != greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(inverse(X_35),X_113)))
| multiply(X_35,least_upper_bound(inverse(X_35),X_113)) != least_upper_bound(identity,multiply(X_35,X_113))
| multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)),greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(inverse(X_35),X_113)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_35,X_113)))]]) ).
cnf(refute_0_1222,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) != greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(inverse(X_35),X_113)))
| multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113))) ),
inference(resolve,[$cnf( $equal(multiply(X_35,least_upper_bound(inverse(X_35),X_113)),least_upper_bound(identity,multiply(X_35,X_113))) )],[refute_0_1220,refute_0_1221]) ).
cnf(refute_0_1223,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113))),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)),greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(inverse(X_35),X_113)))) )],[refute_0_1215,refute_0_1222]) ).
cnf(refute_0_1224,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) = multiply(X_35,greatest_lower_bound(identity,least_upper_bound(inverse(X_35),X_113))),
inference(subst,[],[refute_0_361:[bind(X_27,$fot(X_35)),bind(X_56,$fot(least_upper_bound(inverse(X_35),X_113)))]]) ).
cnf(refute_0_1225,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) != multiply(X_35,greatest_lower_bound(identity,least_upper_bound(inverse(X_35),X_113)))
| multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) != greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113)))
| multiply(X_35,greatest_lower_bound(identity,least_upper_bound(inverse(X_35),X_113))) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)),greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113)))) ),[0],$fot(multiply(X_35,greatest_lower_bound(identity,least_upper_bound(inverse(X_35),X_113))))]]) ).
cnf(refute_0_1226,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)) != greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113)))
| multiply(X_35,greatest_lower_bound(identity,least_upper_bound(inverse(X_35),X_113))) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113))) ),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)),multiply(X_35,greatest_lower_bound(identity,least_upper_bound(inverse(X_35),X_113)))) )],[refute_0_1224,refute_0_1225]) ).
cnf(refute_0_1227,plain,
multiply(X_35,greatest_lower_bound(identity,least_upper_bound(inverse(X_35),X_113))) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113))),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(inverse(X_35),X_113),identity)),greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_113)))) )],[refute_0_1223,refute_0_1226]) ).
cnf(refute_0_1228,plain,
multiply(X_266,greatest_lower_bound(identity,least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)))) = greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))),
inference(subst,[],[refute_0_1227:[bind(X_113,$fot(multiply(inverse(X_266),X_76))),bind(X_35,$fot(X_266))]]) ).
cnf(refute_0_1229,plain,
multiply(inverse(X_266),least_upper_bound(X_76,identity)) = least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(inverse(X_266)))]]) ).
cnf(refute_0_1230,plain,
( multiply(inverse(X_266),least_upper_bound(X_76,identity)) != least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76))
| least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)) = multiply(inverse(X_266),least_upper_bound(X_76,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_266),least_upper_bound(X_76,identity)))),bind(Y0,$fot(least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76))))]]) ).
cnf(refute_0_1231,plain,
least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)) = multiply(inverse(X_266),least_upper_bound(X_76,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_266),least_upper_bound(X_76,identity)),least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76))) )],[refute_0_1229,refute_0_1230]) ).
cnf(refute_0_1232,plain,
( multiply(X_266,greatest_lower_bound(identity,least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)))) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)) != multiply(inverse(X_266),least_upper_bound(X_76,identity))
| multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) = greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_266,greatest_lower_bound(identity,least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)))),greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))) ),[0,1,1],$fot(multiply(inverse(X_266),least_upper_bound(X_76,identity)))]]) ).
cnf(refute_0_1233,plain,
( multiply(X_266,greatest_lower_bound(identity,least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)))) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) = greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)),multiply(inverse(X_266),least_upper_bound(X_76,identity))) )],[refute_0_1231,refute_0_1232]) ).
cnf(refute_0_1234,plain,
multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) = greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))),
inference(resolve,[$cnf( $equal(multiply(X_266,greatest_lower_bound(identity,least_upper_bound(inverse(X_266),multiply(inverse(X_266),X_76)))),greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))) )],[refute_0_1228,refute_0_1233]) ).
cnf(refute_0_1235,plain,
multiply(X_266,identity) = X_266,
inference(subst,[],[refute_0_561:[bind(X,$fot(X_266))]]) ).
cnf(refute_0_1236,plain,
greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)) = greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)))]]) ).
cnf(refute_0_1237,plain,
( multiply(X_266,identity) != X_266
| greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)) != greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity))
| greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)),greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity))) ),[1,0],$fot(X_266)]]) ).
cnf(refute_0_1238,plain,
( multiply(X_266,identity) != X_266
| greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)),greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity))) )],[refute_0_1236,refute_0_1237]) ).
cnf(refute_0_1239,plain,
greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(X_76,identity)),
inference(resolve,[$cnf( $equal(multiply(X_266,identity),X_266) )],[refute_0_1235,refute_0_1238]) ).
cnf(refute_0_1240,plain,
multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))) = greatest_lower_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_63))),
inference(subst,[],[monotony_glb1:[bind(Z,$fot(multiply(inverse(X),X_63)))]]) ).
cnf(refute_0_1241,plain,
X_63 = multiply(X,multiply(inverse(X),X_63)),
inference(subst,[],[refute_0_1015:[bind(X_57,$fot(X)),bind(X_59,$fot(X_63))]]) ).
cnf(refute_0_1242,plain,
( X_63 != multiply(X,multiply(inverse(X),X_63))
| multiply(X,multiply(inverse(X),X_63)) = X_63 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_63)),bind(Y0,$fot(multiply(X,multiply(inverse(X),X_63))))]]) ).
cnf(refute_0_1243,plain,
multiply(X,multiply(inverse(X),X_63)) = X_63,
inference(resolve,[$cnf( $equal(X_63,multiply(X,multiply(inverse(X),X_63))) )],[refute_0_1241,refute_0_1242]) ).
cnf(refute_0_1244,plain,
( multiply(X,multiply(inverse(X),X_63)) != X_63
| multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))) != greatest_lower_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_63)))
| multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))) = greatest_lower_bound(multiply(X,Y),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))),greatest_lower_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_63)))) ),[1,1],$fot(X_63)]]) ).
cnf(refute_0_1245,plain,
( multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))) != greatest_lower_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_63)))
| multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))) = greatest_lower_bound(multiply(X,Y),X_63) ),
inference(resolve,[$cnf( $equal(multiply(X,multiply(inverse(X),X_63)),X_63) )],[refute_0_1243,refute_0_1244]) ).
cnf(refute_0_1246,plain,
multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))) = greatest_lower_bound(multiply(X,Y),X_63),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,multiply(inverse(X),X_63))),greatest_lower_bound(multiply(X,Y),multiply(X,multiply(inverse(X),X_63)))) )],[refute_0_1240,refute_0_1245]) ).
cnf(refute_0_1247,plain,
multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) = greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)),
inference(subst,[],[refute_0_1246:[bind(X,$fot(X_266)),bind(Y,$fot(identity)),bind(X_63,$fot(least_upper_bound(X_76,identity)))]]) ).
cnf(refute_0_1248,plain,
( multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) != greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity))
| greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)) != greatest_lower_bound(X_266,least_upper_bound(X_76,identity))
| multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) = greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)))),bind(Z0,$fot(greatest_lower_bound(X_266,least_upper_bound(X_76,identity))))]]) ).
cnf(refute_0_1249,plain,
( greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)) != greatest_lower_bound(X_266,least_upper_bound(X_76,identity))
| multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) = greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))),greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity))) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) = greatest_lower_bound(X_266,least_upper_bound(X_76,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_266,identity),least_upper_bound(X_76,identity)),greatest_lower_bound(X_266,least_upper_bound(X_76,identity))) )],[refute_0_1239,refute_0_1249]) ).
cnf(refute_0_1251,plain,
( multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) != greatest_lower_bound(X_266,least_upper_bound(X_76,identity))
| multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))),greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))) ),[0],$fot(greatest_lower_bound(X_266,least_upper_bound(X_76,identity)))]]) ).
cnf(refute_0_1252,plain,
( multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) ),
inference(resolve,[$cnf( $equal(multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))),greatest_lower_bound(X_266,least_upper_bound(X_76,identity))) )],[refute_0_1250,refute_0_1251]) ).
cnf(refute_0_1253,plain,
( X_59 != multiply(X_57,multiply(inverse(X_57),X_59))
| multiply(X_57,multiply(inverse(X_57),X_59)) = X_59 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_59)),bind(Y0,$fot(multiply(X_57,multiply(inverse(X_57),X_59))))]]) ).
cnf(refute_0_1254,plain,
multiply(X_57,multiply(inverse(X_57),X_59)) = X_59,
inference(resolve,[$cnf( $equal(X_59,multiply(X_57,multiply(inverse(X_57),X_59))) )],[refute_0_1015,refute_0_1253]) ).
cnf(refute_0_1255,plain,
multiply(X_266,multiply(inverse(X_266),X_76)) = X_76,
inference(subst,[],[refute_0_1254:[bind(X_57,$fot(X_266)),bind(X_59,$fot(X_76))]]) ).
cnf(refute_0_1256,plain,
least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))) = least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))]]) ).
cnf(refute_0_1257,plain,
( multiply(X_266,multiply(inverse(X_266),X_76)) != X_76
| least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))) != least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))
| least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))) = least_upper_bound(identity,X_76) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))),least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) ),[1,1],$fot(X_76)]]) ).
cnf(refute_0_1258,plain,
( multiply(X_266,multiply(inverse(X_266),X_76)) != X_76
| least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))) = least_upper_bound(identity,X_76) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))),least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) )],[refute_0_1256,refute_0_1257]) ).
cnf(refute_0_1259,plain,
least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))) = least_upper_bound(identity,X_76),
inference(resolve,[$cnf( $equal(multiply(X_266,multiply(inverse(X_266),X_76)),X_76) )],[refute_0_1255,refute_0_1258]) ).
cnf(refute_0_1260,plain,
greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) = greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))))]]) ).
cnf(refute_0_1261,plain,
( greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))) != least_upper_bound(identity,X_76)
| greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) = greatest_lower_bound(X_266,least_upper_bound(identity,X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))),greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))) ),[1,1],$fot(least_upper_bound(identity,X_76))]]) ).
cnf(refute_0_1262,plain,
( least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))) != least_upper_bound(identity,X_76)
| greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) = greatest_lower_bound(X_266,least_upper_bound(identity,X_76)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))),greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))) )],[refute_0_1260,refute_0_1261]) ).
cnf(refute_0_1263,plain,
greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) = greatest_lower_bound(X_266,least_upper_bound(identity,X_76)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))),least_upper_bound(identity,X_76)) )],[refute_0_1259,refute_0_1262]) ).
cnf(refute_0_1264,plain,
( greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))) != greatest_lower_bound(X_266,least_upper_bound(identity,X_76))
| greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(identity,X_76)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_266,least_upper_bound(X_76,identity)),greatest_lower_bound(X_266,least_upper_bound(identity,X_76))) ),[0],$fot(greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))))]]) ).
cnf(refute_0_1265,plain,
( greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(identity,X_76)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76)))),greatest_lower_bound(X_266,least_upper_bound(identity,X_76))) )],[refute_0_1263,refute_0_1264]) ).
cnf(refute_0_1266,plain,
( multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))) != greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))
| greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(identity,X_76)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_266,least_upper_bound(X_76,identity)),greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))) )],[refute_0_1252,refute_0_1265]) ).
cnf(refute_0_1267,plain,
greatest_lower_bound(X_266,least_upper_bound(X_76,identity)) = greatest_lower_bound(X_266,least_upper_bound(identity,X_76)),
inference(resolve,[$cnf( $equal(multiply(X_266,greatest_lower_bound(identity,multiply(inverse(X_266),least_upper_bound(X_76,identity)))),greatest_lower_bound(X_266,least_upper_bound(identity,multiply(X_266,multiply(inverse(X_266),X_76))))) )],[refute_0_1234,refute_0_1266]) ).
cnf(refute_0_1268,plain,
greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)) = greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76)),
inference(subst,[],[refute_0_1267:[bind(X_266,$fot(least_upper_bound(X_290,X_289)))]]) ).
cnf(refute_0_1269,plain,
greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)) = greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76)),
inference(subst,[],[refute_0_1200:[bind(X_285,$fot(least_upper_bound(identity,X_76))),bind(X_286,$fot(X_289)),bind(X_287,$fot(X_290))]]) ).
cnf(refute_0_1270,plain,
( greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)) != greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76))
| greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76)) = greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76))))]]) ).
cnf(refute_0_1271,plain,
greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76)) = greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)),greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76))) )],[refute_0_1269,refute_0_1270]) ).
cnf(refute_0_1272,plain,
( greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)) != greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76))
| greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76)) != greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290))
| greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)) = greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)),greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76)))]]) ).
cnf(refute_0_1273,plain,
( greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)) != greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76))
| greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)) = greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76)),greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290))) )],[refute_0_1271,refute_0_1272]) ).
cnf(refute_0_1274,plain,
greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)) = greatest_lower_bound(least_upper_bound(identity,X_76),least_upper_bound(X_289,X_290)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(X_76,identity)),greatest_lower_bound(least_upper_bound(X_290,X_289),least_upper_bound(identity,X_76))) )],[refute_0_1268,refute_0_1273]) ).
cnf(refute_0_1275,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)) = greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)),
inference(subst,[],[refute_0_1274:[bind(X_289,$fot(inverse(X_291))),bind(X_290,$fot(identity)),bind(X_76,$fot(X_291))]]) ).
cnf(refute_0_1276,plain,
( greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)) != greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1277,plain,
( greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)),greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity))) )],[refute_0_1275,refute_0_1276]) ).
cnf(refute_0_1278,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_291),least_upper_bound(inverse(X_291),identity)),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1214,refute_0_1277]) ).
cnf(refute_0_1279,plain,
greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,least_upper_bound(X_47,Y))),
inference(subst,[],[refute_0_132:[bind(X,$fot(least_upper_bound(X_47,Y))),bind(X_26,$fot(X_46)),bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_1280,plain,
greatest_lower_bound(X_47,least_upper_bound(X_47,Y)) = X_47,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_47))]]) ).
cnf(refute_0_1281,plain,
( greatest_lower_bound(X_47,least_upper_bound(X_47,Y)) != X_47
| greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,least_upper_bound(X_47,Y)))
| greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,least_upper_bound(X_47,Y)))) ),[1,1],$fot(X_47)]]) ).
cnf(refute_0_1282,plain,
( greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,least_upper_bound(X_47,Y)))
| greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,X_47) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_47,least_upper_bound(X_47,Y)),X_47) )],[refute_0_1280,refute_0_1281]) ).
cnf(refute_0_1283,plain,
greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,X_47),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,least_upper_bound(X_47,Y)))) )],[refute_0_1279,refute_0_1282]) ).
cnf(refute_0_1284,plain,
greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,least_upper_bound(X_47,Y))),
inference(subst,[],[refute_0_145:[bind(X_45,$fot(X_47)),bind(X_46,$fot(least_upper_bound(X_47,Y))),bind(X_47,$fot(X_46))]]) ).
cnf(refute_0_1285,plain,
( greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,X_47)
| greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_47,greatest_lower_bound(X_46,least_upper_bound(X_47,Y)))
| greatest_lower_bound(X_47,greatest_lower_bound(X_46,least_upper_bound(X_47,Y))) = greatest_lower_bound(X_46,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,X_47)) ),[0],$fot(greatest_lower_bound(X_47,greatest_lower_bound(X_46,least_upper_bound(X_47,Y))))]]) ).
cnf(refute_0_1286,plain,
( greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,X_47)
| greatest_lower_bound(X_47,greatest_lower_bound(X_46,least_upper_bound(X_47,Y))) = greatest_lower_bound(X_46,X_47) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_47,greatest_lower_bound(X_46,least_upper_bound(X_47,Y)))) )],[refute_0_1284,refute_0_1285]) ).
cnf(refute_0_1287,plain,
greatest_lower_bound(X_47,greatest_lower_bound(X_46,least_upper_bound(X_47,Y))) = greatest_lower_bound(X_46,X_47),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_47,Y),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,X_47)) )],[refute_0_1283,refute_0_1286]) ).
cnf(refute_0_1288,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)),
inference(subst,[],[refute_0_1287:[bind(X_46,$fot(least_upper_bound(identity,inverse(X_291)))),bind(X_47,$fot(least_upper_bound(X_291,identity)))]]) ).
cnf(refute_0_1289,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1290,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity))) )],[refute_0_1288,refute_0_1289]) ).
cnf(refute_0_1291,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(X_291,identity)),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1278,refute_0_1290]) ).
cnf(refute_0_1292,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_1293,plain,
( greatest_lower_bound(X_28,X_27) != greatest_lower_bound(X_27,X_28)
| greatest_lower_bound(X_27,X_28) = greatest_lower_bound(X_28,X_27) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_28,X_27))),bind(Y0,$fot(greatest_lower_bound(X_27,X_28)))]]) ).
cnf(refute_0_1294,plain,
greatest_lower_bound(X_27,X_28) = greatest_lower_bound(X_28,X_27),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_28,X_27),greatest_lower_bound(X_27,X_28)) )],[refute_0_18,refute_0_1293]) ).
cnf(refute_0_1295,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28)
| greatest_lower_bound(X_27,X_28) != greatest_lower_bound(X_28,X_27)
| greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28)) ),[0,1],$fot(greatest_lower_bound(X_28,X_27))]]) ).
cnf(refute_0_1296,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28)
| greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,X_28),greatest_lower_bound(X_28,X_27)) )],[refute_0_1294,refute_0_1295]) ).
cnf(refute_0_1297,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) = greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28)) )],[refute_0_1292,refute_0_1296]) ).
cnf(refute_0_1298,plain,
greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_1299,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28)
| greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28))
| greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28))]]) ).
cnf(refute_0_1300,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) != greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28)
| greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28))) )],[refute_0_1298,refute_0_1299]) ).
cnf(refute_0_1301,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,X_28)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(X_28,X_27)),greatest_lower_bound(greatest_lower_bound(X_26,X_27),X_28)) )],[refute_0_1297,refute_0_1300]) ).
cnf(refute_0_1302,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290))),
inference(subst,[],[refute_0_1301:[bind(X_28,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_1303,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)))
| greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)) != greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)))) ),[1,1],$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),X_27))]]) ).
cnf(refute_0_1304,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)))
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)),greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) )],[refute_0_1201,refute_0_1303]) ).
cnf(refute_0_1305,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,least_upper_bound(X_289,X_290)))) )],[refute_0_1302,refute_0_1304]) ).
cnf(refute_0_1306,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27))
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)))),bind(Y0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27))))]]) ).
cnf(refute_0_1307,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27)) = greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_289,X_290),X_27)),greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_290,X_289),X_27))) )],[refute_0_1305,refute_0_1306]) ).
cnf(refute_0_1308,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))) = greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))),
inference(subst,[],[refute_0_1307:[bind(X_26,$fot(least_upper_bound(X_291,identity))),bind(X_27,$fot(least_upper_bound(least_upper_bound(X_291,identity),Y))),bind(X_289,$fot(identity)),bind(X_290,$fot(inverse(X_291)))]]) ).
cnf(refute_0_1309,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))) != greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1310,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))),greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y)))) )],[refute_0_1308,refute_0_1309]) ).
cnf(refute_0_1311,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(identity,inverse(X_291)),least_upper_bound(least_upper_bound(X_291,identity),Y))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1291,refute_0_1310]) ).
cnf(refute_0_1312,plain,
greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X,Y),X_32)) = greatest_lower_bound(X_32,greatest_lower_bound(X,Y)),
inference(subst,[],[refute_0_96:[bind(Y,$fot(greatest_lower_bound(X,Y))),bind(X_21,$fot(X_32))]]) ).
cnf(refute_0_1313,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_32)) = greatest_lower_bound(greatest_lower_bound(X,Y),X_32),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(X_32))]]) ).
cnf(refute_0_1314,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_32)) != greatest_lower_bound(greatest_lower_bound(X,Y),X_32)
| greatest_lower_bound(greatest_lower_bound(X,Y),X_32) = greatest_lower_bound(X,greatest_lower_bound(Y,X_32)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_32)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),X_32)))]]) ).
cnf(refute_0_1315,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_32) = greatest_lower_bound(X,greatest_lower_bound(Y,X_32)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_32)),greatest_lower_bound(greatest_lower_bound(X,Y),X_32)) )],[refute_0_1313,refute_0_1314]) ).
cnf(refute_0_1316,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X,Y),X_32)) != greatest_lower_bound(X_32,greatest_lower_bound(X,Y))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_32) != greatest_lower_bound(X,greatest_lower_bound(Y,X_32))
| greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(Y,X_32))) = greatest_lower_bound(X_32,greatest_lower_bound(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X,Y),X_32)),greatest_lower_bound(X_32,greatest_lower_bound(X,Y))) ),[0,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_32)))]]) ).
cnf(refute_0_1317,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X,Y),X_32)) != greatest_lower_bound(X_32,greatest_lower_bound(X,Y))
| greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(Y,X_32))) = greatest_lower_bound(X_32,greatest_lower_bound(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_32),greatest_lower_bound(X,greatest_lower_bound(Y,X_32))) )],[refute_0_1315,refute_0_1316]) ).
cnf(refute_0_1318,plain,
greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(Y,X_32))) = greatest_lower_bound(X_32,greatest_lower_bound(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(greatest_lower_bound(X,Y),X_32)),greatest_lower_bound(X_32,greatest_lower_bound(X,Y))) )],[refute_0_1312,refute_0_1317]) ).
cnf(refute_0_1319,plain,
greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) = greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290))),
inference(subst,[],[refute_0_1318:[bind(Y,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_1320,plain,
greatest_lower_bound(X,least_upper_bound(X_289,X_290)) = greatest_lower_bound(least_upper_bound(X_290,X_289),X),
inference(subst,[],[refute_0_1200:[bind(X_285,$fot(X)),bind(X_286,$fot(X_289)),bind(X_287,$fot(X_290))]]) ).
cnf(refute_0_1321,plain,
( greatest_lower_bound(X,least_upper_bound(X_289,X_290)) != greatest_lower_bound(least_upper_bound(X_290,X_289),X)
| greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) != greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290)))
| greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) = greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))),greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290)))) ),[1,1],$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),X))]]) ).
cnf(refute_0_1322,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) != greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290)))
| greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) = greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X_289,X_290)),greatest_lower_bound(least_upper_bound(X_290,X_289),X)) )],[refute_0_1320,refute_0_1321]) ).
cnf(refute_0_1323,plain,
greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) = greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))),greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290)))) )],[refute_0_1319,refute_0_1322]) ).
cnf(refute_0_1324,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) != greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290)))
| greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) != greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X))
| greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290))) = greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))),greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X))) ),[0],$fot(greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290))))]]) ).
cnf(refute_0_1325,plain,
( greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))) != greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X))
| greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290))) = greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))),greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290)))) )],[refute_0_1319,refute_0_1324]) ).
cnf(refute_0_1326,plain,
greatest_lower_bound(X_32,greatest_lower_bound(X,least_upper_bound(X_289,X_290))) = greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X_289,X_290),X_32))),greatest_lower_bound(X_32,greatest_lower_bound(least_upper_bound(X_290,X_289),X))) )],[refute_0_1323,refute_0_1325]) ).
cnf(refute_0_1327,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))),
inference(subst,[],[refute_0_1326:[bind(X,$fot(least_upper_bound(least_upper_bound(X_291,identity),Y))),bind(X_289,$fot(identity)),bind(X_290,$fot(inverse(X_291))),bind(X_32,$fot(least_upper_bound(X_291,identity)))]]) ).
cnf(refute_0_1328,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) != greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1329,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))),greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y)))) )],[refute_0_1327,refute_0_1328]) ).
cnf(refute_0_1330,plain,
greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(inverse(X_291),identity),least_upper_bound(least_upper_bound(X_291,identity),Y))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1311,refute_0_1329]) ).
cnf(refute_0_1331,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) != multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))
| greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) != multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))
| multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))),multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))) ),[0],$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))]]) ).
cnf(refute_0_1332,plain,
( greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))) != multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))
| multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))),multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291)))) )],[refute_0_1330,refute_0_1331]) ).
cnf(refute_0_1333,plain,
multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) = multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_291,identity),greatest_lower_bound(least_upper_bound(least_upper_bound(X_291,identity),Y),least_upper_bound(identity,inverse(X_291)))),multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))) )],[refute_0_391,refute_0_1332]) ).
cnf(refute_0_1334,plain,
( multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) != multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))
| multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))))),bind(Y0,$fot(multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))))]]) ).
cnf(refute_0_1335,plain,
multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291))) = multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_291,identity),least_upper_bound(identity,inverse(X_291))),multiply(least_upper_bound(X_291,identity),greatest_lower_bound(identity,inverse(X_291)))) )],[refute_0_1333,refute_0_1334]) ).
cnf(refute_0_1336,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))) = multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),
inference(subst,[],[refute_0_1335:[bind(X_291,$fot(a))]]) ).
cnf(refute_0_1337,plain,
( multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity
| multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))) != multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a)))
| multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))),multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a)))) ),[1],$fot(identity)]]) ).
cnf(refute_0_1338,plain,
( multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity
| multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))) = identity ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))),multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a)))) )],[refute_0_1336,refute_0_1337]) ).
cnf(refute_0_1339,plain,
multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),greatest_lower_bound(identity,inverse(a))),identity) )],[refute_0_1338,refute_0_375]) ).
cnf(refute_0_1340,plain,
multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_1341,plain,
multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = least_upper_bound(X_75,multiply(X_75,least_upper_bound(inverse(X_75),X_113))),
inference(subst,[],[refute_0_53:[bind(X_76,$fot(least_upper_bound(inverse(X_75),X_113)))]]) ).
cnf(refute_0_1342,plain,
multiply(X_75,least_upper_bound(inverse(X_75),X_113)) = least_upper_bound(identity,multiply(X_75,X_113)),
inference(subst,[],[refute_0_1219:[bind(X_77,$fot(X_113))]]) ).
cnf(refute_0_1343,plain,
( multiply(X_75,least_upper_bound(inverse(X_75),X_113)) != least_upper_bound(identity,multiply(X_75,X_113))
| multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) != least_upper_bound(X_75,multiply(X_75,least_upper_bound(inverse(X_75),X_113)))
| multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)),least_upper_bound(X_75,multiply(X_75,least_upper_bound(inverse(X_75),X_113)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_75,X_113)))]]) ).
cnf(refute_0_1344,plain,
( multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) != least_upper_bound(X_75,multiply(X_75,least_upper_bound(inverse(X_75),X_113)))
| multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))) ),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(inverse(X_75),X_113)),least_upper_bound(identity,multiply(X_75,X_113))) )],[refute_0_1342,refute_0_1343]) ).
cnf(refute_0_1345,plain,
multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)),least_upper_bound(X_75,multiply(X_75,least_upper_bound(inverse(X_75),X_113)))) )],[refute_0_1341,refute_0_1344]) ).
cnf(refute_0_1346,plain,
multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = least_upper_bound(multiply(X,least_upper_bound(X_79,inverse(X))),multiply(X,Z)),
inference(subst,[],[monotony_lub1:[bind(Y,$fot(least_upper_bound(X_79,inverse(X))))]]) ).
cnf(refute_0_1347,plain,
multiply(X,least_upper_bound(X_79,inverse(X))) = least_upper_bound(identity,multiply(X,X_79)),
inference(subst,[],[refute_0_641:[bind(X_75,$fot(X)),bind(X_76,$fot(X_79))]]) ).
cnf(refute_0_1348,plain,
( multiply(X,least_upper_bound(X_79,inverse(X))) != least_upper_bound(identity,multiply(X,X_79))
| multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_79,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_79,inverse(X))),multiply(X,Z))) ),[1,0],$fot(least_upper_bound(identity,multiply(X,X_79)))]]) ).
cnf(refute_0_1349,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_79,inverse(X))),multiply(X,Z))
| multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_79,inverse(X))),least_upper_bound(identity,multiply(X,X_79))) )],[refute_0_1347,refute_0_1348]) ).
cnf(refute_0_1350,plain,
multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_79,inverse(X))),multiply(X,Z))) )],[refute_0_1346,refute_0_1349]) ).
cnf(refute_0_1351,plain,
least_upper_bound(least_upper_bound(X_79,inverse(X)),Z) = least_upper_bound(X_79,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_79)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_1352,plain,
multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)))]]) ).
cnf(refute_0_1353,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) != multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z))
| least_upper_bound(least_upper_bound(X_79,inverse(X)),Z) != least_upper_bound(X_79,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z))) ),[1,1],$fot(least_upper_bound(X_79,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_1354,plain,
( least_upper_bound(least_upper_bound(X_79,inverse(X)),Z) != least_upper_bound(X_79,least_upper_bound(inverse(X),Z))
| multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z))) )],[refute_0_1352,refute_0_1353]) ).
cnf(refute_0_1355,plain,
multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) = multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_79,inverse(X)),Z),least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) )],[refute_0_1351,refute_0_1354]) ).
cnf(refute_0_1356,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) != multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z)))
| multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))
| multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))) ),[0],$fot(multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))))]]) ).
cnf(refute_0_1357,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))
| multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z)))) )],[refute_0_1355,refute_0_1356]) ).
cnf(refute_0_1358,plain,
least_upper_bound(multiply(X,X_79),multiply(X,Z)) = multiply(X,least_upper_bound(X_79,Z)),
inference(subst,[],[refute_0_258:[bind(Y,$fot(X_79))]]) ).
cnf(refute_0_1359,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))) = least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))))]]) ).
cnf(refute_0_1360,plain,
( least_upper_bound(multiply(X,X_79),multiply(X,Z)) != multiply(X,least_upper_bound(X_79,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))) != least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z)))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z)))) ),[1,1],$fot(multiply(X,least_upper_bound(X_79,Z)))]]) ).
cnf(refute_0_1361,plain,
( least_upper_bound(multiply(X,X_79),multiply(X,Z)) != multiply(X,least_upper_bound(X_79,Z))
| least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z)))) )],[refute_0_1359,refute_0_1360]) ).
cnf(refute_0_1362,plain,
least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,X_79),multiply(X,Z)),multiply(X,least_upper_bound(X_79,Z))) )],[refute_0_1358,refute_0_1361]) ).
cnf(refute_0_1363,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) = least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))),
inference(subst,[],[refute_0_210:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X,X_79))),bind(Z,$fot(multiply(X,Z)))]]) ).
cnf(refute_0_1364,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) != least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z)))))]]) ).
cnf(refute_0_1365,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z)))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)),least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z)))) )],[refute_0_1363,refute_0_1364]) ).
cnf(refute_0_1366,plain,
least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_79),multiply(X,Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z)))) )],[refute_0_1362,refute_0_1365]) ).
cnf(refute_0_1367,plain,
( multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))
| least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)) != least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z)))
| multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)))]]) ).
cnf(refute_0_1368,plain,
( multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))
| multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z)),least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z)))) )],[refute_0_1366,refute_0_1367]) ).
cnf(refute_0_1369,plain,
( multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))
| multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))),least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))) )],[refute_0_1357,refute_0_1368]) ).
cnf(refute_0_1370,plain,
multiply(X,least_upper_bound(X_79,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_79,Z))),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_79,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_79)),multiply(X,Z))) )],[refute_0_1350,refute_0_1369]) ).
cnf(refute_0_1371,plain,
multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))),
inference(subst,[],[refute_0_1370:[bind(X,$fot(X_75)),bind(Z,$fot(X_113)),bind(X_79,$fot(identity))]]) ).
cnf(refute_0_1372,plain,
multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113))),
inference(subst,[],[refute_0_296:[bind(X_17,$fot(X_75)),bind(X_94,$fot(least_upper_bound(inverse(X_75),X_113)))]]) ).
cnf(refute_0_1373,plain,
( multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113))) != least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113)))
| multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) != multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113)))
| multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)))),bind(Y0,$fot(multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113)))))]]) ).
cnf(refute_0_1374,plain,
( multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113))) != least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113)))
| multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) ),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)),multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113)))) )],[refute_0_1372,refute_0_1373]) ).
cnf(refute_0_1375,plain,
multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) = least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(identity,least_upper_bound(inverse(X_75),X_113))),least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113)))) )],[refute_0_1371,refute_0_1374]) ).
cnf(refute_0_1376,plain,
( multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))
| multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) != least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))) ),[0],$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))))]]) ).
cnf(refute_0_1377,plain,
( multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))) ),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)),least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113)))) )],[refute_0_1375,refute_0_1376]) ).
cnf(refute_0_1378,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(least_upper_bound(inverse(X_75),X_113),identity)),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))) )],[refute_0_1345,refute_0_1377]) ).
cnf(refute_0_1379,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,multiply(X_223,identity)))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))),
inference(subst,[],[refute_0_1378:[bind(X_113,$fot(multiply(X_223,identity)))]]) ).
cnf(refute_0_1380,plain,
multiply(least_upper_bound(X_223,identity),identity) = least_upper_bound(identity,multiply(X_223,identity)),
inference(subst,[],[refute_0_613:[bind(X_80,$fot(identity)),bind(X_81,$fot(X_223))]]) ).
cnf(refute_0_1381,plain,
( multiply(least_upper_bound(X_223,identity),identity) != least_upper_bound(identity,multiply(X_223,identity))
| least_upper_bound(identity,multiply(X_223,identity)) = multiply(least_upper_bound(X_223,identity),identity) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_223,identity),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_223,identity))))]]) ).
cnf(refute_0_1382,plain,
least_upper_bound(identity,multiply(X_223,identity)) = multiply(least_upper_bound(X_223,identity),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_223,identity),identity),least_upper_bound(identity,multiply(X_223,identity))) )],[refute_0_1380,refute_0_1381]) ).
cnf(refute_0_1383,plain,
( least_upper_bound(identity,multiply(X_223,identity)) != multiply(least_upper_bound(X_223,identity),identity)
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,multiply(X_223,identity)))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,multiply(X_223,identity)))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) ),[0,1,1],$fot(multiply(least_upper_bound(X_223,identity),identity))]]) ).
cnf(refute_0_1384,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,multiply(X_223,identity)))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_223,identity)),multiply(least_upper_bound(X_223,identity),identity)) )],[refute_0_1382,refute_0_1383]) ).
cnf(refute_0_1385,plain,
least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,multiply(X_223,identity)))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) )],[refute_0_1379,refute_0_1384]) ).
cnf(refute_0_1386,plain,
multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),
inference(subst,[],[refute_0_561:[bind(X,$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity)))))]]) ).
cnf(refute_0_1387,plain,
multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = least_upper_bound(multiply(X_81,multiply(X_58,X_59)),multiply(inverse(X_58),multiply(X_58,X_59))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(multiply(X_58,X_59))),bind(Y,$fot(X_81)),bind(Z,$fot(inverse(X_58)))]]) ).
cnf(refute_0_1388,plain,
( multiply(inverse(X_58),multiply(X_58,X_59)) != X_59
| multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) != least_upper_bound(multiply(X_81,multiply(X_58,X_59)),multiply(inverse(X_58),multiply(X_58,X_59)))
| multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)),least_upper_bound(multiply(X_81,multiply(X_58,X_59)),multiply(inverse(X_58),multiply(X_58,X_59)))) ),[1,1],$fot(X_59)]]) ).
cnf(refute_0_1389,plain,
( multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) != least_upper_bound(multiply(X_81,multiply(X_58,X_59)),multiply(inverse(X_58),multiply(X_58,X_59)))
| multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),multiply(X_58,X_59)),X_59) )],[refute_0_799,refute_0_1388]) ).
cnf(refute_0_1390,plain,
multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)),least_upper_bound(multiply(X_81,multiply(X_58,X_59)),multiply(inverse(X_58),multiply(X_58,X_59)))) )],[refute_0_1387,refute_0_1389]) ).
cnf(refute_0_1391,plain,
least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59) = least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_59)),bind(Y,$fot(multiply(X_81,multiply(X_58,X_59))))]]) ).
cnf(refute_0_1392,plain,
( multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) != least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59)
| least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59) != least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))
| multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)),least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))) ),[0],$fot(least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59))]]) ).
cnf(refute_0_1393,plain,
( multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) != least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59)
| multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59),least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))) )],[refute_0_1391,refute_0_1392]) ).
cnf(refute_0_1394,plain,
multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)),least_upper_bound(multiply(X_81,multiply(X_58,X_59)),X_59)) )],[refute_0_1390,refute_0_1393]) ).
cnf(refute_0_1395,plain,
multiply(multiply(least_upper_bound(X_84,inverse(Y)),Y),Z) = multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z)),
inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_84,inverse(Y))))]]) ).
cnf(refute_0_1396,plain,
multiply(least_upper_bound(X_84,inverse(Y)),Y) = least_upper_bound(identity,multiply(X_84,Y)),
inference(subst,[],[refute_0_721:[bind(X_80,$fot(Y)),bind(X_81,$fot(X_84))]]) ).
cnf(refute_0_1397,plain,
( multiply(multiply(least_upper_bound(X_84,inverse(Y)),Y),Z) != multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z))
| multiply(least_upper_bound(X_84,inverse(Y)),Y) != least_upper_bound(identity,multiply(X_84,Y))
| multiply(least_upper_bound(identity,multiply(X_84,Y)),Z) = multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(X_84,inverse(Y)),Y),Z),multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z))) ),[0,0],$fot(least_upper_bound(identity,multiply(X_84,Y)))]]) ).
cnf(refute_0_1398,plain,
( multiply(multiply(least_upper_bound(X_84,inverse(Y)),Y),Z) != multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z))
| multiply(least_upper_bound(identity,multiply(X_84,Y)),Z) = multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(Y)),Y),least_upper_bound(identity,multiply(X_84,Y))) )],[refute_0_1396,refute_0_1397]) ).
cnf(refute_0_1399,plain,
multiply(least_upper_bound(identity,multiply(X_84,Y)),Z) = multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_84,inverse(Y)),Y),Z),multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z))) )],[refute_0_1395,refute_0_1398]) ).
cnf(refute_0_1400,plain,
( multiply(least_upper_bound(identity,multiply(X_84,Y)),Z) != multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z))
| multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z)) = multiply(least_upper_bound(identity,multiply(X_84,Y)),Z) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(X_84,Y)),Z))),bind(Y0,$fot(multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z))))]]) ).
cnf(refute_0_1401,plain,
multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z)) = multiply(least_upper_bound(identity,multiply(X_84,Y)),Z),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_84,Y)),Z),multiply(least_upper_bound(X_84,inverse(Y)),multiply(Y,Z))) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) = multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59),
inference(subst,[],[refute_0_1401:[bind(Y,$fot(X_58)),bind(Z,$fot(X_59)),bind(X_84,$fot(X_81))]]) ).
cnf(refute_0_1403,plain,
( multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) != multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59)
| multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) != least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))
| multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59) = least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)),least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))) ),[0],$fot(multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59))]]) ).
cnf(refute_0_1404,plain,
( multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)) != least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))
| multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59) = least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)),multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59)) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59) = least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_58)),multiply(X_58,X_59)),least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))) )],[refute_0_1394,refute_0_1404]) ).
cnf(refute_0_1406,plain,
( multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59) != least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))
| least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))) = multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59))),bind(Y0,$fot(least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))))]]) ).
cnf(refute_0_1407,plain,
least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59))) = multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_81,X_58)),X_59),least_upper_bound(X_59,multiply(X_81,multiply(X_58,X_59)))) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) = multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity),
inference(subst,[],[refute_0_1407:[bind(X_58,$fot(least_upper_bound(X_223,identity))),bind(X_59,$fot(identity)),bind(X_81,$fot(X_75))]]) ).
cnf(refute_0_1409,plain,
( multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity) != least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity)))
| least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) != multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity)
| least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity)))))]]) ).
cnf(refute_0_1410,plain,
( multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity) != least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity)))
| least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))),multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity)) )],[refute_0_1408,refute_0_1409]) ).
cnf(refute_0_1411,plain,
least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),identity),least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity)))) )],[refute_0_1386,refute_0_1410]) ).
cnf(refute_0_1412,plain,
( least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) != least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) ),[0],$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))))]]) ).
cnf(refute_0_1413,plain,
( least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))),least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity)))) )],[refute_0_1411,refute_0_1412]) ).
cnf(refute_0_1414,plain,
multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity) = least_upper_bound(identity,multiply(X_75,X_223)),
inference(subst,[],[refute_0_561:[bind(X,$fot(least_upper_bound(identity,multiply(X_75,X_223))))]]) ).
cnf(refute_0_1415,plain,
least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))) = multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity),
inference(subst,[],[refute_0_1407:[bind(X_58,$fot(X_223)),bind(X_59,$fot(identity)),bind(X_81,$fot(X_75))]]) ).
cnf(refute_0_1416,plain,
( multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity) != least_upper_bound(identity,multiply(X_75,X_223))
| least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))) != multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity)
| least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))) = least_upper_bound(identity,multiply(X_75,X_223)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_75,X_223))))]]) ).
cnf(refute_0_1417,plain,
( multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity) != least_upper_bound(identity,multiply(X_75,X_223))
| least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))) = least_upper_bound(identity,multiply(X_75,X_223)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))),multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity)) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))) = least_upper_bound(identity,multiply(X_75,X_223)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_75,X_223)),identity),least_upper_bound(identity,multiply(X_75,X_223))) )],[refute_0_1414,refute_0_1417]) ).
cnf(refute_0_1419,plain,
least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))))]]) ).
cnf(refute_0_1420,plain,
( least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))) != least_upper_bound(identity,multiply(X_75,X_223))
| least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_75,X_223)))]]) ).
cnf(refute_0_1421,plain,
( least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))) != least_upper_bound(identity,multiply(X_75,X_223))
| least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) )],[refute_0_1419,refute_0_1420]) ).
cnf(refute_0_1422,plain,
least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))),least_upper_bound(identity,multiply(X_75,X_223))) )],[refute_0_1418,refute_0_1421]) ).
cnf(refute_0_1423,plain,
( least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) ),[1],$fot(least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))))]]) ).
cnf(refute_0_1424,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity)))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223)))) )],[refute_0_1422,refute_0_1423]) ).
cnf(refute_0_1425,plain,
( least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) )],[refute_0_1413,refute_0_1424]) ).
cnf(refute_0_1426,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(X_223,identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_223))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,multiply(least_upper_bound(X_223,identity),identity))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,multiply(X_223,identity))))) )],[refute_0_1385,refute_0_1425]) ).
cnf(refute_0_1427,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321)))),
inference(subst,[],[refute_0_1426:[bind(X_223,$fot(greatest_lower_bound(X_322,X_321))),bind(X_75,$fot(inverse(greatest_lower_bound(X_321,X_322))))]]) ).
cnf(refute_0_1428,plain,
multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)),
inference(subst,[],[refute_0_920:[bind(X_36,$fot(X_100)),bind(X_37,$fot(greatest_lower_bound(Y,X_100)))]]) ).
cnf(refute_0_1429,plain,
greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100)) = greatest_lower_bound(X_100,Y),
inference(subst,[],[refute_0_96:[bind(X_21,$fot(X_100))]]) ).
cnf(refute_0_1430,plain,
( multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100))
| greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100)) != greatest_lower_bound(X_100,Y)
| multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100))) ),[0,1],$fot(greatest_lower_bound(X_100,Y))]]) ).
cnf(refute_0_1431,plain,
( multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100))
| multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) )],[refute_0_1429,refute_0_1430]) ).
cnf(refute_0_1432,plain,
multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,greatest_lower_bound(Y,X_100))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100))) )],[refute_0_1428,refute_0_1431]) ).
cnf(refute_0_1433,plain,
multiply(greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)),inverse(X_114)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114))),
inference(subst,[],[refute_0_926:[bind(X_43,$fot(X_114)),bind(X_44,$fot(least_upper_bound(X_13,X_114)))]]) ).
cnf(refute_0_1434,plain,
greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)) = X_114,
inference(subst,[],[refute_0_85:[bind(X_12,$fot(X_114))]]) ).
cnf(refute_0_1435,plain,
( multiply(greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)),inverse(X_114)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))
| greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)) != X_114
| multiply(X_114,inverse(X_114)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)),inverse(X_114)),greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))) ),[0,0],$fot(X_114)]]) ).
cnf(refute_0_1436,plain,
( multiply(greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)),inverse(X_114)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))
| multiply(X_114,inverse(X_114)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)),X_114) )],[refute_0_1434,refute_0_1435]) ).
cnf(refute_0_1437,plain,
multiply(X_114,inverse(X_114)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_114,least_upper_bound(X_13,X_114)),inverse(X_114)),greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))) )],[refute_0_1433,refute_0_1436]) ).
cnf(refute_0_1438,plain,
multiply(X_114,inverse(X_114)) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(X_114))]]) ).
cnf(refute_0_1439,plain,
( multiply(X_114,inverse(X_114)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))
| multiply(X_114,inverse(X_114)) != identity
| identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_114,inverse(X_114)),greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1440,plain,
( multiply(X_114,inverse(X_114)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))
| identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114))) ),
inference(resolve,[$cnf( $equal(multiply(X_114,inverse(X_114)),identity) )],[refute_0_1438,refute_0_1439]) ).
cnf(refute_0_1441,plain,
identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114))),
inference(resolve,[$cnf( $equal(multiply(X_114,inverse(X_114)),greatest_lower_bound(identity,multiply(least_upper_bound(X_13,X_114),inverse(X_114)))) )],[refute_0_1437,refute_0_1440]) ).
cnf(refute_0_1442,plain,
identity = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))),
inference(subst,[],[refute_0_1441:[bind(X_114,$fot(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),bind(X_13,$fot(identity))]]) ).
cnf(refute_0_1443,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) = least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),
inference(subst,[],[refute_0_189:[bind(X_80,$fot(greatest_lower_bound(X_100,X_101))),bind(X_82,$fot(inverse(X_101)))]]) ).
cnf(refute_0_1444,plain,
multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)) = greatest_lower_bound(identity,multiply(inverse(X_101),X_100)),
inference(subst,[],[refute_0_920:[bind(X_36,$fot(X_100)),bind(X_37,$fot(X_101))]]) ).
cnf(refute_0_1445,plain,
( multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)) != greatest_lower_bound(identity,multiply(inverse(X_101),X_100))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) != least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)),least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))]]) ).
cnf(refute_0_1446,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) != least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)),greatest_lower_bound(identity,multiply(inverse(X_101),X_100))) )],[refute_0_1444,refute_0_1445]) ).
cnf(refute_0_1447,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)),least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) )],[refute_0_1443,refute_0_1446]) ).
cnf(refute_0_1448,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) != least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))
| least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))]]) ).
cnf(refute_0_1449,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))
| least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) = least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)),least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) )],[refute_0_1443,refute_0_1448]) ).
cnf(refute_0_1450,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_101),X_100)))]]) ).
cnf(refute_0_1451,plain,
( least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))) != identity
| least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity) ),[0],$fot(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))))]]) ).
cnf(refute_0_1452,plain,
( least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))
| least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100))),identity) )],[refute_0_1450,refute_0_1451]) ).
cnf(refute_0_1453,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)) != least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))
| least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))) )],[refute_0_1449,refute_0_1452]) ).
cnf(refute_0_1454,plain,
least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) = identity,
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_100,X_101)),inverse(X_101)),greatest_lower_bound(X_100,X_101)),least_upper_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_101),X_100)))) )],[refute_0_1447,refute_0_1453]) ).
cnf(refute_0_1455,plain,
( identity != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))
| least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) != identity
| identity = greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))) ),[1,1,0],$fot(identity)]]) ).
cnf(refute_0_1456,plain,
( identity != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))
| identity = greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity) )],[refute_0_1454,refute_0_1455]) ).
cnf(refute_0_1457,plain,
identity = greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))) )],[refute_0_1442,refute_0_1456]) ).
cnf(refute_0_1458,plain,
inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) = multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101),
inference(subst,[],[refute_0_538:[bind(X,$fot(X_101)),bind(X_23,$fot(greatest_lower_bound(X_100,X_101)))]]) ).
cnf(refute_0_1459,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))]]) ).
cnf(refute_0_1460,plain,
( greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) != greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))
| inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) != multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)
| greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) ),[1,1],$fot(multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))]]) ).
cnf(refute_0_1461,plain,
( inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))) != multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)
| greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) )],[refute_0_1459,refute_0_1460]) ).
cnf(refute_0_1462,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) )],[refute_0_1458,refute_0_1461]) ).
cnf(refute_0_1463,plain,
multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))))]]) ).
cnf(refute_0_1464,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))),
inference(subst,[],[refute_0_361:[bind(X_27,$fot(identity)),bind(X_56,$fot(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))]]) ).
cnf(refute_0_1465,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) != greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))
| multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))
| multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))))]]) ).
cnf(refute_0_1466,plain,
( multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) != greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))
| multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) ),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)),multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))) )],[refute_0_1464,refute_0_1465]) ).
cnf(refute_0_1467,plain,
multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))),greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) )],[refute_0_1463,refute_0_1466]) ).
cnf(refute_0_1468,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)),
inference(subst,[],[refute_0_337:[bind(X_35,$fot(identity)),bind(X_36,$fot(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))]]) ).
cnf(refute_0_1469,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)) != greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) != multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))))]]) ).
cnf(refute_0_1470,plain,
( multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)) != greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))),multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity))) )],[refute_0_1468,refute_0_1469]) ).
cnf(refute_0_1471,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))),identity)),greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) )],[refute_0_1467,refute_0_1470]) ).
cnf(refute_0_1472,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) != greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))
| greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))))]]) ).
cnf(refute_0_1473,plain,
( greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))
| greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))),greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) )],[refute_0_1471,refute_0_1472]) ).
cnf(refute_0_1474,plain,
greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))) )],[refute_0_1462,refute_0_1473]) ).
cnf(refute_0_1475,plain,
( greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))
| identity != greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))
| identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))) ),[1],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)))]]) ).
cnf(refute_0_1476,plain,
( identity != greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))
| identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101))))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))) )],[refute_0_1474,refute_0_1475]) ).
cnf(refute_0_1477,plain,
identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(identity,inverse(multiply(inverse(X_101),greatest_lower_bound(X_100,X_101)))))) )],[refute_0_1457,refute_0_1476]) ).
cnf(refute_0_1478,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))))]]) ).
cnf(refute_0_1479,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101)) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_101)),X_101))) )],[refute_0_1477,refute_0_1478]) ).
cnf(refute_0_1480,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)) = identity,
inference(subst,[],[refute_0_1479:[bind(X_100,$fot(Y)),bind(X_101,$fot(X_100))]]) ).
cnf(refute_0_1481,plain,
( multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)) != identity
| multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)))]]) ).
cnf(refute_0_1482,plain,
( multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100))
| multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100)),identity) )],[refute_0_1480,refute_0_1481]) ).
cnf(refute_0_1483,plain,
multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_100)),greatest_lower_bound(X_100,Y)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_100)),X_100))) )],[refute_0_1432,refute_0_1482]) ).
cnf(refute_0_1484,plain,
multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321)) = identity,
inference(subst,[],[refute_0_1483:[bind(Y,$fot(X_321)),bind(X_100,$fot(X_322))]]) ).
cnf(refute_0_1485,plain,
( multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321)) != identity
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) != least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321))))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))),least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_1486,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) != least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321))))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321)),identity) )],[refute_0_1484,refute_0_1485]) ).
cnf(refute_0_1487,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))),least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),greatest_lower_bound(X_322,X_321))))) )],[refute_0_1427,refute_0_1486]) ).
cnf(refute_0_1488,plain,
least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(inverse(greatest_lower_bound(X_322,X_321)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1489,plain,
multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),
inference(subst,[],[refute_0_561:[bind(X,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))))]]) ).
cnf(refute_0_1490,plain,
multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42),
inference(subst,[],[refute_0_114:[bind(X_43,$fot(least_upper_bound(X_295,X_297))),bind(X_44,$fot(least_upper_bound(X_296,least_upper_bound(X_297,X_295))))]]) ).
cnf(refute_0_1491,plain,
greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_64,X_65),X_12)) = X_12,
inference(subst,[],[refute_0_85:[bind(X_13,$fot(least_upper_bound(X_64,X_65)))]]) ).
cnf(refute_0_1492,plain,
least_upper_bound(X_64,least_upper_bound(X_65,X_12)) = least_upper_bound(least_upper_bound(X_64,X_65),X_12),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_64)),bind(Y,$fot(X_65)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_1493,plain,
( least_upper_bound(X_64,least_upper_bound(X_65,X_12)) != least_upper_bound(least_upper_bound(X_64,X_65),X_12)
| least_upper_bound(least_upper_bound(X_64,X_65),X_12) = least_upper_bound(X_64,least_upper_bound(X_65,X_12)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_64,least_upper_bound(X_65,X_12)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_64,X_65),X_12)))]]) ).
cnf(refute_0_1494,plain,
least_upper_bound(least_upper_bound(X_64,X_65),X_12) = least_upper_bound(X_64,least_upper_bound(X_65,X_12)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_64,least_upper_bound(X_65,X_12)),least_upper_bound(least_upper_bound(X_64,X_65),X_12)) )],[refute_0_1492,refute_0_1493]) ).
cnf(refute_0_1495,plain,
( greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_64,X_65),X_12)) != X_12
| least_upper_bound(least_upper_bound(X_64,X_65),X_12) != least_upper_bound(X_64,least_upper_bound(X_65,X_12))
| greatest_lower_bound(X_12,least_upper_bound(X_64,least_upper_bound(X_65,X_12))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_64,X_65),X_12)),X_12) ),[0,1],$fot(least_upper_bound(X_64,least_upper_bound(X_65,X_12)))]]) ).
cnf(refute_0_1496,plain,
( greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_64,X_65),X_12)) != X_12
| greatest_lower_bound(X_12,least_upper_bound(X_64,least_upper_bound(X_65,X_12))) = X_12 ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_64,X_65),X_12),least_upper_bound(X_64,least_upper_bound(X_65,X_12))) )],[refute_0_1494,refute_0_1495]) ).
cnf(refute_0_1497,plain,
greatest_lower_bound(X_12,least_upper_bound(X_64,least_upper_bound(X_65,X_12))) = X_12,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_64,X_65),X_12)),X_12) )],[refute_0_1491,refute_0_1496]) ).
cnf(refute_0_1498,plain,
greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,least_upper_bound(Y,X_74)))) = least_upper_bound(Y,X_74),
inference(subst,[],[refute_0_1497:[bind(X_12,$fot(least_upper_bound(Y,X_74))),bind(X_64,$fot(X_73)),bind(X_65,$fot(X_74))]]) ).
cnf(refute_0_1499,plain,
least_upper_bound(X_74,least_upper_bound(Y,X_74)) = least_upper_bound(X_74,Y),
inference(subst,[],[refute_0_214:[bind(X_15,$fot(X_74))]]) ).
cnf(refute_0_1500,plain,
( greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,least_upper_bound(Y,X_74)))) != least_upper_bound(Y,X_74)
| least_upper_bound(X_74,least_upper_bound(Y,X_74)) != least_upper_bound(X_74,Y)
| greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,Y))) = least_upper_bound(Y,X_74) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,least_upper_bound(Y,X_74)))),least_upper_bound(Y,X_74)) ),[0,1,1],$fot(least_upper_bound(X_74,Y))]]) ).
cnf(refute_0_1501,plain,
( greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,least_upper_bound(Y,X_74)))) != least_upper_bound(Y,X_74)
| greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,Y))) = least_upper_bound(Y,X_74) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_74,least_upper_bound(Y,X_74)),least_upper_bound(X_74,Y)) )],[refute_0_1499,refute_0_1500]) ).
cnf(refute_0_1502,plain,
greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,Y))) = least_upper_bound(Y,X_74),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_74),least_upper_bound(X_73,least_upper_bound(X_74,least_upper_bound(Y,X_74)))),least_upper_bound(Y,X_74)) )],[refute_0_1498,refute_0_1501]) ).
cnf(refute_0_1503,plain,
greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) = least_upper_bound(X_295,X_297),
inference(subst,[],[refute_0_1502:[bind(Y,$fot(X_295)),bind(X_73,$fot(X_296)),bind(X_74,$fot(X_297))]]) ).
cnf(refute_0_1504,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) != multiply(greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)
| greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) != least_upper_bound(X_295,X_297)
| multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(least_upper_bound(X_295,X_297),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42),multiply(greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)) ),[1,0],$fot(least_upper_bound(X_295,X_297))]]) ).
cnf(refute_0_1505,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) != multiply(greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)
| multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(least_upper_bound(X_295,X_297),X_42) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),least_upper_bound(X_295,X_297)) )],[refute_0_1503,refute_0_1504]) ).
cnf(refute_0_1506,plain,
multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(least_upper_bound(X_295,X_297),X_42),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42),multiply(greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)) )],[refute_0_1490,refute_0_1505]) ).
cnf(refute_0_1507,plain,
greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) = least_upper_bound(X_297,X_295),
inference(subst,[],[refute_0_85:[bind(X_12,$fot(least_upper_bound(X_297,X_295))),bind(X_13,$fot(X_296))]]) ).
cnf(refute_0_1508,plain,
multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42) = multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42))]]) ).
cnf(refute_0_1509,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42) != multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)
| greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) != least_upper_bound(X_297,X_295)
| multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42) = multiply(least_upper_bound(X_297,X_295),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42),multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)) ),[1,0],$fot(least_upper_bound(X_297,X_295))]]) ).
cnf(refute_0_1510,plain,
( greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) != least_upper_bound(X_297,X_295)
| multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42) = multiply(least_upper_bound(X_297,X_295),X_42) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42),multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)) )],[refute_0_1508,refute_0_1509]) ).
cnf(refute_0_1511,plain,
multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42) = multiply(least_upper_bound(X_297,X_295),X_42),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),least_upper_bound(X_297,X_295)) )],[refute_0_1507,refute_0_1510]) ).
cnf(refute_0_1512,plain,
multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X) = greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)),
inference(subst,[],[monotony_glb2:[bind(Z,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_1513,plain,
greatest_lower_bound(Y,least_upper_bound(X_289,X_290)) = greatest_lower_bound(least_upper_bound(X_290,X_289),Y),
inference(subst,[],[refute_0_1200:[bind(X_285,$fot(Y)),bind(X_286,$fot(X_289)),bind(X_287,$fot(X_290))]]) ).
cnf(refute_0_1514,plain,
( multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X) != greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X))
| greatest_lower_bound(Y,least_upper_bound(X_289,X_290)) != greatest_lower_bound(least_upper_bound(X_290,X_289),Y)
| multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) = greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X),greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X))) ),[0,0],$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),Y))]]) ).
cnf(refute_0_1515,plain,
( multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X) != greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X))
| multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) = greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) )],[refute_0_1513,refute_0_1514]) ).
cnf(refute_0_1516,plain,
multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) = greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X),greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X))) )],[refute_0_1512,refute_0_1515]) ).
cnf(refute_0_1517,plain,
greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)) = multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X),
inference(subst,[],[refute_0_110:[bind(Z,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_1518,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) != greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X))
| greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)) != multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X)
| multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) = multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X),multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X)) ),[0],$fot(greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)))]]) ).
cnf(refute_0_1519,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) != greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X))
| multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) = multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X)),multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X)) )],[refute_0_1517,refute_0_1518]) ).
cnf(refute_0_1520,plain,
multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) = multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X),greatest_lower_bound(multiply(Y,X),multiply(least_upper_bound(X_289,X_290),X))) )],[refute_0_1516,refute_0_1519]) ).
cnf(refute_0_1521,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) != multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X)
| multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X) = multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X))),bind(Y0,$fot(multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X)))]]) ).
cnf(refute_0_1522,plain,
multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X) = multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_290,X_289),Y),X),multiply(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),X)) )],[refute_0_1520,refute_0_1521]) ).
cnf(refute_0_1523,plain,
multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42),
inference(subst,[],[refute_0_1522:[bind(X,$fot(X_42)),bind(Y,$fot(least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),bind(X_289,$fot(X_295)),bind(X_290,$fot(X_297))]]) ).
cnf(refute_0_1524,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) != multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)
| multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42) != multiply(least_upper_bound(X_297,X_295),X_42)
| multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(least_upper_bound(X_297,X_295),X_42) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42))),bind(Z0,$fot(multiply(least_upper_bound(X_297,X_295),X_42)))]]) ).
cnf(refute_0_1525,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42) != multiply(least_upper_bound(X_297,X_295),X_42)
| multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(least_upper_bound(X_297,X_295),X_42) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42),multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42)) )],[refute_0_1523,refute_0_1524]) ).
cnf(refute_0_1526,plain,
multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) = multiply(least_upper_bound(X_297,X_295),X_42),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),X_42),multiply(least_upper_bound(X_297,X_295),X_42)) )],[refute_0_1511,refute_0_1525]) ).
cnf(refute_0_1527,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) != multiply(least_upper_bound(X_295,X_297),X_42)
| multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) != multiply(least_upper_bound(X_297,X_295),X_42)
| multiply(least_upper_bound(X_297,X_295),X_42) = multiply(least_upper_bound(X_295,X_297),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42),multiply(least_upper_bound(X_295,X_297),X_42)) ),[0],$fot(multiply(least_upper_bound(X_297,X_295),X_42))]]) ).
cnf(refute_0_1528,plain,
( multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42) != multiply(least_upper_bound(X_295,X_297),X_42)
| multiply(least_upper_bound(X_297,X_295),X_42) = multiply(least_upper_bound(X_295,X_297),X_42) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42),multiply(least_upper_bound(X_297,X_295),X_42)) )],[refute_0_1526,refute_0_1527]) ).
cnf(refute_0_1529,plain,
multiply(least_upper_bound(X_297,X_295),X_42) = multiply(least_upper_bound(X_295,X_297),X_42),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297)),X_42),multiply(least_upper_bound(X_295,X_297),X_42)) )],[refute_0_1506,refute_0_1528]) ).
cnf(refute_0_1530,plain,
( multiply(least_upper_bound(X_297,X_295),X_42) != multiply(least_upper_bound(X_295,X_297),X_42)
| multiply(least_upper_bound(X_295,X_297),X_42) = multiply(least_upper_bound(X_297,X_295),X_42) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_297,X_295),X_42))),bind(Y0,$fot(multiply(least_upper_bound(X_295,X_297),X_42)))]]) ).
cnf(refute_0_1531,plain,
multiply(least_upper_bound(X_295,X_297),X_42) = multiply(least_upper_bound(X_297,X_295),X_42),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_297,X_295),X_42),multiply(least_upper_bound(X_295,X_297),X_42)) )],[refute_0_1529,refute_0_1530]) ).
cnf(refute_0_1532,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity) = multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity),
inference(subst,[],[refute_0_1531:[bind(X_295,$fot(inverse(greatest_lower_bound(X_322,X_321)))),bind(X_297,$fot(identity)),bind(X_42,$fot(identity))]]) ).
cnf(refute_0_1533,plain,
( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity) != multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity)
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))))]]) ).
cnf(refute_0_1534,plain,
( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity)) )],[refute_0_1532,refute_0_1533]) ).
cnf(refute_0_1535,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),identity),least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) )],[refute_0_1489,refute_0_1534]) ).
cnf(refute_0_1536,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)) = multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity),
inference(subst,[],[refute_0_615:[bind(X_80,$fot(identity)),bind(X_81,$fot(inverse(greatest_lower_bound(X_322,X_321))))]]) ).
cnf(refute_0_1537,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)) != multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity)
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))))]]) ).
cnf(refute_0_1538,plain,
( multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)),multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity)) )],[refute_0_1536,refute_0_1537]) ).
cnf(refute_0_1539,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(X_322,X_321)),identity),identity),least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) )],[refute_0_1535,refute_0_1538]) ).
cnf(refute_0_1540,plain,
multiply(inverse(greatest_lower_bound(X_204,X_203)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79)),
inference(subst,[],[refute_0_902:[bind(X,$fot(greatest_lower_bound(X_204,X_203)))]]) ).
cnf(refute_0_1541,plain,
inverse(greatest_lower_bound(X_114,X_115)) = multiply(inverse(X_114),inverse(multiply(greatest_lower_bound(X_114,X_115),inverse(X_114)))),
inference(subst,[],[refute_0_523:[bind(X,$fot(greatest_lower_bound(X_114,X_115))),bind(Y,$fot(inverse(X_114)))]]) ).
cnf(refute_0_1542,plain,
multiply(greatest_lower_bound(X_114,X_115),inverse(X_114)) = greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),
inference(subst,[],[refute_0_926:[bind(X_43,$fot(X_114)),bind(X_44,$fot(X_115))]]) ).
cnf(refute_0_1543,plain,
( multiply(greatest_lower_bound(X_114,X_115),inverse(X_114)) != greatest_lower_bound(identity,multiply(X_115,inverse(X_114)))
| inverse(greatest_lower_bound(X_114,X_115)) != multiply(inverse(X_114),inverse(multiply(greatest_lower_bound(X_114,X_115),inverse(X_114))))
| inverse(greatest_lower_bound(X_114,X_115)) = multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_114,X_115)),multiply(inverse(X_114),inverse(multiply(greatest_lower_bound(X_114,X_115),inverse(X_114))))) ),[1,1,0],$fot(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))]]) ).
cnf(refute_0_1544,plain,
( inverse(greatest_lower_bound(X_114,X_115)) != multiply(inverse(X_114),inverse(multiply(greatest_lower_bound(X_114,X_115),inverse(X_114))))
| inverse(greatest_lower_bound(X_114,X_115)) = multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_114,X_115),inverse(X_114)),greatest_lower_bound(identity,multiply(X_115,inverse(X_114)))) )],[refute_0_1542,refute_0_1543]) ).
cnf(refute_0_1545,plain,
inverse(greatest_lower_bound(X_114,X_115)) = multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_114,X_115)),multiply(inverse(X_114),inverse(multiply(greatest_lower_bound(X_114,X_115),inverse(X_114))))) )],[refute_0_1541,refute_0_1544]) ).
cnf(refute_0_1546,plain,
multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))) = inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114)),
inference(subst,[],[refute_0_508:[bind(X,$fot(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))),bind(Y,$fot(X_114))]]) ).
cnf(refute_0_1547,plain,
( multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))) != inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114))
| inverse(greatest_lower_bound(X_114,X_115)) != multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114)))))
| inverse(greatest_lower_bound(X_114,X_115)) = inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_114,X_115)),multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114)))))) ),[1],$fot(inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114)))]]) ).
cnf(refute_0_1548,plain,
( inverse(greatest_lower_bound(X_114,X_115)) != multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114)))))
| inverse(greatest_lower_bound(X_114,X_115)) = inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))))),inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114))) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
inverse(greatest_lower_bound(X_114,X_115)) = inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_114,X_115)),multiply(inverse(X_114),inverse(greatest_lower_bound(identity,multiply(X_115,inverse(X_114)))))) )],[refute_0_1545,refute_0_1548]) ).
cnf(refute_0_1550,plain,
inverse(greatest_lower_bound(X_201,X_202)) = inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201)),
inference(subst,[],[refute_0_1549:[bind(X_114,$fot(X_201)),bind(X_115,$fot(X_202))]]) ).
cnf(refute_0_1551,plain,
greatest_lower_bound(X_202,X_201) = greatest_lower_bound(X_201,X_202),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_202)),bind(Y,$fot(X_201))]]) ).
cnf(refute_0_1552,plain,
( greatest_lower_bound(X_202,X_201) != greatest_lower_bound(X_201,X_202)
| greatest_lower_bound(X_201,X_202) = greatest_lower_bound(X_202,X_201) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_202,X_201))),bind(Y0,$fot(greatest_lower_bound(X_201,X_202)))]]) ).
cnf(refute_0_1553,plain,
greatest_lower_bound(X_201,X_202) = greatest_lower_bound(X_202,X_201),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_202,X_201),greatest_lower_bound(X_201,X_202)) )],[refute_0_1551,refute_0_1552]) ).
cnf(refute_0_1554,plain,
( greatest_lower_bound(X_201,X_202) != greatest_lower_bound(X_202,X_201)
| inverse(greatest_lower_bound(X_201,X_202)) != inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))
| inverse(greatest_lower_bound(X_202,X_201)) = inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_201,X_202)),inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))) ),[0,0],$fot(greatest_lower_bound(X_202,X_201))]]) ).
cnf(refute_0_1555,plain,
( inverse(greatest_lower_bound(X_201,X_202)) != inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))
| inverse(greatest_lower_bound(X_202,X_201)) = inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_201,X_202),greatest_lower_bound(X_202,X_201)) )],[refute_0_1553,refute_0_1554]) ).
cnf(refute_0_1556,plain,
inverse(greatest_lower_bound(X_202,X_201)) = inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_201,X_202)),inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))) )],[refute_0_1550,refute_0_1555]) ).
cnf(refute_0_1557,plain,
( inverse(greatest_lower_bound(X_114,X_115)) != inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114))
| inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114)) = inverse(greatest_lower_bound(X_114,X_115)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(X_114,X_115)))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114))))]]) ).
cnf(refute_0_1558,plain,
inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114)) = inverse(greatest_lower_bound(X_114,X_115)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_114,X_115)),inverse(multiply(greatest_lower_bound(identity,multiply(X_115,inverse(X_114))),X_114))) )],[refute_0_1549,refute_0_1557]) ).
cnf(refute_0_1559,plain,
inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201)) = inverse(greatest_lower_bound(X_201,X_202)),
inference(subst,[],[refute_0_1558:[bind(X_114,$fot(X_201)),bind(X_115,$fot(X_202))]]) ).
cnf(refute_0_1560,plain,
( inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201)) != inverse(greatest_lower_bound(X_201,X_202))
| inverse(greatest_lower_bound(X_202,X_201)) != inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))
| inverse(greatest_lower_bound(X_202,X_201)) = inverse(greatest_lower_bound(X_201,X_202)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_202,X_201)),inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))) ),[1],$fot(inverse(greatest_lower_bound(X_201,X_202)))]]) ).
cnf(refute_0_1561,plain,
( inverse(greatest_lower_bound(X_202,X_201)) != inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))
| inverse(greatest_lower_bound(X_202,X_201)) = inverse(greatest_lower_bound(X_201,X_202)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201)),inverse(greatest_lower_bound(X_201,X_202))) )],[refute_0_1559,refute_0_1560]) ).
cnf(refute_0_1562,plain,
inverse(greatest_lower_bound(X_202,X_201)) = inverse(greatest_lower_bound(X_201,X_202)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_202,X_201)),inverse(multiply(greatest_lower_bound(identity,multiply(X_202,inverse(X_201))),X_201))) )],[refute_0_1556,refute_0_1561]) ).
cnf(refute_0_1563,plain,
inverse(greatest_lower_bound(X_204,X_203)) = inverse(greatest_lower_bound(X_203,X_204)),
inference(subst,[],[refute_0_1562:[bind(X_201,$fot(X_203)),bind(X_202,$fot(X_204))]]) ).
cnf(refute_0_1564,plain,
( multiply(inverse(greatest_lower_bound(X_204,X_203)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79))
| inverse(greatest_lower_bound(X_204,X_203)) != inverse(greatest_lower_bound(X_203,X_204))
| multiply(inverse(greatest_lower_bound(X_203,X_204)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_204,X_203)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79))) ),[0,0],$fot(inverse(greatest_lower_bound(X_203,X_204)))]]) ).
cnf(refute_0_1565,plain,
( multiply(inverse(greatest_lower_bound(X_204,X_203)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79))
| multiply(inverse(greatest_lower_bound(X_203,X_204)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_204,X_203)),inverse(greatest_lower_bound(X_203,X_204))) )],[refute_0_1563,refute_0_1564]) ).
cnf(refute_0_1566,plain,
multiply(inverse(greatest_lower_bound(X_203,X_204)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_204,X_203)),least_upper_bound(X_79,greatest_lower_bound(X_204,X_203))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_204,X_203)),X_79))) )],[refute_0_1540,refute_0_1565]) ).
cnf(refute_0_1567,plain,
multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)),
inference(subst,[],[refute_0_1566:[bind(X_203,$fot(X_321)),bind(X_204,$fot(X_322)),bind(X_79,$fot(identity))]]) ).
cnf(refute_0_1568,plain,
( multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)))),bind(Z0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))))]]) ).
cnf(refute_0_1569,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity))) )],[refute_0_1567,refute_0_1568]) ).
cnf(refute_0_1570,plain,
multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_322,X_321)),identity)),least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) )],[refute_0_1539,refute_0_1569]) ).
cnf(refute_0_1571,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))))]]) ).
cnf(refute_0_1572,plain,
( multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))))) ),[1,1],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))))]]) ).
cnf(refute_0_1573,plain,
( multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))))) )],[refute_0_1571,refute_0_1572]) ).
cnf(refute_0_1574,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))),least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) )],[refute_0_1570,refute_0_1573]) ).
cnf(refute_0_1575,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) != least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))))
| least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))))]]) ).
cnf(refute_0_1576,plain,
( least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))),least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))))) )],[refute_0_1574,refute_0_1575]) ).
cnf(refute_0_1577,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))),least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) )],[refute_0_1488,refute_0_1576]) ).
cnf(refute_0_1578,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))),
inference(subst,[],[refute_0_1426:[bind(X_223,$fot(X_113))]]) ).
cnf(refute_0_1579,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))
| least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))))),bind(Y0,$fot(least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))))]]) ).
cnf(refute_0_1580,plain,
least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))) )],[refute_0_1578,refute_0_1579]) ).
cnf(refute_0_1581,plain,
( least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))) != least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))) ),[1],$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))))]]) ).
cnf(refute_0_1582,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113))),least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity)))) )],[refute_0_1580,refute_0_1581]) ).
cnf(refute_0_1583,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,X_113)))) )],[refute_0_1378,refute_0_1582]) ).
cnf(refute_0_1584,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) != least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity)))))]]) ).
cnf(refute_0_1585,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,X_113))),least_upper_bound(identity,multiply(X_75,least_upper_bound(X_113,identity)))) )],[refute_0_1583,refute_0_1584]) ).
cnf(refute_0_1586,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))),
inference(subst,[],[refute_0_1585:[bind(X_113,$fot(greatest_lower_bound(X_322,X_321))),bind(X_75,$fot(inverse(greatest_lower_bound(X_321,X_322))))]]) ).
cnf(refute_0_1587,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))))]]) ).
cnf(refute_0_1588,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321))))) )],[refute_0_1586,refute_0_1587]) ).
cnf(refute_0_1589,plain,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,greatest_lower_bound(X_322,X_321)))),least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) )],[refute_0_1577,refute_0_1588]) ).
cnf(refute_0_1590,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))
| least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) != least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) = least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))),least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))))]]) ).
cnf(refute_0_1591,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) != least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) = least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))),least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321)))) )],[refute_0_1589,refute_0_1590]) ).
cnf(refute_0_1592,plain,
least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(inverse(greatest_lower_bound(X_321,X_322)))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1593,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = least_upper_bound(X_222,multiply(least_upper_bound(inverse(X_222),X_82),X_222)),
inference(subst,[],[refute_0_613:[bind(X_80,$fot(X_222)),bind(X_81,$fot(least_upper_bound(inverse(X_222),X_82)))]]) ).
cnf(refute_0_1594,plain,
multiply(least_upper_bound(inverse(X_222),X_82),X_222) = least_upper_bound(identity,multiply(X_82,X_222)),
inference(subst,[],[refute_0_189:[bind(X_80,$fot(X_222))]]) ).
cnf(refute_0_1595,plain,
( multiply(least_upper_bound(inverse(X_222),X_82),X_222) != least_upper_bound(identity,multiply(X_82,X_222))
| multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) != least_upper_bound(X_222,multiply(least_upper_bound(inverse(X_222),X_82),X_222))
| multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222),least_upper_bound(X_222,multiply(least_upper_bound(inverse(X_222),X_82),X_222))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_82,X_222)))]]) ).
cnf(refute_0_1596,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) != least_upper_bound(X_222,multiply(least_upper_bound(inverse(X_222),X_82),X_222))
| multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_222),X_82),X_222),least_upper_bound(identity,multiply(X_82,X_222))) )],[refute_0_1594,refute_0_1595]) ).
cnf(refute_0_1597,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222),least_upper_bound(X_222,multiply(least_upper_bound(inverse(X_222),X_82),X_222))) )],[refute_0_1593,refute_0_1596]) ).
cnf(refute_0_1598,plain,
multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = least_upper_bound(multiply(least_upper_bound(X_84,inverse(X)),X),multiply(Z,X)),
inference(subst,[],[monotony_lub2:[bind(Y,$fot(least_upper_bound(X_84,inverse(X))))]]) ).
cnf(refute_0_1599,plain,
multiply(least_upper_bound(X_84,inverse(X)),X) = least_upper_bound(identity,multiply(X_84,X)),
inference(subst,[],[refute_0_721:[bind(X_80,$fot(X)),bind(X_81,$fot(X_84))]]) ).
cnf(refute_0_1600,plain,
( multiply(least_upper_bound(X_84,inverse(X)),X) != least_upper_bound(identity,multiply(X_84,X))
| multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_84,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_84,inverse(X)),X),multiply(Z,X))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_84,X)))]]) ).
cnf(refute_0_1601,plain,
( multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_84,inverse(X)),X),multiply(Z,X))
| multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,inverse(X)),X),least_upper_bound(identity,multiply(X_84,X))) )],[refute_0_1599,refute_0_1600]) ).
cnf(refute_0_1602,plain,
multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_84,inverse(X)),X),multiply(Z,X))) )],[refute_0_1598,refute_0_1601]) ).
cnf(refute_0_1603,plain,
least_upper_bound(least_upper_bound(X_84,inverse(X)),Z) = least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_84)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_1604,plain,
multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X))]]) ).
cnf(refute_0_1605,plain,
( multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) != multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X)
| least_upper_bound(least_upper_bound(X_84,inverse(X)),Z) != least_upper_bound(X_84,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X)) ),[1,0],$fot(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)))]]) ).
cnf(refute_0_1606,plain,
( least_upper_bound(least_upper_bound(X_84,inverse(X)),Z) != least_upper_bound(X_84,least_upper_bound(inverse(X),Z))
| multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X)) )],[refute_0_1604,refute_0_1605]) ).
cnf(refute_0_1607,plain,
multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) = multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),least_upper_bound(X_84,least_upper_bound(inverse(X),Z))) )],[refute_0_1603,refute_0_1606]) ).
cnf(refute_0_1608,plain,
( multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) != multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X)
| multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))
| multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))) ),[0],$fot(multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X))]]) ).
cnf(refute_0_1609,plain,
( multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))
| multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X)) )],[refute_0_1607,refute_0_1608]) ).
cnf(refute_0_1610,plain,
least_upper_bound(multiply(X_84,X),multiply(Z,X)) = multiply(least_upper_bound(X_84,Z),X),
inference(subst,[],[refute_0_580:[bind(Y,$fot(X_84))]]) ).
cnf(refute_0_1611,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))) = least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))))]]) ).
cnf(refute_0_1612,plain,
( least_upper_bound(multiply(X_84,X),multiply(Z,X)) != multiply(least_upper_bound(X_84,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))) != least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X)))
| least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X)))) ),[1,1],$fot(multiply(least_upper_bound(X_84,Z),X))]]) ).
cnf(refute_0_1613,plain,
( least_upper_bound(multiply(X_84,X),multiply(Z,X)) != multiply(least_upper_bound(X_84,Z),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X)))) )],[refute_0_1611,refute_0_1612]) ).
cnf(refute_0_1614,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_84,X),multiply(Z,X)),multiply(least_upper_bound(X_84,Z),X)) )],[refute_0_1610,refute_0_1613]) ).
cnf(refute_0_1615,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) = least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))),
inference(subst,[],[refute_0_210:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_84,X))),bind(Z,$fot(multiply(Z,X)))]]) ).
cnf(refute_0_1616,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) != least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X)))
| least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X))))]]) ).
cnf(refute_0_1617,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X))
| least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)),least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X)))) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_84,X),multiply(Z,X))),least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X))) )],[refute_0_1614,refute_0_1617]) ).
cnf(refute_0_1619,plain,
( multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))
| least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)) != least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X))
| multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X),least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)))]]) ).
cnf(refute_0_1620,plain,
( multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))
| multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X)),least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X))) )],[refute_0_1618,refute_0_1619]) ).
cnf(refute_0_1621,plain,
( multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))
| multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X),least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))) )],[refute_0_1609,refute_0_1620]) ).
cnf(refute_0_1622,plain,
multiply(least_upper_bound(X_84,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_84,Z),X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_84,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_84,X)),multiply(Z,X))) )],[refute_0_1602,refute_0_1621]) ).
cnf(refute_0_1623,plain,
multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)),
inference(subst,[],[refute_0_1622:[bind(X,$fot(X_222)),bind(Z,$fot(X_82)),bind(X_84,$fot(identity))]]) ).
cnf(refute_0_1624,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = least_upper_bound(X_17,multiply(X_223,X_17)),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(multiply(X_223,X_17)))]]) ).
cnf(refute_0_1625,plain,
multiply(least_upper_bound(X_223,identity),X_17) = least_upper_bound(X_17,multiply(X_223,X_17)),
inference(subst,[],[refute_0_613:[bind(X_80,$fot(X_17)),bind(X_81,$fot(X_223))]]) ).
cnf(refute_0_1626,plain,
( multiply(least_upper_bound(X_223,identity),X_17) != least_upper_bound(X_17,multiply(X_223,X_17))
| least_upper_bound(X_17,multiply(X_223,X_17)) = multiply(least_upper_bound(X_223,identity),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_223,identity),X_17))),bind(Y0,$fot(least_upper_bound(X_17,multiply(X_223,X_17))))]]) ).
cnf(refute_0_1627,plain,
least_upper_bound(X_17,multiply(X_223,X_17)) = multiply(least_upper_bound(X_223,identity),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_223,identity),X_17),least_upper_bound(X_17,multiply(X_223,X_17))) )],[refute_0_1625,refute_0_1626]) ).
cnf(refute_0_1628,plain,
( least_upper_bound(X_17,multiply(X_223,X_17)) != multiply(least_upper_bound(X_223,identity),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) != least_upper_bound(X_17,multiply(X_223,X_17))
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(X_223,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))),least_upper_bound(X_17,multiply(X_223,X_17))) ),[1],$fot(multiply(least_upper_bound(X_223,identity),X_17))]]) ).
cnf(refute_0_1629,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) != least_upper_bound(X_17,multiply(X_223,X_17))
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(X_223,identity),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(X_223,X_17)),multiply(least_upper_bound(X_223,identity),X_17)) )],[refute_0_1627,refute_0_1628]) ).
cnf(refute_0_1630,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(X_223,identity),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))),least_upper_bound(X_17,multiply(X_223,X_17))) )],[refute_0_1624,refute_0_1629]) ).
cnf(refute_0_1631,plain,
least_upper_bound(identity,least_upper_bound(X_223,identity)) = least_upper_bound(identity,X_223),
inference(subst,[],[refute_0_214:[bind(Y,$fot(X_223)),bind(X_15,$fot(identity))]]) ).
cnf(refute_0_1632,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17))]]) ).
cnf(refute_0_1633,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)
| least_upper_bound(identity,least_upper_bound(X_223,identity)) != least_upper_bound(identity,X_223)
| multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) = multiply(least_upper_bound(identity,X_223),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)) ),[1,0],$fot(least_upper_bound(identity,X_223))]]) ).
cnf(refute_0_1634,plain,
( least_upper_bound(identity,least_upper_bound(X_223,identity)) != least_upper_bound(identity,X_223)
| multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) = multiply(least_upper_bound(identity,X_223),X_17) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)) )],[refute_0_1632,refute_0_1633]) ).
cnf(refute_0_1635,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) = multiply(least_upper_bound(identity,X_223),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_223,identity)),least_upper_bound(identity,X_223)) )],[refute_0_1631,refute_0_1634]) ).
cnf(refute_0_1636,plain,
multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17),
inference(subst,[],[refute_0_600:[bind(X_80,$fot(X_17)),bind(X_81,$fot(identity)),bind(X_82,$fot(least_upper_bound(X_223,identity)))]]) ).
cnf(refute_0_1637,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)) = multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17),
inference(subst,[],[refute_0_615:[bind(X_80,$fot(X_17)),bind(X_81,$fot(least_upper_bound(X_223,identity)))]]) ).
cnf(refute_0_1638,plain,
( multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)) != multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)))]]) ).
cnf(refute_0_1639,plain,
( multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17) != multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)
| least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)),multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17)) )],[refute_0_1637,refute_0_1638]) ).
cnf(refute_0_1640,plain,
least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_223,identity),identity),X_17),multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)) )],[refute_0_1636,refute_0_1639]) ).
cnf(refute_0_1641,plain,
least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))) = least_upper_bound(X_21,least_upper_bound(Y,multiply(X_223,Y))),
inference(subst,[],[refute_0_477:[bind(X_69,$fot(multiply(X_223,Y)))]]) ).
cnf(refute_0_1642,plain,
multiply(least_upper_bound(X_223,identity),Y) = least_upper_bound(Y,multiply(X_223,Y)),
inference(subst,[],[refute_0_613:[bind(X_80,$fot(Y)),bind(X_81,$fot(X_223))]]) ).
cnf(refute_0_1643,plain,
( multiply(least_upper_bound(X_223,identity),Y) != least_upper_bound(Y,multiply(X_223,Y))
| least_upper_bound(Y,multiply(X_223,Y)) = multiply(least_upper_bound(X_223,identity),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(X_223,identity),Y))),bind(Y0,$fot(least_upper_bound(Y,multiply(X_223,Y))))]]) ).
cnf(refute_0_1644,plain,
least_upper_bound(Y,multiply(X_223,Y)) = multiply(least_upper_bound(X_223,identity),Y),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_223,identity),Y),least_upper_bound(Y,multiply(X_223,Y))) )],[refute_0_1642,refute_0_1643]) ).
cnf(refute_0_1645,plain,
( least_upper_bound(Y,multiply(X_223,Y)) != multiply(least_upper_bound(X_223,identity),Y)
| least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))) != least_upper_bound(X_21,least_upper_bound(Y,multiply(X_223,Y)))
| least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))) = least_upper_bound(X_21,multiply(least_upper_bound(X_223,identity),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))),least_upper_bound(X_21,least_upper_bound(Y,multiply(X_223,Y)))) ),[1,1],$fot(multiply(least_upper_bound(X_223,identity),Y))]]) ).
cnf(refute_0_1646,plain,
( least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))) != least_upper_bound(X_21,least_upper_bound(Y,multiply(X_223,Y)))
| least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))) = least_upper_bound(X_21,multiply(least_upper_bound(X_223,identity),Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,multiply(X_223,Y)),multiply(least_upper_bound(X_223,identity),Y)) )],[refute_0_1644,refute_0_1645]) ).
cnf(refute_0_1647,plain,
least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))) = least_upper_bound(X_21,multiply(least_upper_bound(X_223,identity),Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_21,multiply(X_223,Y))),least_upper_bound(X_21,least_upper_bound(Y,multiply(X_223,Y)))) )],[refute_0_1641,refute_0_1646]) ).
cnf(refute_0_1648,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)),
inference(subst,[],[refute_0_1647:[bind(Y,$fot(X_17)),bind(X_21,$fot(X_17))]]) ).
cnf(refute_0_1649,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)) != multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) != least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17))
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))))),bind(Y0,$fot(least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)))]]) ).
cnf(refute_0_1650,plain,
( least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)) != multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))),least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17))) )],[refute_0_1648,refute_0_1649]) ).
cnf(refute_0_1651,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,multiply(least_upper_bound(X_223,identity),X_17)),multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)) )],[refute_0_1640,refute_0_1650]) ).
cnf(refute_0_1652,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) != multiply(least_upper_bound(identity,X_223),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) != multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(identity,X_223),X_17) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_223),X_17)))]]) ).
cnf(refute_0_1653,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17) != multiply(least_upper_bound(identity,X_223),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(identity,X_223),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))),multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17)) )],[refute_0_1651,refute_0_1652]) ).
cnf(refute_0_1654,plain,
least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) = multiply(least_upper_bound(identity,X_223),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_223,identity)),X_17),multiply(least_upper_bound(identity,X_223),X_17)) )],[refute_0_1635,refute_0_1653]) ).
cnf(refute_0_1655,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) != multiply(least_upper_bound(X_223,identity),X_17)
| least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) != multiply(least_upper_bound(identity,X_223),X_17)
| multiply(least_upper_bound(identity,X_223),X_17) = multiply(least_upper_bound(X_223,identity),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))),multiply(least_upper_bound(X_223,identity),X_17)) ),[0],$fot(multiply(least_upper_bound(identity,X_223),X_17))]]) ).
cnf(refute_0_1656,plain,
( least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))) != multiply(least_upper_bound(X_223,identity),X_17)
| multiply(least_upper_bound(identity,X_223),X_17) = multiply(least_upper_bound(X_223,identity),X_17) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))),multiply(least_upper_bound(identity,X_223),X_17)) )],[refute_0_1654,refute_0_1655]) ).
cnf(refute_0_1657,plain,
multiply(least_upper_bound(identity,X_223),X_17) = multiply(least_upper_bound(X_223,identity),X_17),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_17,multiply(X_223,X_17))),multiply(least_upper_bound(X_223,identity),X_17)) )],[refute_0_1630,refute_0_1656]) ).
cnf(refute_0_1658,plain,
( multiply(least_upper_bound(identity,X_223),X_17) != multiply(least_upper_bound(X_223,identity),X_17)
| multiply(least_upper_bound(X_223,identity),X_17) = multiply(least_upper_bound(identity,X_223),X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,X_223),X_17))),bind(Y0,$fot(multiply(least_upper_bound(X_223,identity),X_17)))]]) ).
cnf(refute_0_1659,plain,
multiply(least_upper_bound(X_223,identity),X_17) = multiply(least_upper_bound(identity,X_223),X_17),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_223),X_17),multiply(least_upper_bound(X_223,identity),X_17)) )],[refute_0_1657,refute_0_1658]) ).
cnf(refute_0_1660,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222),
inference(subst,[],[refute_0_1659:[bind(X_17,$fot(X_222)),bind(X_223,$fot(least_upper_bound(inverse(X_222),X_82)))]]) ).
cnf(refute_0_1661,plain,
( multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222))
| multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) != multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222)
| multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222))))]]) ).
cnf(refute_0_1662,plain,
( multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222))
| multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222),multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222)) )],[refute_0_1660,refute_0_1661]) ).
cnf(refute_0_1663,plain,
multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) = least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(inverse(X_222),X_82)),X_222),least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222))) )],[refute_0_1623,refute_0_1662]) ).
cnf(refute_0_1664,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) != least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222)))
| multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) != least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222))
| least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)) = least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222),least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222)))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)))]]) ).
cnf(refute_0_1665,plain,
( multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222) != least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222)))
| least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)) = least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222),least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222))) )],[refute_0_1663,refute_0_1664]) ).
cnf(refute_0_1666,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,X_82),X_222)) = least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(X_222),X_82),identity),X_222),least_upper_bound(X_222,least_upper_bound(identity,multiply(X_82,X_222)))) )],[refute_0_1597,refute_0_1665]) ).
cnf(refute_0_1667,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)) = least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))),
inference(subst,[],[refute_0_1666:[bind(X_222,$fot(X_305)),bind(X_82,$fot(multiply(X_84,inverse(X_305))))]]) ).
cnf(refute_0_1668,plain,
least_upper_bound(X_84,X_305) = multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305),
inference(subst,[],[refute_0_758:[bind(X_224,$fot(X_305))]]) ).
cnf(refute_0_1669,plain,
( least_upper_bound(X_84,X_305) != multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)
| multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305) = least_upper_bound(X_84,X_305) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_84,X_305))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)))]]) ).
cnf(refute_0_1670,plain,
multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305) = least_upper_bound(X_84,X_305),
inference(resolve,[$cnf( $equal(least_upper_bound(X_84,X_305),multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)) )],[refute_0_1668,refute_0_1669]) ).
cnf(refute_0_1671,plain,
( multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305) != least_upper_bound(X_84,X_305)
| least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)) != least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))
| least_upper_bound(identity,least_upper_bound(X_84,X_305)) = least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)),least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))) ),[0,1],$fot(least_upper_bound(X_84,X_305))]]) ).
cnf(refute_0_1672,plain,
( least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)) != least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))
| least_upper_bound(identity,least_upper_bound(X_84,X_305)) = least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305),least_upper_bound(X_84,X_305)) )],[refute_0_1670,refute_0_1671]) ).
cnf(refute_0_1673,plain,
least_upper_bound(identity,least_upper_bound(X_84,X_305)) = least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_84,inverse(X_305))),X_305)),least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))) )],[refute_0_1667,refute_0_1672]) ).
cnf(refute_0_1674,plain,
multiply(X_84,identity) = X_84,
inference(subst,[],[refute_0_561:[bind(X,$fot(X_84))]]) ).
cnf(refute_0_1675,plain,
multiply(inverse(X_305),X_305) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_305))]]) ).
cnf(refute_0_1676,plain,
multiply(X_84,multiply(inverse(X_305),X_305)) = multiply(X_84,multiply(inverse(X_305),X_305)),
introduced(tautology,[refl,[$fot(multiply(X_84,multiply(inverse(X_305),X_305)))]]) ).
cnf(refute_0_1677,plain,
( multiply(X_84,multiply(inverse(X_305),X_305)) != multiply(X_84,multiply(inverse(X_305),X_305))
| multiply(inverse(X_305),X_305) != identity
| multiply(X_84,multiply(inverse(X_305),X_305)) = multiply(X_84,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_84,multiply(inverse(X_305),X_305)),multiply(X_84,multiply(inverse(X_305),X_305))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1678,plain,
( multiply(inverse(X_305),X_305) != identity
| multiply(X_84,multiply(inverse(X_305),X_305)) = multiply(X_84,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_84,multiply(inverse(X_305),X_305)),multiply(X_84,multiply(inverse(X_305),X_305))) )],[refute_0_1676,refute_0_1677]) ).
cnf(refute_0_1679,plain,
multiply(X_84,multiply(inverse(X_305),X_305)) = multiply(X_84,identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_305),X_305),identity) )],[refute_0_1675,refute_0_1678]) ).
cnf(refute_0_1680,plain,
( multiply(X_84,multiply(inverse(X_305),X_305)) != multiply(X_84,identity)
| multiply(X_84,identity) != X_84
| multiply(X_84,multiply(inverse(X_305),X_305)) = X_84 ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X_84,multiply(inverse(X_305),X_305)))),bind(Y0,$fot(multiply(X_84,identity))),bind(Z0,$fot(X_84))]]) ).
cnf(refute_0_1681,plain,
( multiply(X_84,identity) != X_84
| multiply(X_84,multiply(inverse(X_305),X_305)) = X_84 ),
inference(resolve,[$cnf( $equal(multiply(X_84,multiply(inverse(X_305),X_305)),multiply(X_84,identity)) )],[refute_0_1679,refute_0_1680]) ).
cnf(refute_0_1682,plain,
multiply(X_84,multiply(inverse(X_305),X_305)) = X_84,
inference(resolve,[$cnf( $equal(multiply(X_84,identity),X_84) )],[refute_0_1674,refute_0_1681]) ).
cnf(refute_0_1683,plain,
multiply(multiply(X_84,inverse(X_305)),X_305) = multiply(X_84,multiply(inverse(X_305),X_305)),
inference(subst,[],[associativity:[bind(X,$fot(X_84)),bind(Y,$fot(inverse(X_305))),bind(Z,$fot(X_305))]]) ).
cnf(refute_0_1684,plain,
( multiply(X_84,multiply(inverse(X_305),X_305)) != X_84
| multiply(multiply(X_84,inverse(X_305)),X_305) != multiply(X_84,multiply(inverse(X_305),X_305))
| multiply(multiply(X_84,inverse(X_305)),X_305) = X_84 ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(multiply(X_84,inverse(X_305)),X_305))),bind(Y0,$fot(multiply(X_84,multiply(inverse(X_305),X_305)))),bind(Z0,$fot(X_84))]]) ).
cnf(refute_0_1685,plain,
( multiply(X_84,multiply(inverse(X_305),X_305)) != X_84
| multiply(multiply(X_84,inverse(X_305)),X_305) = X_84 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_84,inverse(X_305)),X_305),multiply(X_84,multiply(inverse(X_305),X_305))) )],[refute_0_1683,refute_0_1684]) ).
cnf(refute_0_1686,plain,
multiply(multiply(X_84,inverse(X_305)),X_305) = X_84,
inference(resolve,[$cnf( $equal(multiply(X_84,multiply(inverse(X_305),X_305)),X_84) )],[refute_0_1682,refute_0_1685]) ).
cnf(refute_0_1687,plain,
least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)) = least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))]]) ).
cnf(refute_0_1688,plain,
( multiply(multiply(X_84,inverse(X_305)),X_305) != X_84
| least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)) != least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))
| least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)) = least_upper_bound(identity,X_84) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)),least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) ),[1,1],$fot(X_84)]]) ).
cnf(refute_0_1689,plain,
( multiply(multiply(X_84,inverse(X_305)),X_305) != X_84
| least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)) = least_upper_bound(identity,X_84) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)),least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) )],[refute_0_1687,refute_0_1688]) ).
cnf(refute_0_1690,plain,
least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)) = least_upper_bound(identity,X_84),
inference(resolve,[$cnf( $equal(multiply(multiply(X_84,inverse(X_305)),X_305),X_84) )],[refute_0_1686,refute_0_1689]) ).
cnf(refute_0_1691,plain,
least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) = least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))))]]) ).
cnf(refute_0_1692,plain,
( least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) != least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))
| least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)) != least_upper_bound(identity,X_84)
| least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) = least_upper_bound(X_305,least_upper_bound(identity,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))),least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))) ),[1,1],$fot(least_upper_bound(identity,X_84))]]) ).
cnf(refute_0_1693,plain,
( least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)) != least_upper_bound(identity,X_84)
| least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) = least_upper_bound(X_305,least_upper_bound(identity,X_84)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))),least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))) )],[refute_0_1691,refute_0_1692]) ).
cnf(refute_0_1694,plain,
least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) = least_upper_bound(X_305,least_upper_bound(identity,X_84)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)),least_upper_bound(identity,X_84)) )],[refute_0_1690,refute_0_1693]) ).
cnf(refute_0_1695,plain,
( least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))) != least_upper_bound(X_305,least_upper_bound(identity,X_84))
| least_upper_bound(identity,least_upper_bound(X_84,X_305)) != least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))
| least_upper_bound(identity,least_upper_bound(X_84,X_305)) = least_upper_bound(X_305,least_upper_bound(identity,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_84,X_305)),least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))) ),[1],$fot(least_upper_bound(X_305,least_upper_bound(identity,X_84)))]]) ).
cnf(refute_0_1696,plain,
( least_upper_bound(identity,least_upper_bound(X_84,X_305)) != least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))
| least_upper_bound(identity,least_upper_bound(X_84,X_305)) = least_upper_bound(X_305,least_upper_bound(identity,X_84)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305))),least_upper_bound(X_305,least_upper_bound(identity,X_84))) )],[refute_0_1694,refute_0_1695]) ).
cnf(refute_0_1697,plain,
least_upper_bound(identity,least_upper_bound(X_84,X_305)) = least_upper_bound(X_305,least_upper_bound(identity,X_84)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_84,X_305)),least_upper_bound(X_305,least_upper_bound(identity,multiply(multiply(X_84,inverse(X_305)),X_305)))) )],[refute_0_1673,refute_0_1696]) ).
cnf(refute_0_1698,plain,
( least_upper_bound(identity,least_upper_bound(X_84,X_305)) != least_upper_bound(X_305,least_upper_bound(identity,X_84))
| least_upper_bound(X_305,least_upper_bound(identity,X_84)) = least_upper_bound(identity,least_upper_bound(X_84,X_305)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_84,X_305)))),bind(Y0,$fot(least_upper_bound(X_305,least_upper_bound(identity,X_84))))]]) ).
cnf(refute_0_1699,plain,
least_upper_bound(X_305,least_upper_bound(identity,X_84)) = least_upper_bound(identity,least_upper_bound(X_84,X_305)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_84,X_305)),least_upper_bound(X_305,least_upper_bound(identity,X_84))) )],[refute_0_1697,refute_0_1698]) ).
cnf(refute_0_1700,plain,
least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) = least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))),
inference(subst,[],[refute_0_1699:[bind(X_305,$fot(inverse(greatest_lower_bound(X_321,X_322)))),bind(X_84,$fot(identity))]]) ).
cnf(refute_0_1701,plain,
( least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))
| least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) != least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))))
| least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))))]]) ).
cnf(refute_0_1702,plain,
( least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))
| least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)),least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))))) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))),least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))) )],[refute_0_1592,refute_0_1702]) ).
cnf(refute_0_1704,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) != least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))
| least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)))]]) ).
cnf(refute_0_1705,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) != least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity)),least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322)))) )],[refute_0_1703,refute_0_1704]) ).
cnf(refute_0_1706,plain,
( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))) != least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))),least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))) )],[refute_0_1591,refute_0_1705]) ).
cnf(refute_0_1707,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_322,X_321))) = least_upper_bound(identity,inverse(greatest_lower_bound(X_321,X_322))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(greatest_lower_bound(X_322,X_321),identity))),least_upper_bound(inverse(greatest_lower_bound(X_321,X_322)),least_upper_bound(identity,identity))) )],[refute_0_1487,refute_0_1706]) ).
cnf(refute_0_1708,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(X_76,identity)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),
inference(subst,[],[refute_0_1707:[bind(X_321,$fot(least_upper_bound(X_76,identity))),bind(X_322,$fot(X_350))]]) ).
cnf(refute_0_1709,plain,
greatest_lower_bound(X_350,least_upper_bound(X_76,identity)) = greatest_lower_bound(X_350,least_upper_bound(identity,X_76)),
inference(subst,[],[refute_0_1267:[bind(X_266,$fot(X_350))]]) ).
cnf(refute_0_1710,plain,
( greatest_lower_bound(X_350,least_upper_bound(X_76,identity)) != greatest_lower_bound(X_350,least_upper_bound(identity,X_76))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(X_76,identity)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(X_76,identity)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) ),[0,1,0],$fot(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))]]) ).
cnf(refute_0_1711,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(X_76,identity)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_350,least_upper_bound(X_76,identity)),greatest_lower_bound(X_350,least_upper_bound(identity,X_76))) )],[refute_0_1709,refute_0_1710]) ).
cnf(refute_0_1712,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(X_76,identity)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) )],[refute_0_1708,refute_0_1711]) ).
cnf(refute_0_1713,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))) = greatest_lower_bound(X_350,identity),
inference(subst,[],[refute_0_1287:[bind(Y,$fot(X_76)),bind(X_46,$fot(X_350)),bind(X_47,$fot(identity))]]) ).
cnf(refute_0_1714,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))))]]) ).
cnf(refute_0_1715,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))) != greatest_lower_bound(X_350,identity)
| inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(X_350,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))))) ),[1,0],$fot(greatest_lower_bound(X_350,identity))]]) ).
cnf(refute_0_1716,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))) != greatest_lower_bound(X_350,identity)
| inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(X_350,identity)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))))) )],[refute_0_1714,refute_0_1715]) ).
cnf(refute_0_1717,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(X_350,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))),greatest_lower_bound(X_350,identity)) )],[refute_0_1713,refute_0_1716]) ).
cnf(refute_0_1718,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)))),
inference(subst,[],[refute_0_1227:[bind(X_113,$fot(greatest_lower_bound(X_189,identity))),bind(X_35,$fot(inverse(greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1719,plain,
inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))),
inference(subst,[],[p20x_3:[bind(X,$fot(inverse(greatest_lower_bound(X_189,identity)))),bind(Y,$fot(greatest_lower_bound(identity,inverse(X_189))))]]) ).
cnf(refute_0_1720,plain,
inverse(X_106) = multiply(inverse(greatest_lower_bound(X_106,identity)),multiply(greatest_lower_bound(X_106,identity),inverse(X_106))),
inference(subst,[],[refute_0_505:[bind(X_58,$fot(greatest_lower_bound(X_106,identity))),bind(X_59,$fot(inverse(X_106)))]]) ).
cnf(refute_0_1721,plain,
( multiply(greatest_lower_bound(X_106,identity),inverse(X_106)) != greatest_lower_bound(identity,inverse(X_106))
| inverse(X_106) != multiply(inverse(greatest_lower_bound(X_106,identity)),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| inverse(X_106) = multiply(inverse(greatest_lower_bound(X_106,identity)),greatest_lower_bound(identity,inverse(X_106))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_106),multiply(inverse(greatest_lower_bound(X_106,identity)),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_106)))]]) ).
cnf(refute_0_1722,plain,
( inverse(X_106) != multiply(inverse(greatest_lower_bound(X_106,identity)),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))
| inverse(X_106) = multiply(inverse(greatest_lower_bound(X_106,identity)),greatest_lower_bound(identity,inverse(X_106))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_106,identity),inverse(X_106)),greatest_lower_bound(identity,inverse(X_106))) )],[refute_0_816,refute_0_1721]) ).
cnf(refute_0_1723,plain,
inverse(X_106) = multiply(inverse(greatest_lower_bound(X_106,identity)),greatest_lower_bound(identity,inverse(X_106))),
inference(resolve,[$cnf( $equal(inverse(X_106),multiply(inverse(greatest_lower_bound(X_106,identity)),multiply(greatest_lower_bound(X_106,identity),inverse(X_106)))) )],[refute_0_1720,refute_0_1722]) ).
cnf(refute_0_1724,plain,
inverse(X_189) = multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189))),
inference(subst,[],[refute_0_1723:[bind(X_106,$fot(X_189))]]) ).
cnf(refute_0_1725,plain,
( inverse(X_189) != multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))
| multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189))) = inverse(X_189) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_189))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1726,plain,
multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189))) = inverse(X_189),
inference(resolve,[$cnf( $equal(inverse(X_189),multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))) )],[refute_0_1724,refute_0_1725]) ).
cnf(refute_0_1727,plain,
( multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189))) != inverse(X_189)
| inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))
| inverse(inverse(X_189)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))) ),[0,0],$fot(inverse(X_189))]]) ).
cnf(refute_0_1728,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))
| inverse(inverse(X_189)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189))),inverse(X_189)) )],[refute_0_1726,refute_0_1727]) ).
cnf(refute_0_1729,plain,
inverse(inverse(X_189)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))) )],[refute_0_1719,refute_0_1728]) ).
cnf(refute_0_1730,plain,
inverse(inverse(X_189)) = X_189,
inference(subst,[],[p20x_2:[bind(X,$fot(X_189))]]) ).
cnf(refute_0_1731,plain,
( inverse(inverse(X_189)) != X_189
| inverse(inverse(X_189)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))
| X_189 = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_189)),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))) ),[0],$fot(X_189)]]) ).
cnf(refute_0_1732,plain,
( inverse(inverse(X_189)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))
| X_189 = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_189)),X_189) )],[refute_0_1730,refute_0_1731]) ).
cnf(refute_0_1733,plain,
inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)),
inference(subst,[],[refute_0_538:[bind(X,$fot(greatest_lower_bound(X_189,identity))),bind(X_23,$fot(greatest_lower_bound(identity,inverse(X_189))))]]) ).
cnf(refute_0_1734,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) = inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))),
inference(subst,[],[refute_0_508:[bind(X,$fot(inverse(greatest_lower_bound(X_189,identity)))),bind(Y,$fot(greatest_lower_bound(identity,inverse(X_189))))]]) ).
cnf(refute_0_1735,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) != inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189))))
| inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))))),bind(Y0,$fot(inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))]]) ).
cnf(refute_0_1736,plain,
( inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))),inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189))))) )],[refute_0_1734,refute_0_1735]) ).
cnf(refute_0_1737,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_189,identity)),greatest_lower_bound(identity,inverse(X_189)))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))) )],[refute_0_1733,refute_0_1736]) ).
cnf(refute_0_1738,plain,
( X_189 != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))
| X_189 = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_189,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))))]]) ).
cnf(refute_0_1739,plain,
( X_189 != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))
| X_189 = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity)))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))) )],[refute_0_1737,refute_0_1738]) ).
cnf(refute_0_1740,plain,
( inverse(inverse(X_189)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))
| X_189 = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) ),
inference(resolve,[$cnf( $equal(X_189,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))) )],[refute_0_1732,refute_0_1739]) ).
cnf(refute_0_1741,plain,
X_189 = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_189)),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),inverse(inverse(greatest_lower_bound(X_189,identity))))) )],[refute_0_1729,refute_0_1740]) ).
cnf(refute_0_1742,plain,
( X_189 != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) = X_189 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_189)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))]]) ).
cnf(refute_0_1743,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) = X_189,
inference(resolve,[$cnf( $equal(X_189,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))) )],[refute_0_1741,refute_0_1742]) ).
cnf(refute_0_1744,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)) != X_189
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))) ),[1,1,1],$fot(X_189)]]) ).
cnf(refute_0_1745,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)),X_189) )],[refute_0_1743,refute_0_1744]) ).
cnf(refute_0_1746,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))) )],[refute_0_1718,refute_0_1745]) ).
cnf(refute_0_1747,plain,
multiply(X_189,identity) = X_189,
inference(subst,[],[refute_0_561:[bind(X,$fot(X_189))]]) ).
cnf(refute_0_1748,plain,
inverse(multiply(X_189,identity)) = inverse(multiply(X_189,identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(X_189,identity)))]]) ).
cnf(refute_0_1749,plain,
( multiply(X_189,identity) != X_189
| inverse(multiply(X_189,identity)) != inverse(multiply(X_189,identity))
| inverse(multiply(X_189,identity)) = inverse(X_189) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_189,identity)),inverse(multiply(X_189,identity))) ),[1,0],$fot(X_189)]]) ).
cnf(refute_0_1750,plain,
( multiply(X_189,identity) != X_189
| inverse(multiply(X_189,identity)) = inverse(X_189) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_189,identity)),inverse(multiply(X_189,identity))) )],[refute_0_1748,refute_0_1749]) ).
cnf(refute_0_1751,plain,
inverse(multiply(X_189,identity)) = inverse(X_189),
inference(resolve,[$cnf( $equal(multiply(X_189,identity),X_189) )],[refute_0_1747,refute_0_1750]) ).
cnf(refute_0_1752,plain,
greatest_lower_bound(identity,inverse(multiply(X_189,identity))) = greatest_lower_bound(identity,inverse(multiply(X_189,identity))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(X_189,identity))))]]) ).
cnf(refute_0_1753,plain,
( greatest_lower_bound(identity,inverse(multiply(X_189,identity))) != greatest_lower_bound(identity,inverse(multiply(X_189,identity)))
| inverse(multiply(X_189,identity)) != inverse(X_189)
| greatest_lower_bound(identity,inverse(multiply(X_189,identity))) = greatest_lower_bound(identity,inverse(X_189)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_189,identity))),greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) ),[1,1],$fot(inverse(X_189))]]) ).
cnf(refute_0_1754,plain,
( inverse(multiply(X_189,identity)) != inverse(X_189)
| greatest_lower_bound(identity,inverse(multiply(X_189,identity))) = greatest_lower_bound(identity,inverse(X_189)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_189,identity))),greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) )],[refute_0_1752,refute_0_1753]) ).
cnf(refute_0_1755,plain,
greatest_lower_bound(identity,inverse(multiply(X_189,identity))) = greatest_lower_bound(identity,inverse(X_189)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_189,identity)),inverse(X_189)) )],[refute_0_1751,refute_0_1754]) ).
cnf(refute_0_1756,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) = inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))))]]) ).
cnf(refute_0_1757,plain,
( greatest_lower_bound(identity,inverse(multiply(X_189,identity))) != greatest_lower_bound(identity,inverse(X_189))
| inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) != inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity))))
| inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))),inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_189)))]]) ).
cnf(refute_0_1758,plain,
( greatest_lower_bound(identity,inverse(multiply(X_189,identity))) != greatest_lower_bound(identity,inverse(X_189))
| inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))),inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity))))) )],[refute_0_1756,refute_0_1757]) ).
cnf(refute_0_1759,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_189))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_189,identity))),greatest_lower_bound(identity,inverse(X_189))) )],[refute_0_1755,refute_0_1758]) ).
cnf(refute_0_1760,plain,
inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))),
inference(subst,[],[p20x_3:[bind(X,$fot(inverse(X_40))),bind(Y,$fot(greatest_lower_bound(X_40,X_41)))]]) ).
cnf(refute_0_1761,plain,
multiply(inverse(X_40),greatest_lower_bound(X_40,X_41)) = greatest_lower_bound(identity,multiply(inverse(X_40),X_41)),
inference(subst,[],[refute_0_765:[bind(X_36,$fot(X_40)),bind(X_37,$fot(X_41))]]) ).
cnf(refute_0_1762,plain,
( multiply(inverse(X_40),greatest_lower_bound(X_40,X_41)) != greatest_lower_bound(identity,multiply(inverse(X_40),X_41))
| inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))) != multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))),multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_40),X_41)))]]) ).
cnf(refute_0_1763,plain,
( inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))) != multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41)),greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) )],[refute_0_1761,refute_0_1762]) ).
cnf(refute_0_1764,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))),multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))) )],[refute_0_1760,refute_0_1763]) ).
cnf(refute_0_1765,plain,
inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40),
inference(subst,[],[refute_0_538:[bind(X,$fot(X_40)),bind(X_23,$fot(greatest_lower_bound(X_40,X_41)))]]) ).
cnf(refute_0_1766,plain,
multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) = inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))),
inference(subst,[],[refute_0_508:[bind(X,$fot(inverse(X_40))),bind(Y,$fot(greatest_lower_bound(X_40,X_41)))]]) ).
cnf(refute_0_1767,plain,
( multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) != inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41)))
| inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))) != multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40)
| multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))))),bind(Y0,$fot(inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40)))]]) ).
cnf(refute_0_1768,plain,
( inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))) != multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40)
| multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))),inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41)))) )],[refute_0_1766,refute_0_1767]) ).
cnf(refute_0_1769,plain,
multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_40),greatest_lower_bound(X_40,X_41))),multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40)) )],[refute_0_1765,refute_0_1768]) ).
cnf(refute_0_1770,plain,
( multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))) != multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40)
| inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) != multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))),multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40))]]) ).
cnf(refute_0_1771,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) != multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40))),multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40)) )],[refute_0_1769,refute_0_1770]) ).
cnf(refute_0_1772,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))) = multiply(inverse(greatest_lower_bound(X_40,X_41)),X_40),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_40),X_41))),multiply(inverse(greatest_lower_bound(X_40,X_41)),inverse(inverse(X_40)))) )],[refute_0_1764,refute_0_1771]) ).
cnf(refute_0_1773,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X_126),inverse(X)))) = multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126),
inference(subst,[],[refute_0_1772:[bind(X_40,$fot(X_126)),bind(X_41,$fot(inverse(X)))]]) ).
cnf(refute_0_1774,plain,
inverse(multiply(X,X_126)) = multiply(inverse(X_126),inverse(X)),
inference(subst,[],[p20x_3:[bind(Y,$fot(X_126))]]) ).
cnf(refute_0_1775,plain,
( inverse(multiply(X,X_126)) != multiply(inverse(X_126),inverse(X))
| multiply(inverse(X_126),inverse(X)) = inverse(multiply(X,X_126)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(multiply(X,X_126)))),bind(Y0,$fot(multiply(inverse(X_126),inverse(X))))]]) ).
cnf(refute_0_1776,plain,
multiply(inverse(X_126),inverse(X)) = inverse(multiply(X,X_126)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,X_126)),multiply(inverse(X_126),inverse(X))) )],[refute_0_1774,refute_0_1775]) ).
cnf(refute_0_1777,plain,
( multiply(inverse(X_126),inverse(X)) != inverse(multiply(X,X_126))
| inverse(greatest_lower_bound(identity,multiply(inverse(X_126),inverse(X)))) != multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126)
| inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))) = multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_126),inverse(X)))),multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126)) ),[0,0,1],$fot(inverse(multiply(X,X_126)))]]) ).
cnf(refute_0_1778,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(X_126),inverse(X)))) != multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126)
| inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))) = multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_126),inverse(X)),inverse(multiply(X,X_126))) )],[refute_0_1776,refute_0_1777]) ).
cnf(refute_0_1779,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))) = multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_126),inverse(X)))),multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126)) )],[refute_0_1773,refute_0_1778]) ).
cnf(refute_0_1780,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))) != multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126)
| multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126) = inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126)))]]) ).
cnf(refute_0_1781,plain,
multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126) = inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X,X_126)))),multiply(inverse(greatest_lower_bound(X_126,inverse(X))),X_126)) )],[refute_0_1779,refute_0_1780]) ).
cnf(refute_0_1782,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) = inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))),
inference(subst,[],[refute_0_1781:[bind(X,$fot(X_189)),bind(X_126,$fot(identity))]]) ).
cnf(refute_0_1783,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) != inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity))))
| inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) != inverse(greatest_lower_bound(identity,inverse(X_189)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1784,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))) != inverse(greatest_lower_bound(identity,inverse(X_189)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity),inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity))))) )],[refute_0_1782,refute_0_1783]) ).
cnf(refute_0_1785,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) = inverse(greatest_lower_bound(identity,inverse(X_189))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_189,identity)))),inverse(greatest_lower_bound(identity,inverse(X_189)))) )],[refute_0_1759,refute_0_1784]) ).
cnf(refute_0_1786,plain,
greatest_lower_bound(identity,least_upper_bound(X_189,identity)) = identity,
inference(subst,[],[refute_0_85:[bind(X_12,$fot(identity)),bind(X_13,$fot(X_189))]]) ).
cnf(refute_0_1787,plain,
multiply(least_upper_bound(X_189,identity),identity) = least_upper_bound(X_189,identity),
inference(subst,[],[refute_0_561:[bind(X,$fot(least_upper_bound(X_189,identity)))]]) ).
cnf(refute_0_1788,plain,
least_upper_bound(identity,multiply(X_189,identity)) = multiply(least_upper_bound(X_189,identity),identity),
inference(subst,[],[refute_0_615:[bind(X_80,$fot(identity)),bind(X_81,$fot(X_189))]]) ).
cnf(refute_0_1789,plain,
( multiply(least_upper_bound(X_189,identity),identity) != least_upper_bound(X_189,identity)
| least_upper_bound(identity,multiply(X_189,identity)) != multiply(least_upper_bound(X_189,identity),identity)
| least_upper_bound(identity,multiply(X_189,identity)) = least_upper_bound(X_189,identity) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(X_189,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_189,identity),identity))),bind(Z0,$fot(least_upper_bound(X_189,identity)))]]) ).
cnf(refute_0_1790,plain,
( multiply(least_upper_bound(X_189,identity),identity) != least_upper_bound(X_189,identity)
| least_upper_bound(identity,multiply(X_189,identity)) = least_upper_bound(X_189,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_189,identity)),multiply(least_upper_bound(X_189,identity),identity)) )],[refute_0_1788,refute_0_1789]) ).
cnf(refute_0_1791,plain,
least_upper_bound(identity,multiply(X_189,identity)) = least_upper_bound(X_189,identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_189,identity),identity),least_upper_bound(X_189,identity)) )],[refute_0_1787,refute_0_1790]) ).
cnf(refute_0_1792,plain,
multiply(X_189,least_upper_bound(identity,inverse(X_189))) = least_upper_bound(identity,multiply(X_189,identity)),
inference(subst,[],[refute_0_641:[bind(X_75,$fot(X_189)),bind(X_76,$fot(identity))]]) ).
cnf(refute_0_1793,plain,
( multiply(X_189,least_upper_bound(identity,inverse(X_189))) != least_upper_bound(identity,multiply(X_189,identity))
| least_upper_bound(identity,multiply(X_189,identity)) != least_upper_bound(X_189,identity)
| multiply(X_189,least_upper_bound(identity,inverse(X_189))) = least_upper_bound(X_189,identity) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X_189,least_upper_bound(identity,inverse(X_189))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_189,identity)))),bind(Z0,$fot(least_upper_bound(X_189,identity)))]]) ).
cnf(refute_0_1794,plain,
( least_upper_bound(identity,multiply(X_189,identity)) != least_upper_bound(X_189,identity)
| multiply(X_189,least_upper_bound(identity,inverse(X_189))) = least_upper_bound(X_189,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_189,least_upper_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(X_189,identity))) )],[refute_0_1792,refute_0_1793]) ).
cnf(refute_0_1795,plain,
multiply(X_189,least_upper_bound(identity,inverse(X_189))) = least_upper_bound(X_189,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_189,identity)),least_upper_bound(X_189,identity)) )],[refute_0_1791,refute_0_1794]) ).
cnf(refute_0_1796,plain,
greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1797,plain,
( multiply(X_189,least_upper_bound(identity,inverse(X_189))) != least_upper_bound(X_189,identity)
| greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) != greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189))))
| greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,least_upper_bound(X_189,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))),greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189))))) ),[1,1],$fot(least_upper_bound(X_189,identity))]]) ).
cnf(refute_0_1798,plain,
( multiply(X_189,least_upper_bound(identity,inverse(X_189))) != least_upper_bound(X_189,identity)
| greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,least_upper_bound(X_189,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))),greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189))))) )],[refute_0_1796,refute_0_1797]) ).
cnf(refute_0_1799,plain,
greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,least_upper_bound(X_189,identity)),
inference(resolve,[$cnf( $equal(multiply(X_189,least_upper_bound(identity,inverse(X_189))),least_upper_bound(X_189,identity)) )],[refute_0_1795,refute_0_1798]) ).
cnf(refute_0_1800,plain,
( greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) != greatest_lower_bound(identity,least_upper_bound(X_189,identity))
| greatest_lower_bound(identity,least_upper_bound(X_189,identity)) != identity
| greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_189,identity)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1801,plain,
( greatest_lower_bound(identity,least_upper_bound(X_189,identity)) != identity
| greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))),greatest_lower_bound(identity,least_upper_bound(X_189,identity))) )],[refute_0_1799,refute_0_1800]) ).
cnf(refute_0_1802,plain,
greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_189,identity)),identity) )],[refute_0_1786,refute_0_1801]) ).
cnf(refute_0_1803,plain,
greatest_lower_bound(X_162,greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))) = greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161))),
inference(subst,[],[refute_0_380:[bind(Y,$fot(X_161)),bind(X_26,$fot(X_162)),bind(X_28,$fot(multiply(X_43,least_upper_bound(X_162,X_161))))]]) ).
cnf(refute_0_1804,plain,
multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161)) = greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161))),
inference(subst,[],[refute_0_22:[bind(X_42,$fot(least_upper_bound(X_162,X_161)))]]) ).
cnf(refute_0_1805,plain,
( multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161)) != greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))
| greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161))) = multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))))]]) ).
cnf(refute_0_1806,plain,
greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161))) = multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161)),greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))) )],[refute_0_1804,refute_0_1805]) ).
cnf(refute_0_1807,plain,
( greatest_lower_bound(X_162,greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))) != greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161)))
| greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161))) != multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161))
| greatest_lower_bound(X_162,multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161))) = greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_162,greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))),greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161)))) ),[0,1],$fot(multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161)))]]) ).
cnf(refute_0_1808,plain,
( greatest_lower_bound(X_162,greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))) != greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161)))
| greatest_lower_bound(X_162,multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161))) = greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161))),multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161))) )],[refute_0_1806,refute_0_1807]) ).
cnf(refute_0_1809,plain,
greatest_lower_bound(X_162,multiply(greatest_lower_bound(X_43,identity),least_upper_bound(X_162,X_161))) = greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_162,greatest_lower_bound(least_upper_bound(X_162,X_161),multiply(X_43,least_upper_bound(X_162,X_161)))),greatest_lower_bound(X_162,multiply(X_43,least_upper_bound(X_162,X_161)))) )],[refute_0_1803,refute_0_1808]) ).
cnf(refute_0_1810,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))),
inference(subst,[],[refute_0_1809:[bind(X_161,$fot(inverse(X_189))),bind(X_162,$fot(identity)),bind(X_43,$fot(X_189))]]) ).
cnf(refute_0_1811,plain,
( greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) != greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189))))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1812,plain,
( greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))),greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189))))) )],[refute_0_1810,refute_0_1811]) ).
cnf(refute_0_1813,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_189,least_upper_bound(identity,inverse(X_189)))),identity) )],[refute_0_1802,refute_0_1812]) ).
cnf(refute_0_1814,plain,
least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) = multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))),
inference(subst,[],[refute_0_825:[bind(X_106,$fot(X_189))]]) ).
cnf(refute_0_1815,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1816,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) != greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))
| least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) != multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) ),[1,1],$fot(multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))))]]) ).
cnf(refute_0_1817,plain,
( least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))) != multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) )],[refute_0_1815,refute_0_1816]) ).
cnf(refute_0_1818,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))),multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) )],[refute_0_1814,refute_0_1817]) ).
cnf(refute_0_1819,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) != identity
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1820,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))) != identity
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189))))) )],[refute_0_1818,refute_0_1819]) ).
cnf(refute_0_1821,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_189,identity),least_upper_bound(identity,inverse(X_189)))),identity) )],[refute_0_1813,refute_0_1820]) ).
cnf(refute_0_1822,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))))]]) ).
cnf(refute_0_1823,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) != identity
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1824,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))) != identity
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))) )],[refute_0_1822,refute_0_1823]) ).
cnf(refute_0_1825,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))),identity) )],[refute_0_1821,refute_0_1824]) ).
cnf(refute_0_1826,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) != inverse(greatest_lower_bound(identity,inverse(X_189)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1827,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity) != inverse(greatest_lower_bound(identity,inverse(X_189)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity)) )],[refute_0_1825,refute_0_1826]) ).
cnf(refute_0_1828,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) = inverse(greatest_lower_bound(identity,inverse(X_189))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),identity),inverse(greatest_lower_bound(identity,inverse(X_189)))) )],[refute_0_1785,refute_0_1827]) ).
cnf(refute_0_1829,plain,
multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) = greatest_lower_bound(inverse(X_120),multiply(inverse(X_120),least_upper_bound(X_121,X_120))),
inference(subst,[],[refute_0_182:[bind(X_35,$fot(inverse(X_120))),bind(X_36,$fot(least_upper_bound(X_121,X_120)))]]) ).
cnf(refute_0_1830,plain,
multiply(inverse(X_120),least_upper_bound(X_121,X_120)) = least_upper_bound(identity,multiply(inverse(X_120),X_121)),
inference(subst,[],[refute_0_902:[bind(X,$fot(X_120)),bind(X_79,$fot(X_121))]]) ).
cnf(refute_0_1831,plain,
( multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) != greatest_lower_bound(inverse(X_120),multiply(inverse(X_120),least_upper_bound(X_121,X_120)))
| multiply(inverse(X_120),least_upper_bound(X_121,X_120)) != least_upper_bound(identity,multiply(inverse(X_120),X_121))
| multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) = greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)),greatest_lower_bound(inverse(X_120),multiply(inverse(X_120),least_upper_bound(X_121,X_120)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_120),X_121)))]]) ).
cnf(refute_0_1832,plain,
( multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) != greatest_lower_bound(inverse(X_120),multiply(inverse(X_120),least_upper_bound(X_121,X_120)))
| multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) = greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_120),least_upper_bound(X_121,X_120)),least_upper_bound(identity,multiply(inverse(X_120),X_121))) )],[refute_0_1830,refute_0_1831]) ).
cnf(refute_0_1833,plain,
multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) = greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)),greatest_lower_bound(inverse(X_120),multiply(inverse(X_120),least_upper_bound(X_121,X_120)))) )],[refute_0_1829,refute_0_1832]) ).
cnf(refute_0_1834,plain,
multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) = multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))),
inference(subst,[],[refute_0_361:[bind(X_27,$fot(inverse(X_120))),bind(X_56,$fot(least_upper_bound(X_121,X_120)))]]) ).
cnf(refute_0_1835,plain,
( multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) != multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120)))
| multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) != greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121)))
| multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))) = greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)),greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121)))) ),[0],$fot(multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))))]]) ).
cnf(refute_0_1836,plain,
( multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)) != greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121)))
| multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))) = greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)),multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120)))) )],[refute_0_1834,refute_0_1835]) ).
cnf(refute_0_1837,plain,
multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))) = greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_120),greatest_lower_bound(least_upper_bound(X_121,X_120),identity)),greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121)))) )],[refute_0_1833,refute_0_1836]) ).
cnf(refute_0_1838,plain,
( multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))) != greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121)))
| greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))) = multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121)))))]]) ).
cnf(refute_0_1839,plain,
greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121))) = multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_120),greatest_lower_bound(identity,least_upper_bound(X_121,X_120))),greatest_lower_bound(inverse(X_120),least_upper_bound(identity,multiply(inverse(X_120),X_121)))) )],[refute_0_1837,refute_0_1838]) ).
cnf(refute_0_1840,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),
inference(subst,[],[refute_0_1839:[bind(X_120,$fot(greatest_lower_bound(identity,inverse(X_189)))),bind(X_121,$fot(greatest_lower_bound(X_189,identity)))]]) ).
cnf(refute_0_1841,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) = greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(X_79,inverse(X_35)))),
inference(subst,[],[refute_0_182:[bind(X_36,$fot(least_upper_bound(X_79,inverse(X_35))))]]) ).
cnf(refute_0_1842,plain,
multiply(X_35,least_upper_bound(X_79,inverse(X_35))) = least_upper_bound(identity,multiply(X_35,X_79)),
inference(subst,[],[refute_0_641:[bind(X_75,$fot(X_35)),bind(X_76,$fot(X_79))]]) ).
cnf(refute_0_1843,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) != greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(X_79,inverse(X_35))))
| multiply(X_35,least_upper_bound(X_79,inverse(X_35))) != least_upper_bound(identity,multiply(X_35,X_79))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)),greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(X_79,inverse(X_35))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_35,X_79)))]]) ).
cnf(refute_0_1844,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) != greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(X_79,inverse(X_35))))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79))) ),
inference(resolve,[$cnf( $equal(multiply(X_35,least_upper_bound(X_79,inverse(X_35))),least_upper_bound(identity,multiply(X_35,X_79))) )],[refute_0_1842,refute_0_1843]) ).
cnf(refute_0_1845,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79))),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)),greatest_lower_bound(X_35,multiply(X_35,least_upper_bound(X_79,inverse(X_35))))) )],[refute_0_1841,refute_0_1844]) ).
cnf(refute_0_1846,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) = multiply(X_35,greatest_lower_bound(identity,least_upper_bound(X_79,inverse(X_35)))),
inference(subst,[],[refute_0_361:[bind(X_27,$fot(X_35)),bind(X_56,$fot(least_upper_bound(X_79,inverse(X_35))))]]) ).
cnf(refute_0_1847,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) != multiply(X_35,greatest_lower_bound(identity,least_upper_bound(X_79,inverse(X_35))))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) != greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79)))
| multiply(X_35,greatest_lower_bound(identity,least_upper_bound(X_79,inverse(X_35)))) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)),greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79)))) ),[0],$fot(multiply(X_35,greatest_lower_bound(identity,least_upper_bound(X_79,inverse(X_35)))))]]) ).
cnf(refute_0_1848,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)) != greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79)))
| multiply(X_35,greatest_lower_bound(identity,least_upper_bound(X_79,inverse(X_35)))) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79))) ),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)),multiply(X_35,greatest_lower_bound(identity,least_upper_bound(X_79,inverse(X_35))))) )],[refute_0_1846,refute_0_1847]) ).
cnf(refute_0_1849,plain,
multiply(X_35,greatest_lower_bound(identity,least_upper_bound(X_79,inverse(X_35)))) = greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79))),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_79,inverse(X_35)),identity)),greatest_lower_bound(X_35,least_upper_bound(identity,multiply(X_35,X_79)))) )],[refute_0_1845,refute_0_1848]) ).
cnf(refute_0_1850,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)))),
inference(subst,[],[refute_0_1849:[bind(X_35,$fot(inverse(greatest_lower_bound(identity,inverse(X_189))))),bind(X_79,$fot(greatest_lower_bound(X_189,identity)))]]) ).
cnf(refute_0_1851,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))))]]) ).
cnf(refute_0_1852,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity))))) )],[refute_0_1850,refute_0_1851]) ).
cnf(refute_0_1853,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(X_189,identity)))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))) )],[refute_0_1840,refute_0_1852]) ).
cnf(refute_0_1854,plain,
multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) = greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(inverse(X),X_113))),
inference(subst,[],[monotony_glb1:[bind(Z,$fot(least_upper_bound(inverse(X),X_113)))]]) ).
cnf(refute_0_1855,plain,
multiply(X,least_upper_bound(inverse(X),X_113)) = least_upper_bound(identity,multiply(X,X_113)),
inference(subst,[],[refute_0_1219:[bind(X_75,$fot(X)),bind(X_77,$fot(X_113))]]) ).
cnf(refute_0_1856,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(inverse(X),X_113)))
| multiply(X,least_upper_bound(inverse(X),X_113)) != least_upper_bound(identity,multiply(X,X_113))
| multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) = greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))),greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(inverse(X),X_113)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X,X_113)))]]) ).
cnf(refute_0_1857,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(inverse(X),X_113)))
| multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) = greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(inverse(X),X_113)),least_upper_bound(identity,multiply(X,X_113))) )],[refute_0_1855,refute_0_1856]) ).
cnf(refute_0_1858,plain,
multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) = greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))),greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(inverse(X),X_113)))) )],[refute_0_1854,refute_0_1857]) ).
cnf(refute_0_1859,plain,
multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) = greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_79,inverse(X)))),
inference(subst,[],[monotony_glb1:[bind(Z,$fot(least_upper_bound(X_79,inverse(X))))]]) ).
cnf(refute_0_1860,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_79,inverse(X))))
| multiply(X,least_upper_bound(X_79,inverse(X))) != least_upper_bound(identity,multiply(X,X_79))
| multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) = greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))),greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_79,inverse(X))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X,X_79)))]]) ).
cnf(refute_0_1861,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_79,inverse(X))))
| multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) = greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79))) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_79,inverse(X))),least_upper_bound(identity,multiply(X,X_79))) )],[refute_0_1347,refute_0_1860]) ).
cnf(refute_0_1862,plain,
multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) = greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))),greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_79,inverse(X))))) )],[refute_0_1859,refute_0_1861]) ).
cnf(refute_0_1863,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) != greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79)))
| greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79))) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79)))))]]) ).
cnf(refute_0_1864,plain,
greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79))) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(X_79,inverse(X)))),greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_79)))) )],[refute_0_1862,refute_0_1863]) ).
cnf(refute_0_1865,plain,
greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113))) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_113,inverse(X)))),
inference(subst,[],[refute_0_1864:[bind(X_79,$fot(X_113))]]) ).
cnf(refute_0_1866,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) != greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113)))
| greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113))) != multiply(X,greatest_lower_bound(Y,least_upper_bound(X_113,inverse(X))))
| multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_113,inverse(X)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))),multiply(X,greatest_lower_bound(Y,least_upper_bound(X_113,inverse(X))))) ),[0],$fot(greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113))))]]) ).
cnf(refute_0_1867,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) != greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113)))
| multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_113,inverse(X)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113))),multiply(X,greatest_lower_bound(Y,least_upper_bound(X_113,inverse(X))))) )],[refute_0_1865,refute_0_1866]) ).
cnf(refute_0_1868,plain,
multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_113,inverse(X)))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(inverse(X),X_113))),greatest_lower_bound(multiply(X,Y),least_upper_bound(identity,multiply(X,X_113)))) )],[refute_0_1858,refute_0_1867]) ).
cnf(refute_0_1869,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))),
inference(subst,[],[refute_0_1868:[bind(X,$fot(inverse(greatest_lower_bound(identity,inverse(X_189))))),bind(Y,$fot(identity)),bind(X_113,$fot(greatest_lower_bound(X_189,identity)))]]) ).
cnf(refute_0_1870,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))))]]) ).
cnf(refute_0_1871,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))))))) )],[refute_0_1869,refute_0_1870]) ).
cnf(refute_0_1872,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_189))))))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))) )],[refute_0_1853,refute_0_1871]) ).
cnf(refute_0_1873,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) != inverse(greatest_lower_bound(identity,inverse(X_189)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1874,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))) != inverse(greatest_lower_bound(identity,inverse(X_189)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_189))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))),multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189)))))) )],[refute_0_1872,refute_0_1873]) ).
cnf(refute_0_1875,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_189))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(X_189,identity),greatest_lower_bound(identity,inverse(X_189))))),inverse(greatest_lower_bound(identity,inverse(X_189)))) )],[refute_0_1828,refute_0_1874]) ).
cnf(refute_0_1876,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != inverse(greatest_lower_bound(identity,inverse(X_189)))
| inverse(greatest_lower_bound(identity,inverse(X_189))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(X_189))))]]) ).
cnf(refute_0_1877,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))
| inverse(greatest_lower_bound(identity,inverse(X_189))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))),inverse(greatest_lower_bound(identity,inverse(X_189)))) )],[refute_0_1875,refute_0_1876]) ).
cnf(refute_0_1878,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)) = greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189)))),
inference(subst,[],[refute_0_1192:[bind(Y,$fot(X_189)),bind(X_21,$fot(identity)),bind(X_258,$fot(inverse(greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1879,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)) != greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189))))
| inverse(greatest_lower_bound(identity,inverse(X_189))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))
| inverse(greatest_lower_bound(identity,inverse(X_189))) = greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))) ),[1],$fot(greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189)))))]]) ).
cnf(refute_0_1880,plain,
( inverse(greatest_lower_bound(identity,inverse(X_189))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))
| inverse(greatest_lower_bound(identity,inverse(X_189))) = greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189)),greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189))))) )],[refute_0_1878,refute_0_1879]) ).
cnf(refute_0_1881,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))
| inverse(greatest_lower_bound(identity,inverse(X_189))) = greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))) )],[refute_0_1877,refute_0_1880]) ).
cnf(refute_0_1882,plain,
inverse(greatest_lower_bound(identity,inverse(X_189))) = greatest_lower_bound(least_upper_bound(X_189,identity),inverse(greatest_lower_bound(identity,inverse(X_189)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_189))),greatest_lower_bound(identity,least_upper_bound(inverse(inverse(greatest_lower_bound(identity,inverse(X_189)))),greatest_lower_bound(X_189,identity)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X_189))),least_upper_bound(identity,X_189))) )],[refute_0_1746,refute_0_1881]) ).
cnf(refute_0_1883,plain,
inverse(greatest_lower_bound(identity,inverse(inverse(X)))) = greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))),
inference(subst,[],[refute_0_1882:[bind(X_189,$fot(inverse(X)))]]) ).
cnf(refute_0_1884,plain,
( inverse(greatest_lower_bound(identity,inverse(inverse(X)))) != greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))
| inverse(inverse(X)) != X
| inverse(greatest_lower_bound(identity,X)) = greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X)))),greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))) ),[0,0,1],$fot(X)]]) ).
cnf(refute_0_1885,plain,
( inverse(greatest_lower_bound(identity,inverse(inverse(X)))) != greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))
| inverse(greatest_lower_bound(identity,X)) = greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_1884]) ).
cnf(refute_0_1886,plain,
inverse(greatest_lower_bound(identity,X)) = greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X)))),greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))) )],[refute_0_1883,refute_0_1885]) ).
cnf(refute_0_1887,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),
inference(subst,[],[refute_0_1378:[bind(X_113,$fot(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))]]) ).
cnf(refute_0_1888,plain,
multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) = greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(inverse(X),X_39))),
inference(subst,[],[monotony_glb1:[bind(Z,$fot(greatest_lower_bound(inverse(X),X_39)))]]) ).
cnf(refute_0_1889,plain,
multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)) = greatest_lower_bound(multiply(X_35,inverse(X_35)),multiply(X_35,X_37)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_35)),bind(Y,$fot(inverse(X_35))),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_1890,plain,
multiply(X_35,inverse(X_35)) = identity,
inference(subst,[],[refute_0_633:[bind(X_1,$fot(X_35))]]) ).
cnf(refute_0_1891,plain,
( multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)) != greatest_lower_bound(multiply(X_35,inverse(X_35)),multiply(X_35,X_37))
| multiply(X_35,inverse(X_35)) != identity
| multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)) = greatest_lower_bound(identity,multiply(X_35,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)),greatest_lower_bound(multiply(X_35,inverse(X_35)),multiply(X_35,X_37))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1892,plain,
( multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)) != greatest_lower_bound(multiply(X_35,inverse(X_35)),multiply(X_35,X_37))
| multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)) = greatest_lower_bound(identity,multiply(X_35,X_37)) ),
inference(resolve,[$cnf( $equal(multiply(X_35,inverse(X_35)),identity) )],[refute_0_1890,refute_0_1891]) ).
cnf(refute_0_1893,plain,
multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)) = greatest_lower_bound(identity,multiply(X_35,X_37)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(inverse(X_35),X_37)),greatest_lower_bound(multiply(X_35,inverse(X_35)),multiply(X_35,X_37))) )],[refute_0_1889,refute_0_1892]) ).
cnf(refute_0_1894,plain,
multiply(X,greatest_lower_bound(inverse(X),X_39)) = greatest_lower_bound(identity,multiply(X,X_39)),
inference(subst,[],[refute_0_1893:[bind(X_35,$fot(X)),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_1895,plain,
( multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) != greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(inverse(X),X_39)))
| multiply(X,greatest_lower_bound(inverse(X),X_39)) != greatest_lower_bound(identity,multiply(X,X_39))
| multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) = greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))),greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(inverse(X),X_39)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X,X_39)))]]) ).
cnf(refute_0_1896,plain,
( multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) != greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(inverse(X),X_39)))
| multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) = greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(inverse(X),X_39)),greatest_lower_bound(identity,multiply(X,X_39))) )],[refute_0_1894,refute_0_1895]) ).
cnf(refute_0_1897,plain,
multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) = greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))),greatest_lower_bound(multiply(X,Y),multiply(X,greatest_lower_bound(inverse(X),X_39)))) )],[refute_0_1888,refute_0_1896]) ).
cnf(refute_0_1898,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,X_39)) = multiply(X,greatest_lower_bound(Y,X_39)),
inference(subst,[],[refute_0_252:[bind(Z,$fot(X_39))]]) ).
cnf(refute_0_1899,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))))]]) ).
cnf(refute_0_1900,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,X_39)) != multiply(X,greatest_lower_bound(Y,X_39))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))),greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Y,X_39)))]]) ).
cnf(refute_0_1901,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,X_39)) != multiply(X,greatest_lower_bound(Y,X_39))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))),greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39)))) )],[refute_0_1899,refute_0_1900]) ).
cnf(refute_0_1902,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,X_39)),multiply(X,greatest_lower_bound(Y,X_39))) )],[refute_0_1898,refute_0_1901]) ).
cnf(refute_0_1903,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Y,X_34))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(Y,X_34)))]]) ).
cnf(refute_0_1904,plain,
greatest_lower_bound(Y,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,X_34),
inference(subst,[],[refute_0_71:[bind(X_27,$fot(Y)),bind(X_28,$fot(X_34))]]) ).
cnf(refute_0_1905,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Y,X_34))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34))
| greatest_lower_bound(Y,greatest_lower_bound(Y,X_34)) != greatest_lower_bound(Y,X_34)
| greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Y,X_34))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34))) ),[0,1],$fot(greatest_lower_bound(Y,X_34))]]) ).
cnf(refute_0_1906,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Y,X_34))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(Y,X_34)),greatest_lower_bound(Y,X_34)) )],[refute_0_1904,refute_0_1905]) ).
cnf(refute_0_1907,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Y,X_34))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34))) )],[refute_0_1903,refute_0_1906]) ).
cnf(refute_0_1908,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)),
inference(subst,[],[refute_0_1174:[bind(X,$fot(Y)),bind(Z,$fot(X_34)),bind(X_31,$fot(X))]]) ).
cnf(refute_0_1909,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_34) = greatest_lower_bound(X,greatest_lower_bound(Y,X_34)),
inference(subst,[],[refute_0_92:[bind(Z,$fot(X_34))]]) ).
cnf(refute_0_1910,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)))]]) ).
cnf(refute_0_1911,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_34) != greatest_lower_bound(X,greatest_lower_bound(Y,X_34))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34))) ),[1,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_34)))]]) ).
cnf(refute_0_1912,plain,
( greatest_lower_bound(greatest_lower_bound(X,Y),X_34) != greatest_lower_bound(X,greatest_lower_bound(Y,X_34))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34))) )],[refute_0_1910,refute_0_1911]) ).
cnf(refute_0_1913,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_34),greatest_lower_bound(X,greatest_lower_bound(Y,X_34))) )],[refute_0_1909,refute_0_1912]) ).
cnf(refute_0_1914,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))) != greatest_lower_bound(Y,greatest_lower_bound(X,X_34))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) != greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34)))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_34))))]]) ).
cnf(refute_0_1915,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))) != greatest_lower_bound(Y,greatest_lower_bound(X,X_34))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)),greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34)))) )],[refute_0_1913,refute_0_1914]) ).
cnf(refute_0_1916,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_34))),greatest_lower_bound(Y,greatest_lower_bound(X,X_34))) )],[refute_0_1908,refute_0_1915]) ).
cnf(refute_0_1917,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)),
inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(X_31,Y)))]]) ).
cnf(refute_0_1918,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y))
| greatest_lower_bound(Y,greatest_lower_bound(X_31,Y)) != greatest_lower_bound(Y,X_31)
| greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y))) ),[0,1],$fot(greatest_lower_bound(Y,X_31))]]) ).
cnf(refute_0_1919,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_31,Y)),greatest_lower_bound(Y,X_31)) )],[refute_0_875,refute_0_1918]) ).
cnf(refute_0_1920,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_31,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y))) )],[refute_0_1917,refute_0_1919]) ).
cnf(refute_0_1921,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)),
inference(subst,[],[refute_0_1174:[bind(X,$fot(Y)),bind(Z,$fot(X_31)),bind(X_31,$fot(X))]]) ).
cnf(refute_0_1922,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),X_31) = greatest_lower_bound(X,greatest_lower_bound(Y,X_31)),
inference(subst,[],[refute_0_92:[bind(Z,$fot(X_31))]]) ).
cnf(refute_0_1923,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)))]]) ).
cnf(refute_0_1924,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31))
| greatest_lower_bound(greatest_lower_bound(X,Y),X_31) != greatest_lower_bound(X,greatest_lower_bound(Y,X_31))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31))) ),[1,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_31)))]]) ).
cnf(refute_0_1925,plain,
( greatest_lower_bound(greatest_lower_bound(X,Y),X_31) != greatest_lower_bound(X,greatest_lower_bound(Y,X_31))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31))) )],[refute_0_1923,refute_0_1924]) ).
cnf(refute_0_1926,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),X_31),greatest_lower_bound(X,greatest_lower_bound(Y,X_31))) )],[refute_0_1922,refute_0_1925]) ).
cnf(refute_0_1927,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))) != greatest_lower_bound(Y,greatest_lower_bound(X,X_31))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) != greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31)))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_31))))]]) ).
cnf(refute_0_1928,plain,
( greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))) != greatest_lower_bound(Y,greatest_lower_bound(X,X_31))
| greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)),greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31)))) )],[refute_0_1926,refute_0_1927]) ).
cnf(refute_0_1929,plain,
greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X,greatest_lower_bound(Y,X_31))),greatest_lower_bound(Y,greatest_lower_bound(X,X_31))) )],[refute_0_1921,refute_0_1928]) ).
cnf(refute_0_1930,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) != greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))
| greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) = greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)))),bind(Y0,$fot(greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))))]]) ).
cnf(refute_0_1931,plain,
greatest_lower_bound(X_26,greatest_lower_bound(X_27,X)) = greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_26,X_27)),greatest_lower_bound(X_26,greatest_lower_bound(X_27,X))) )],[refute_0_132,refute_0_1930]) ).
cnf(refute_0_1932,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)),
inference(subst,[],[refute_0_1931:[bind(X,$fot(Y)),bind(X_26,$fot(greatest_lower_bound(X,Y))),bind(X_27,$fot(X_31))]]) ).
cnf(refute_0_1933,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_31))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_31))))]]) ).
cnf(refute_0_1934,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_31))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31))) )],[refute_0_1932,refute_0_1933]) ).
cnf(refute_0_1935,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_31)),greatest_lower_bound(Y,greatest_lower_bound(X,X_31))) )],[refute_0_1929,refute_0_1934]) ).
cnf(refute_0_1936,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_31))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_31)),greatest_lower_bound(Y,greatest_lower_bound(X,X_31))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)))]]) ).
cnf(refute_0_1937,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y)),greatest_lower_bound(Y,greatest_lower_bound(X,X_31))) )],[refute_0_1935,refute_0_1936]) ).
cnf(refute_0_1938,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_31)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_31)),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_31,Y))) )],[refute_0_1920,refute_0_1937]) ).
cnf(refute_0_1939,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_31))
| greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_31)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_31)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_31))))]]) ).
cnf(refute_0_1940,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,X_31)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_31)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_31)),greatest_lower_bound(Y,greatest_lower_bound(X,X_31))) )],[refute_0_1938,refute_0_1939]) ).
cnf(refute_0_1941,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)),
inference(subst,[],[refute_0_1940:[bind(X,$fot(Y)),bind(Y,$fot(greatest_lower_bound(X,Y))),bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_1942,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_34))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_34))))]]) ).
cnf(refute_0_1943,plain,
( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_34))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34))) )],[refute_0_1941,refute_0_1942]) ).
cnf(refute_0_1944,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X,Y),X_34)),greatest_lower_bound(Y,greatest_lower_bound(X,X_34))) )],[refute_0_1916,refute_0_1943]) ).
cnf(refute_0_1945,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34))
| greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_34))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_34)),greatest_lower_bound(Y,greatest_lower_bound(X,X_34))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)))]]) ).
cnf(refute_0_1946,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34))
| greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34)),greatest_lower_bound(Y,greatest_lower_bound(X,X_34))) )],[refute_0_1944,refute_0_1945]) ).
cnf(refute_0_1947,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(Y,greatest_lower_bound(X,X_34)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_34)),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X_34))) )],[refute_0_1907,refute_0_1946]) ).
cnf(refute_0_1948,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) != greatest_lower_bound(Y,greatest_lower_bound(X,X_34))
| greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_34)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,X_34)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X,X_34))))]]) ).
cnf(refute_0_1949,plain,
greatest_lower_bound(Y,greatest_lower_bound(X,X_34)) = greatest_lower_bound(X,greatest_lower_bound(Y,X_34)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,X_34)),greatest_lower_bound(Y,greatest_lower_bound(X,X_34))) )],[refute_0_1947,refute_0_1948]) ).
cnf(refute_0_1950,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))),
inference(subst,[],[refute_0_1949:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X,Y))),bind(X_34,$fot(multiply(X,X_39)))]]) ).
cnf(refute_0_1951,plain,
( greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39)))
| greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))) != greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39)))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39)))))]]) ).
cnf(refute_0_1952,plain,
( greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))) != greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39)))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))),greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39)))) )],[refute_0_1950,refute_0_1951]) ).
cnf(refute_0_1953,plain,
greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X,Y),multiply(X,X_39))),greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39)))) )],[refute_0_1902,refute_0_1952]) ).
cnf(refute_0_1954,plain,
( multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) != greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39)))
| greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))) != greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39)))
| multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))),greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39)))) ),[0],$fot(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))))]]) ).
cnf(refute_0_1955,plain,
( multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) != greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39)))
| multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39))),greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39)))) )],[refute_0_1953,refute_0_1954]) ).
cnf(refute_0_1956,plain,
multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))) = greatest_lower_bound(identity,multiply(X,greatest_lower_bound(Y,X_39))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,greatest_lower_bound(inverse(X),X_39))),greatest_lower_bound(multiply(X,Y),greatest_lower_bound(identity,multiply(X,X_39)))) )],[refute_0_1897,refute_0_1955]) ).
cnf(refute_0_1957,plain,
multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))) = greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))),
inference(subst,[],[refute_0_1956:[bind(X,$fot(X_75)),bind(Y,$fot(X_301)),bind(X_39,$fot(X_302))]]) ).
cnf(refute_0_1958,plain,
( multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))) != greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))]]) ).
cnf(refute_0_1959,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) ),
inference(resolve,[$cnf( $equal(multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))),greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) )],[refute_0_1957,refute_0_1958]) ).
cnf(refute_0_1960,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(X_75,least_upper_bound(identity,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))) )],[refute_0_1887,refute_0_1959]) ).
cnf(refute_0_1961,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_75,greatest_lower_bound(X_301,X_302))))]]) ).
cnf(refute_0_1962,plain,
least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) = least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))))]]) ).
cnf(refute_0_1963,plain,
( least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) != least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) != identity
| least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) = least_upper_bound(X_75,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))),least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1964,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) != identity
| least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) = least_upper_bound(X_75,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))),least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))) )],[refute_0_1962,refute_0_1963]) ).
cnf(refute_0_1965,plain,
least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) = least_upper_bound(X_75,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))),identity) )],[refute_0_1961,refute_0_1964]) ).
cnf(refute_0_1966,plain,
( least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) != least_upper_bound(X_75,identity)
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(X_75,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))) ),[1],$fot(least_upper_bound(X_75,identity))]]) ).
cnf(refute_0_1967,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(X_75,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))),least_upper_bound(X_75,identity)) )],[refute_0_1965,refute_0_1966]) ).
cnf(refute_0_1968,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(X_75,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(X_75,least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))) )],[refute_0_1960,refute_0_1967]) ).
cnf(refute_0_1969,plain,
least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))) = X,
inference(subst,[],[lub_absorbtion:[bind(Y,$fot(greatest_lower_bound(X_47,X_45)))]]) ).
cnf(refute_0_1970,plain,
greatest_lower_bound(X_45,greatest_lower_bound(X,X_47)) = greatest_lower_bound(X,greatest_lower_bound(X_47,X_45)),
inference(subst,[],[refute_0_132:[bind(X,$fot(X_45)),bind(X_26,$fot(X)),bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_1971,plain,
( greatest_lower_bound(X_45,greatest_lower_bound(X,X_47)) != greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))
| greatest_lower_bound(X,greatest_lower_bound(X_47,X_45)) = greatest_lower_bound(X_45,greatest_lower_bound(X,X_47)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_45,greatest_lower_bound(X,X_47)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))))]]) ).
cnf(refute_0_1972,plain,
greatest_lower_bound(X,greatest_lower_bound(X_47,X_45)) = greatest_lower_bound(X_45,greatest_lower_bound(X,X_47)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_45,greatest_lower_bound(X,X_47)),greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))) )],[refute_0_1970,refute_0_1971]) ).
cnf(refute_0_1973,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_47,X_45)) != greatest_lower_bound(X_45,greatest_lower_bound(X,X_47))
| least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))) != X
| least_upper_bound(X,greatest_lower_bound(X_45,greatest_lower_bound(X,X_47))) = X ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))),X) ),[0,1],$fot(greatest_lower_bound(X_45,greatest_lower_bound(X,X_47)))]]) ).
cnf(refute_0_1974,plain,
( least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))) != X
| least_upper_bound(X,greatest_lower_bound(X_45,greatest_lower_bound(X,X_47))) = X ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_47,X_45)),greatest_lower_bound(X_45,greatest_lower_bound(X,X_47))) )],[refute_0_1972,refute_0_1973]) ).
cnf(refute_0_1975,plain,
least_upper_bound(X,greatest_lower_bound(X_45,greatest_lower_bound(X,X_47))) = X,
inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(X_47,X_45))),X) )],[refute_0_1969,refute_0_1974]) ).
cnf(refute_0_1976,plain,
least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47))) = least_upper_bound(X_45,X_161),
inference(subst,[],[refute_0_1975:[bind(X,$fot(least_upper_bound(X_45,X_161)))]]) ).
cnf(refute_0_1977,plain,
greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47)) = greatest_lower_bound(X_45,X_47),
inference(subst,[],[refute_0_380:[bind(Y,$fot(X_161)),bind(X_26,$fot(X_45)),bind(X_28,$fot(X_47))]]) ).
cnf(refute_0_1978,plain,
( greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47)) != greatest_lower_bound(X_45,X_47)
| least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47))) != least_upper_bound(X_45,X_161)
| least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)) = least_upper_bound(X_45,X_161) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47))),least_upper_bound(X_45,X_161)) ),[0,1],$fot(greatest_lower_bound(X_45,X_47))]]) ).
cnf(refute_0_1979,plain,
( least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47))) != least_upper_bound(X_45,X_161)
| least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)) = least_upper_bound(X_45,X_161) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47)),greatest_lower_bound(X_45,X_47)) )],[refute_0_1977,refute_0_1978]) ).
cnf(refute_0_1980,plain,
least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)) = least_upper_bound(X_45,X_161),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,greatest_lower_bound(least_upper_bound(X_45,X_161),X_47))),least_upper_bound(X_45,X_161)) )],[refute_0_1976,refute_0_1979]) ).
cnf(refute_0_1981,plain,
least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)) = least_upper_bound(X_45,least_upper_bound(X_161,greatest_lower_bound(X_45,X_47))),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_45)),bind(Y,$fot(X_161)),bind(Z,$fot(greatest_lower_bound(X_45,X_47)))]]) ).
cnf(refute_0_1982,plain,
( least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)) != least_upper_bound(X_45,X_161)
| least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)) != least_upper_bound(X_45,least_upper_bound(X_161,greatest_lower_bound(X_45,X_47)))
| least_upper_bound(X_45,least_upper_bound(X_161,greatest_lower_bound(X_45,X_47))) = least_upper_bound(X_45,X_161) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)),least_upper_bound(X_45,X_161)) ),[0],$fot(least_upper_bound(X_45,least_upper_bound(X_161,greatest_lower_bound(X_45,X_47))))]]) ).
cnf(refute_0_1983,plain,
( least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)) != least_upper_bound(X_45,X_161)
| least_upper_bound(X_45,least_upper_bound(X_161,greatest_lower_bound(X_45,X_47))) = least_upper_bound(X_45,X_161) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)),least_upper_bound(X_45,least_upper_bound(X_161,greatest_lower_bound(X_45,X_47)))) )],[refute_0_1981,refute_0_1982]) ).
cnf(refute_0_1984,plain,
least_upper_bound(X_45,least_upper_bound(X_161,greatest_lower_bound(X_45,X_47))) = least_upper_bound(X_45,X_161),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_45,X_161),greatest_lower_bound(X_45,X_47)),least_upper_bound(X_45,X_161)) )],[refute_0_1980,refute_0_1983]) ).
cnf(refute_0_1985,plain,
least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) = least_upper_bound(identity,X_75),
inference(subst,[],[refute_0_1984:[bind(X_161,$fot(X_75)),bind(X_45,$fot(identity)),bind(X_47,$fot(multiply(X_75,greatest_lower_bound(X_301,X_302))))]]) ).
cnf(refute_0_1986,plain,
multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) = least_upper_bound(X_75,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))),
inference(subst,[],[refute_0_53:[bind(X_76,$fot(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))]]) ).
cnf(refute_0_1987,plain,
( multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))) != greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))
| multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) != least_upper_bound(X_75,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))
| multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) = least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)),least_upper_bound(X_75,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))]]) ).
cnf(refute_0_1988,plain,
( multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) != least_upper_bound(X_75,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))
| multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) = least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) ),
inference(resolve,[$cnf( $equal(multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))),greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) )],[refute_0_1957,refute_0_1987]) ).
cnf(refute_0_1989,plain,
multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) = least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)),least_upper_bound(X_75,multiply(X_75,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) )],[refute_0_1986,refute_0_1988]) ).
cnf(refute_0_1990,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),
inference(subst,[],[refute_0_332:[bind(X_36,$fot(least_upper_bound(X_295,X_297))),bind(X_37,$fot(least_upper_bound(X_296,least_upper_bound(X_297,X_295))))]]) ).
cnf(refute_0_1991,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) != multiply(X_35,greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))
| greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) != least_upper_bound(X_295,X_297)
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,least_upper_bound(X_295,X_297)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))),multiply(X_35,greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))) ),[1,1],$fot(least_upper_bound(X_295,X_297))]]) ).
cnf(refute_0_1992,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) != multiply(X_35,greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,least_upper_bound(X_295,X_297)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),least_upper_bound(X_295,X_297)) )],[refute_0_1503,refute_0_1991]) ).
cnf(refute_0_1993,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,least_upper_bound(X_295,X_297)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))),multiply(X_35,greatest_lower_bound(least_upper_bound(X_295,X_297),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))) )],[refute_0_1990,refute_0_1992]) ).
cnf(refute_0_1994,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) = multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),
introduced(tautology,[refl,[$fot(multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))))]]) ).
cnf(refute_0_1995,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) != multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))
| greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) != least_upper_bound(X_297,X_295)
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) = multiply(X_35,least_upper_bound(X_297,X_295)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))) ),[1,1],$fot(least_upper_bound(X_297,X_295))]]) ).
cnf(refute_0_1996,plain,
( greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))) != least_upper_bound(X_297,X_295)
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) = multiply(X_35,least_upper_bound(X_297,X_295)) ),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))) )],[refute_0_1994,refute_0_1995]) ).
cnf(refute_0_1997,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) = multiply(X_35,least_upper_bound(X_297,X_295)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))),least_upper_bound(X_297,X_295)) )],[refute_0_1507,refute_0_1996]) ).
cnf(refute_0_1998,plain,
multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) = greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))),
inference(subst,[],[monotony_glb1:[bind(Z,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_1999,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290)))
| greatest_lower_bound(Y,least_upper_bound(X_289,X_290)) != greatest_lower_bound(least_upper_bound(X_290,X_289),Y)
| multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) = greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))),greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290)))) ),[0,1],$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),Y))]]) ).
cnf(refute_0_2000,plain,
( multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290)))
| multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) = greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) )],[refute_0_1513,refute_0_1999]) ).
cnf(refute_0_2001,plain,
multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) = greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))),greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290)))) )],[refute_0_1998,refute_0_2000]) ).
cnf(refute_0_2002,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))),
inference(subst,[],[refute_0_252:[bind(Z,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_2003,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290)))
| greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))) != multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290)))
| multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)),multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290)))) ),[0],$fot(greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))))]]) ).
cnf(refute_0_2004,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) != greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290)))
| multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290))),multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290)))) )],[refute_0_2002,refute_0_2003]) ).
cnf(refute_0_2005,plain,
multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) = multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)),greatest_lower_bound(multiply(X,Y),multiply(X,least_upper_bound(X_289,X_290)))) )],[refute_0_2001,refute_0_2004]) ).
cnf(refute_0_2006,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) != multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290)))
| multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) = multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290)))))]]) ).
cnf(refute_0_2007,plain,
multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) = multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(X_290,X_289),Y)),multiply(X,greatest_lower_bound(Y,least_upper_bound(X_289,X_290)))) )],[refute_0_2005,refute_0_2006]) ).
cnf(refute_0_2008,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),
inference(subst,[],[refute_0_2007:[bind(X,$fot(X_35)),bind(Y,$fot(least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),bind(X_289,$fot(X_295)),bind(X_290,$fot(X_297))]]) ).
cnf(refute_0_2009,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) != multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) != multiply(X_35,least_upper_bound(X_297,X_295))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,least_upper_bound(X_297,X_295)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))))),bind(Y0,$fot(multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))))),bind(Z0,$fot(multiply(X_35,least_upper_bound(X_297,X_295))))]]) ).
cnf(refute_0_2010,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))) != multiply(X_35,least_upper_bound(X_297,X_295))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,least_upper_bound(X_297,X_295)) ),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))),multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295))))) )],[refute_0_2008,refute_0_2009]) ).
cnf(refute_0_2011,plain,
multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) = multiply(X_35,least_upper_bound(X_297,X_295)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_297,X_295),least_upper_bound(X_296,least_upper_bound(X_297,X_295)))),multiply(X_35,least_upper_bound(X_297,X_295))) )],[refute_0_1997,refute_0_2010]) ).
cnf(refute_0_2012,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) != multiply(X_35,least_upper_bound(X_295,X_297))
| multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) != multiply(X_35,least_upper_bound(X_297,X_295))
| multiply(X_35,least_upper_bound(X_297,X_295)) = multiply(X_35,least_upper_bound(X_295,X_297)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))),multiply(X_35,least_upper_bound(X_295,X_297))) ),[0],$fot(multiply(X_35,least_upper_bound(X_297,X_295)))]]) ).
cnf(refute_0_2013,plain,
( multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))) != multiply(X_35,least_upper_bound(X_295,X_297))
| multiply(X_35,least_upper_bound(X_297,X_295)) = multiply(X_35,least_upper_bound(X_295,X_297)) ),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))),multiply(X_35,least_upper_bound(X_297,X_295))) )],[refute_0_2011,refute_0_2012]) ).
cnf(refute_0_2014,plain,
multiply(X_35,least_upper_bound(X_297,X_295)) = multiply(X_35,least_upper_bound(X_295,X_297)),
inference(resolve,[$cnf( $equal(multiply(X_35,greatest_lower_bound(least_upper_bound(X_296,least_upper_bound(X_297,X_295)),least_upper_bound(X_295,X_297))),multiply(X_35,least_upper_bound(X_295,X_297))) )],[refute_0_1993,refute_0_2013]) ).
cnf(refute_0_2015,plain,
( multiply(X_35,least_upper_bound(X_297,X_295)) != multiply(X_35,least_upper_bound(X_295,X_297))
| multiply(X_35,least_upper_bound(X_295,X_297)) = multiply(X_35,least_upper_bound(X_297,X_295)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_35,least_upper_bound(X_297,X_295)))),bind(Y0,$fot(multiply(X_35,least_upper_bound(X_295,X_297))))]]) ).
cnf(refute_0_2016,plain,
multiply(X_35,least_upper_bound(X_295,X_297)) = multiply(X_35,least_upper_bound(X_297,X_295)),
inference(resolve,[$cnf( $equal(multiply(X_35,least_upper_bound(X_297,X_295)),multiply(X_35,least_upper_bound(X_295,X_297))) )],[refute_0_2014,refute_0_2015]) ).
cnf(refute_0_2017,plain,
multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) = multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))),
inference(subst,[],[refute_0_2016:[bind(X_295,$fot(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))),bind(X_297,$fot(identity)),bind(X_35,$fot(X_75))]]) ).
cnf(refute_0_2018,plain,
( multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) != multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))
| multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) != least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))
| multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))) = least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)),least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) ),[0],$fot(multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))]]) ).
cnf(refute_0_2019,plain,
( multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)) != least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))
| multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))) = least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))) ),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)),multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) )],[refute_0_2017,refute_0_2018]) ).
cnf(refute_0_2020,plain,
multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))) = least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)),identity)),least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) )],[refute_0_1989,refute_0_2019]) ).
cnf(refute_0_2021,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))))]]) ).
cnf(refute_0_2022,plain,
( multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))) != least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))) ),[1,1],$fot(least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))]]) ).
cnf(refute_0_2023,plain,
( multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))) != least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))))) )],[refute_0_2021,refute_0_2022]) ).
cnf(refute_0_2024,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))),
inference(resolve,[$cnf( $equal(multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302)))),least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) )],[refute_0_2020,refute_0_2023]) ).
cnf(refute_0_2025,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))
| least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) != least_upper_bound(identity,X_75)
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(identity,X_75) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))))),bind(Z0,$fot(least_upper_bound(identity,X_75)))]]) ).
cnf(refute_0_2026,plain,
( least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))) != least_upper_bound(identity,X_75)
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(identity,X_75) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302)))))) )],[refute_0_2024,refute_0_2025]) ).
cnf(refute_0_2027,plain,
least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) = least_upper_bound(identity,X_75),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_75,greatest_lower_bound(identity,multiply(X_75,greatest_lower_bound(X_301,X_302))))),least_upper_bound(identity,X_75)) )],[refute_0_1985,refute_0_2026]) ).
cnf(refute_0_2028,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(X_75,identity)
| least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(identity,X_75)
| least_upper_bound(identity,X_75) = least_upper_bound(X_75,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(X_75,identity)) ),[0],$fot(least_upper_bound(identity,X_75))]]) ).
cnf(refute_0_2029,plain,
( least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))) != least_upper_bound(X_75,identity)
| least_upper_bound(identity,X_75) = least_upper_bound(X_75,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(identity,X_75)) )],[refute_0_2027,refute_0_2028]) ).
cnf(refute_0_2030,plain,
least_upper_bound(identity,X_75) = least_upper_bound(X_75,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_75,least_upper_bound(identity,greatest_lower_bound(X_301,greatest_lower_bound(inverse(X_75),X_302))))),least_upper_bound(X_75,identity)) )],[refute_0_1968,refute_0_2029]) ).
cnf(refute_0_2031,plain,
( least_upper_bound(identity,X_75) != least_upper_bound(X_75,identity)
| least_upper_bound(X_75,identity) = least_upper_bound(identity,X_75) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(identity,X_75))),bind(Y0,$fot(least_upper_bound(X_75,identity)))]]) ).
cnf(refute_0_2032,plain,
least_upper_bound(X_75,identity) = least_upper_bound(identity,X_75),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_75),least_upper_bound(X_75,identity)) )],[refute_0_2030,refute_0_2031]) ).
cnf(refute_0_2033,plain,
least_upper_bound(inverse(X),identity) = least_upper_bound(identity,inverse(X)),
inference(subst,[],[refute_0_2032:[bind(X_75,$fot(inverse(X)))]]) ).
cnf(refute_0_2034,plain,
least_upper_bound(least_upper_bound(X_386,identity),greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))) = least_upper_bound(X_386,identity),
inference(subst,[],[lub_absorbtion:[bind(X,$fot(least_upper_bound(X_386,identity))),bind(Y,$fot(inverse(greatest_lower_bound(identity,inverse(X_386)))))]]) ).
cnf(refute_0_2035,plain,
inverse(greatest_lower_bound(identity,inverse(X_386))) = greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))),
inference(subst,[],[refute_0_1882:[bind(X_189,$fot(X_386))]]) ).
cnf(refute_0_2036,plain,
( inverse(greatest_lower_bound(identity,inverse(X_386))) != greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))
| greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = inverse(greatest_lower_bound(identity,inverse(X_386))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_386))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))))]]) ).
cnf(refute_0_2037,plain,
greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = inverse(greatest_lower_bound(identity,inverse(X_386))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_386))),greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))) )],[refute_0_2035,refute_0_2036]) ).
cnf(refute_0_2038,plain,
( greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(least_upper_bound(X_386,identity),greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))) != least_upper_bound(X_386,identity)
| least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = least_upper_bound(X_386,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_386,identity),greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))),least_upper_bound(X_386,identity)) ),[0,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_386))))]]) ).
cnf(refute_0_2039,plain,
( least_upper_bound(least_upper_bound(X_386,identity),greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))) != least_upper_bound(X_386,identity)
| least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = least_upper_bound(X_386,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))),inverse(greatest_lower_bound(identity,inverse(X_386)))) )],[refute_0_2037,refute_0_2038]) ).
cnf(refute_0_2040,plain,
least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = least_upper_bound(X_386,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_386,identity),greatest_lower_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386))))),least_upper_bound(X_386,identity)) )],[refute_0_2034,refute_0_2039]) ).
cnf(refute_0_2041,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234)))),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(inverse(greatest_lower_bound(X_233,inverse(X_234))))),bind(X_76,$fot(greatest_lower_bound(identity,multiply(X_233,X_234))))]]) ).
cnf(refute_0_2042,plain,
X_59 = multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59)),
inference(subst,[],[refute_0_505:[bind(X_58,$fot(greatest_lower_bound(X_232,inverse(X_59))))]]) ).
cnf(refute_0_2043,plain,
multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) = greatest_lower_bound(multiply(X_43,X_42),multiply(inverse(X_42),X_42)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(inverse(X_42)))]]) ).
cnf(refute_0_2044,plain,
multiply(inverse(X_42),X_42) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_2045,plain,
( multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) != greatest_lower_bound(multiply(X_43,X_42),multiply(inverse(X_42),X_42))
| multiply(inverse(X_42),X_42) != identity
| multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) = greatest_lower_bound(multiply(X_43,X_42),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42),greatest_lower_bound(multiply(X_43,X_42),multiply(inverse(X_42),X_42))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2046,plain,
( multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) != greatest_lower_bound(multiply(X_43,X_42),multiply(inverse(X_42),X_42))
| multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) = greatest_lower_bound(multiply(X_43,X_42),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),X_42),identity) )],[refute_0_2044,refute_0_2045]) ).
cnf(refute_0_2047,plain,
multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) = greatest_lower_bound(multiply(X_43,X_42),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42),greatest_lower_bound(multiply(X_43,X_42),multiply(inverse(X_42),X_42))) )],[refute_0_2043,refute_0_2046]) ).
cnf(refute_0_2048,plain,
greatest_lower_bound(multiply(X_43,X_42),identity) = greatest_lower_bound(identity,multiply(X_43,X_42)),
inference(subst,[],[refute_0_18:[bind(X_27,$fot(identity)),bind(X_28,$fot(multiply(X_43,X_42)))]]) ).
cnf(refute_0_2049,plain,
( multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) != greatest_lower_bound(multiply(X_43,X_42),identity)
| greatest_lower_bound(multiply(X_43,X_42),identity) != greatest_lower_bound(identity,multiply(X_43,X_42))
| multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) = greatest_lower_bound(identity,multiply(X_43,X_42)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42),greatest_lower_bound(identity,multiply(X_43,X_42))) ),[0],$fot(greatest_lower_bound(multiply(X_43,X_42),identity))]]) ).
cnf(refute_0_2050,plain,
( multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) != greatest_lower_bound(multiply(X_43,X_42),identity)
| multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) = greatest_lower_bound(identity,multiply(X_43,X_42)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_43,X_42),identity),greatest_lower_bound(identity,multiply(X_43,X_42))) )],[refute_0_2048,refute_0_2049]) ).
cnf(refute_0_2051,plain,
multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42) = greatest_lower_bound(identity,multiply(X_43,X_42)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_43,inverse(X_42)),X_42),greatest_lower_bound(multiply(X_43,X_42),identity)) )],[refute_0_2047,refute_0_2050]) ).
cnf(refute_0_2052,plain,
multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59) = greatest_lower_bound(identity,multiply(X_232,X_59)),
inference(subst,[],[refute_0_2051:[bind(X_42,$fot(X_59)),bind(X_43,$fot(X_232))]]) ).
cnf(refute_0_2053,plain,
( X_59 != multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59))
| multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59) != greatest_lower_bound(identity,multiply(X_232,X_59))
| X_59 = multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),greatest_lower_bound(identity,multiply(X_232,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_232,X_59)))]]) ).
cnf(refute_0_2054,plain,
( X_59 != multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59))
| X_59 = multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),greatest_lower_bound(identity,multiply(X_232,X_59))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59),greatest_lower_bound(identity,multiply(X_232,X_59))) )],[refute_0_2052,refute_0_2053]) ).
cnf(refute_0_2055,plain,
X_59 = multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),greatest_lower_bound(identity,multiply(X_232,X_59))),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(greatest_lower_bound(X_232,inverse(X_59))),multiply(greatest_lower_bound(X_232,inverse(X_59)),X_59))) )],[refute_0_2042,refute_0_2054]) ).
cnf(refute_0_2056,plain,
X_234 = multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))),
inference(subst,[],[refute_0_2055:[bind(X_232,$fot(X_233)),bind(X_59,$fot(X_234))]]) ).
cnf(refute_0_2057,plain,
( X_234 != multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234)))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))) = X_234 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_234)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234)))))]]) ).
cnf(refute_0_2058,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))) = X_234,
inference(resolve,[$cnf( $equal(X_234,multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234)))) )],[refute_0_2056,refute_0_2057]) ).
cnf(refute_0_2059,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))) != X_234
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) != least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)),least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))))) ),[1,1],$fot(X_234)]]) ).
cnf(refute_0_2060,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) != least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))),X_234) )],[refute_0_2058,refute_0_2059]) ).
cnf(refute_0_2061,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)),least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),greatest_lower_bound(identity,multiply(X_233,X_234))))) )],[refute_0_2041,refute_0_2060]) ).
cnf(refute_0_2062,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity) = inverse(greatest_lower_bound(X_233,inverse(X_234))),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(greatest_lower_bound(X_233,inverse(X_234)))))]]) ).
cnf(refute_0_2063,plain,
least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_233,X_234)))]]) ).
cnf(refute_0_2064,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) = multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))))]]) ).
cnf(refute_0_2065,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) != multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))))
| least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))) != identity
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) = multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2066,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))) != identity
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) = multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))))) )],[refute_0_2064,refute_0_2065]) ).
cnf(refute_0_2067,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) = multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))),identity) )],[refute_0_2063,refute_0_2066]) ).
cnf(refute_0_2068,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity) != inverse(greatest_lower_bound(X_233,inverse(X_234)))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) != multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity)
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) = inverse(greatest_lower_bound(X_233,inverse(X_234))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(X_233,inverse(X_234)))))]]) ).
cnf(refute_0_2069,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity) != inverse(greatest_lower_bound(X_233,inverse(X_234)))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) = inverse(greatest_lower_bound(X_233,inverse(X_234))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity)) )],[refute_0_2067,refute_0_2068]) ).
cnf(refute_0_2070,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) = inverse(greatest_lower_bound(X_233,inverse(X_234))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),identity),inverse(greatest_lower_bound(X_233,inverse(X_234)))) )],[refute_0_2062,refute_0_2069]) ).
cnf(refute_0_2071,plain,
multiply(X_228,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y))) = multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))),
inference(subst,[],[refute_0_332:[bind(X_35,$fot(X_228)),bind(X_36,$fot(least_upper_bound(X_21,Y))),bind(X_37,$fot(least_upper_bound(Y,X_21)))]]) ).
cnf(refute_0_2072,plain,
( multiply(X_228,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y))) != multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))
| greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)) != least_upper_bound(Y,X_21)
| multiply(X_228,least_upper_bound(Y,X_21)) = multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_228,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y))),multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))) ),[0,1],$fot(least_upper_bound(Y,X_21))]]) ).
cnf(refute_0_2073,plain,
( multiply(X_228,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y))) != multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))
| multiply(X_228,least_upper_bound(Y,X_21)) = multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y)),least_upper_bound(Y,X_21)) )],[refute_0_238,refute_0_2072]) ).
cnf(refute_0_2074,plain,
multiply(X_228,least_upper_bound(Y,X_21)) = multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))),
inference(resolve,[$cnf( $equal(multiply(X_228,greatest_lower_bound(least_upper_bound(Y,X_21),least_upper_bound(X_21,Y))),multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))) )],[refute_0_2071,refute_0_2073]) ).
cnf(refute_0_2075,plain,
greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y),
inference(subst,[],[refute_0_238:[bind(Y,$fot(X_21)),bind(X_21,$fot(Y))]]) ).
cnf(refute_0_2076,plain,
multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) = multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))),
introduced(tautology,[refl,[$fot(multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))))]]) ).
cnf(refute_0_2077,plain,
( multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) != multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))
| greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)) != least_upper_bound(X_21,Y)
| multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) = multiply(X_228,least_upper_bound(X_21,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))),multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))) ),[1,1],$fot(least_upper_bound(X_21,Y))]]) ).
cnf(refute_0_2078,plain,
( greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)) != least_upper_bound(X_21,Y)
| multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) = multiply(X_228,least_upper_bound(X_21,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))),multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))) )],[refute_0_2076,refute_0_2077]) ).
cnf(refute_0_2079,plain,
multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) = multiply(X_228,least_upper_bound(X_21,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)),least_upper_bound(X_21,Y)) )],[refute_0_2075,refute_0_2078]) ).
cnf(refute_0_2080,plain,
( multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))) != multiply(X_228,least_upper_bound(X_21,Y))
| multiply(X_228,least_upper_bound(Y,X_21)) != multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))
| multiply(X_228,least_upper_bound(Y,X_21)) = multiply(X_228,least_upper_bound(X_21,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_228,least_upper_bound(Y,X_21)),multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))) ),[1],$fot(multiply(X_228,least_upper_bound(X_21,Y)))]]) ).
cnf(refute_0_2081,plain,
( multiply(X_228,least_upper_bound(Y,X_21)) != multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))
| multiply(X_228,least_upper_bound(Y,X_21)) = multiply(X_228,least_upper_bound(X_21,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21))),multiply(X_228,least_upper_bound(X_21,Y))) )],[refute_0_2079,refute_0_2080]) ).
cnf(refute_0_2082,plain,
multiply(X_228,least_upper_bound(Y,X_21)) = multiply(X_228,least_upper_bound(X_21,Y)),
inference(resolve,[$cnf( $equal(multiply(X_228,least_upper_bound(Y,X_21)),multiply(X_228,greatest_lower_bound(least_upper_bound(X_21,Y),least_upper_bound(Y,X_21)))) )],[refute_0_2074,refute_0_2081]) ).
cnf(refute_0_2083,plain,
( multiply(X_228,least_upper_bound(Y,X_21)) != multiply(X_228,least_upper_bound(X_21,Y))
| multiply(X_228,least_upper_bound(X_21,Y)) = multiply(X_228,least_upper_bound(Y,X_21)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_228,least_upper_bound(Y,X_21)))),bind(Y0,$fot(multiply(X_228,least_upper_bound(X_21,Y))))]]) ).
cnf(refute_0_2084,plain,
multiply(X_228,least_upper_bound(X_21,Y)) = multiply(X_228,least_upper_bound(Y,X_21)),
inference(resolve,[$cnf( $equal(multiply(X_228,least_upper_bound(Y,X_21)),multiply(X_228,least_upper_bound(X_21,Y))) )],[refute_0_2082,refute_0_2083]) ).
cnf(refute_0_2085,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))),
inference(subst,[],[refute_0_2084:[bind(Y,$fot(identity)),bind(X_21,$fot(greatest_lower_bound(identity,multiply(X_233,X_234)))),bind(X_228,$fot(inverse(greatest_lower_bound(X_233,inverse(X_234)))))]]) ).
cnf(refute_0_2086,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) != multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) != inverse(greatest_lower_bound(X_233,inverse(X_234)))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = inverse(greatest_lower_bound(X_233,inverse(X_234))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_233,inverse(X_234)))))]]) ).
cnf(refute_0_2087,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))) != inverse(greatest_lower_bound(X_233,inverse(X_234)))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = inverse(greatest_lower_bound(X_233,inverse(X_234))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)),multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234))))) )],[refute_0_2085,refute_0_2086]) ).
cnf(refute_0_2088,plain,
multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) = inverse(greatest_lower_bound(X_233,inverse(X_234))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_233,X_234)))),inverse(greatest_lower_bound(X_233,inverse(X_234)))) )],[refute_0_2070,refute_0_2087]) ).
cnf(refute_0_2089,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) != inverse(greatest_lower_bound(X_233,inverse(X_234)))
| multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) != least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)
| inverse(greatest_lower_bound(X_233,inverse(X_234))) = least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)),least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)) ),[0],$fot(inverse(greatest_lower_bound(X_233,inverse(X_234))))]]) ).
cnf(refute_0_2090,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) != least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)
| inverse(greatest_lower_bound(X_233,inverse(X_234))) = least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)),inverse(greatest_lower_bound(X_233,inverse(X_234)))) )],[refute_0_2088,refute_0_2089]) ).
cnf(refute_0_2091,plain,
least_upper_bound(X_76,inverse(X_135)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,multiply(X_135,least_upper_bound(X_76,inverse(X_135))))),
inference(subst,[],[refute_0_529:[bind(X_59,$fot(least_upper_bound(X_76,inverse(X_135)))),bind(X_86,$fot(X_135))]]) ).
cnf(refute_0_2092,plain,
multiply(X_135,least_upper_bound(X_76,inverse(X_135))) = least_upper_bound(identity,multiply(X_135,X_76)),
inference(subst,[],[refute_0_641:[bind(X_75,$fot(X_135))]]) ).
cnf(refute_0_2093,plain,
( multiply(X_135,least_upper_bound(X_76,inverse(X_135))) != least_upper_bound(identity,multiply(X_135,X_76))
| least_upper_bound(X_76,inverse(X_135)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,multiply(X_135,least_upper_bound(X_76,inverse(X_135)))))
| least_upper_bound(X_76,inverse(X_135)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_76,inverse(X_135)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,multiply(X_135,least_upper_bound(X_76,inverse(X_135)))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(X_135,X_76)))]]) ).
cnf(refute_0_2094,plain,
( least_upper_bound(X_76,inverse(X_135)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,multiply(X_135,least_upper_bound(X_76,inverse(X_135)))))
| least_upper_bound(X_76,inverse(X_135)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) ),
inference(resolve,[$cnf( $equal(multiply(X_135,least_upper_bound(X_76,inverse(X_135))),least_upper_bound(identity,multiply(X_135,X_76))) )],[refute_0_2092,refute_0_2093]) ).
cnf(refute_0_2095,plain,
least_upper_bound(X_76,inverse(X_135)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_76,inverse(X_135)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,multiply(X_135,least_upper_bound(X_76,inverse(X_135)))))) )],[refute_0_2091,refute_0_2094]) ).
cnf(refute_0_2096,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(identity,multiply(X_135,X_76)),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(multiply(X_135,X_76))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2097,plain,
multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))))]]) ).
cnf(refute_0_2098,plain,
( multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))) != least_upper_bound(identity,multiply(X_135,X_76))
| multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_135,X_76)))]]) ).
cnf(refute_0_2099,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))) != least_upper_bound(identity,multiply(X_135,X_76))
| multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))) )],[refute_0_2097,refute_0_2098]) ).
cnf(refute_0_2100,plain,
multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))),least_upper_bound(identity,multiply(X_135,X_76))) )],[refute_0_2096,refute_0_2099]) ).
cnf(refute_0_2101,plain,
inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)) = inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),
inference(subst,[],[refute_0_1104:[bind(X_122,$fot(inverse(least_upper_bound(X_76,inverse(X_135))))),bind(X_123,$fot(X_135))]]) ).
cnf(refute_0_2102,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))))]]) ).
cnf(refute_0_2103,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))
| inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)) != inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))) ),[1,0],$fot(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))))]]) ).
cnf(refute_0_2104,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)) != inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))) )],[refute_0_2102,refute_0_2103]) ).
cnf(refute_0_2105,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))))) )],[refute_0_2101,refute_0_2104]) ).
cnf(refute_0_2106,plain,
( multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))))]]) ).
cnf(refute_0_2107,plain,
( multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))) )],[refute_0_2105,refute_0_2106]) ).
cnf(refute_0_2108,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))) )],[refute_0_2100,refute_0_2107]) ).
cnf(refute_0_2109,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))
| least_upper_bound(X_76,inverse(X_135)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))
| least_upper_bound(X_76,inverse(X_135)) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_76,inverse(X_135)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))) ),[1],$fot(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))))]]) ).
cnf(refute_0_2110,plain,
( least_upper_bound(X_76,inverse(X_135)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))
| least_upper_bound(X_76,inverse(X_135)) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76)))),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))) )],[refute_0_2108,refute_0_2109]) ).
cnf(refute_0_2111,plain,
least_upper_bound(X_76,inverse(X_135)) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_76,inverse(X_135)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_76,inverse(X_135))),X_135)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_135,X_76))))) )],[refute_0_2095,refute_0_2110]) ).
cnf(refute_0_2112,plain,
multiply(inverse(X_135),identity) = inverse(X_135),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(X_135)))]]) ).
cnf(refute_0_2113,plain,
least_upper_bound(multiply(inverse(X_135),identity),X_76) = least_upper_bound(multiply(inverse(X_135),identity),X_76),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(X_135),identity),X_76))]]) ).
cnf(refute_0_2114,plain,
( multiply(inverse(X_135),identity) != inverse(X_135)
| least_upper_bound(multiply(inverse(X_135),identity),X_76) != least_upper_bound(multiply(inverse(X_135),identity),X_76)
| least_upper_bound(multiply(inverse(X_135),identity),X_76) = least_upper_bound(inverse(X_135),X_76) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(X_135),identity),X_76),least_upper_bound(multiply(inverse(X_135),identity),X_76)) ),[1,0],$fot(inverse(X_135))]]) ).
cnf(refute_0_2115,plain,
( multiply(inverse(X_135),identity) != inverse(X_135)
| least_upper_bound(multiply(inverse(X_135),identity),X_76) = least_upper_bound(inverse(X_135),X_76) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_135),identity),X_76),least_upper_bound(multiply(inverse(X_135),identity),X_76)) )],[refute_0_2113,refute_0_2114]) ).
cnf(refute_0_2116,plain,
least_upper_bound(multiply(inverse(X_135),identity),X_76) = least_upper_bound(inverse(X_135),X_76),
inference(resolve,[$cnf( $equal(multiply(inverse(X_135),identity),inverse(X_135)) )],[refute_0_2112,refute_0_2115]) ).
cnf(refute_0_2117,plain,
multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))) = least_upper_bound(multiply(inverse(X_58),X_76),multiply(inverse(X_58),multiply(X_58,X_59))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_58))),bind(Y,$fot(X_76)),bind(Z,$fot(multiply(X_58,X_59)))]]) ).
cnf(refute_0_2118,plain,
( multiply(inverse(X_58),multiply(X_58,X_59)) != X_59
| multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))) != least_upper_bound(multiply(inverse(X_58),X_76),multiply(inverse(X_58),multiply(X_58,X_59)))
| multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))) = least_upper_bound(multiply(inverse(X_58),X_76),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))),least_upper_bound(multiply(inverse(X_58),X_76),multiply(inverse(X_58),multiply(X_58,X_59)))) ),[1,1],$fot(X_59)]]) ).
cnf(refute_0_2119,plain,
( multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))) != least_upper_bound(multiply(inverse(X_58),X_76),multiply(inverse(X_58),multiply(X_58,X_59)))
| multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))) = least_upper_bound(multiply(inverse(X_58),X_76),X_59) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),multiply(X_58,X_59)),X_59) )],[refute_0_799,refute_0_2118]) ).
cnf(refute_0_2120,plain,
multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))) = least_upper_bound(multiply(inverse(X_58),X_76),X_59),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),least_upper_bound(X_76,multiply(X_58,X_59))),least_upper_bound(multiply(inverse(X_58),X_76),multiply(inverse(X_58),multiply(X_58,X_59)))) )],[refute_0_2117,refute_0_2119]) ).
cnf(refute_0_2121,plain,
multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(multiply(inverse(X_135),identity),X_76),
inference(subst,[],[refute_0_2120:[bind(X_58,$fot(X_135)),bind(X_59,$fot(X_76)),bind(X_76,$fot(identity))]]) ).
cnf(refute_0_2122,plain,
( multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) != least_upper_bound(multiply(inverse(X_135),identity),X_76)
| least_upper_bound(multiply(inverse(X_135),identity),X_76) != least_upper_bound(inverse(X_135),X_76)
| multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(inverse(X_135),X_76) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(X_135),identity),X_76))),bind(Z0,$fot(least_upper_bound(inverse(X_135),X_76)))]]) ).
cnf(refute_0_2123,plain,
( least_upper_bound(multiply(inverse(X_135),identity),X_76) != least_upper_bound(inverse(X_135),X_76)
| multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(inverse(X_135),X_76) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))),least_upper_bound(multiply(inverse(X_135),identity),X_76)) )],[refute_0_2121,refute_0_2122]) ).
cnf(refute_0_2124,plain,
multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(inverse(X_135),X_76),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_135),identity),X_76),least_upper_bound(inverse(X_135),X_76)) )],[refute_0_2116,refute_0_2123]) ).
cnf(refute_0_2125,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140)))),
inference(subst,[],[refute_0_53:[bind(X_75,$fot(inverse(least_upper_bound(X_141,inverse(X_140))))),bind(X_76,$fot(least_upper_bound(identity,multiply(X_141,X_140))))]]) ).
cnf(refute_0_2126,plain,
X_140 = multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))),
inference(subst,[],[refute_0_1030:[bind(X_59,$fot(X_140)),bind(X_84,$fot(X_141))]]) ).
cnf(refute_0_2127,plain,
( X_140 != multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140)))
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))) = X_140 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_140)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140)))))]]) ).
cnf(refute_0_2128,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))) = X_140,
inference(resolve,[$cnf( $equal(X_140,multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140)))) )],[refute_0_2126,refute_0_2127]) ).
cnf(refute_0_2129,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))) != X_140
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) != least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))))
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)),least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))))) ),[1,1],$fot(X_140)]]) ).
cnf(refute_0_2130,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) != least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))))
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))),X_140) )],[refute_0_2128,refute_0_2129]) ).
cnf(refute_0_2131,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)),least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))))) )],[refute_0_2125,refute_0_2130]) ).
cnf(refute_0_2132,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))) = least_upper_bound(identity,multiply(X_141,X_140)),
inference(subst,[],[refute_0_221:[bind(X_16,$fot(multiply(X_141,X_140))),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_2133,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) = multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))))]]) ).
cnf(refute_0_2134,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) != multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))))
| least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))) != least_upper_bound(identity,multiply(X_141,X_140))
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) = multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_141,X_140)))]]) ).
cnf(refute_0_2135,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))) != least_upper_bound(identity,multiply(X_141,X_140))
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) = multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))))) )],[refute_0_2133,refute_0_2134]) ).
cnf(refute_0_2136,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) = multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))),least_upper_bound(identity,multiply(X_141,X_140))) )],[refute_0_2132,refute_0_2135]) ).
cnf(refute_0_2137,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))) != X_140
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) != multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140)))
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) = X_140 ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))))),bind(Z0,$fot(X_140))]]) ).
cnf(refute_0_2138,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))) != X_140
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) = X_140 ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140)))) )],[refute_0_2136,refute_0_2137]) ).
cnf(refute_0_2139,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) = X_140,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,multiply(X_141,X_140))),X_140) )],[refute_0_2128,refute_0_2138]) ).
cnf(refute_0_2140,plain,
inverse(multiply(inverse(least_upper_bound(X_124,identity)),X_23)) = multiply(inverse(X_23),least_upper_bound(X_124,identity)),
inference(subst,[],[refute_0_538:[bind(X,$fot(least_upper_bound(X_124,identity)))]]) ).
cnf(refute_0_2141,plain,
( inverse(multiply(inverse(least_upper_bound(X_124,identity)),X_23)) != multiply(inverse(X_23),least_upper_bound(X_124,identity))
| inverse(least_upper_bound(X_124,identity)) != inverse(least_upper_bound(identity,X_124))
| inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)) = multiply(inverse(X_23),least_upper_bound(X_124,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_124,identity)),X_23)),multiply(inverse(X_23),least_upper_bound(X_124,identity))) ),[0,0,0],$fot(inverse(least_upper_bound(identity,X_124)))]]) ).
cnf(refute_0_2142,plain,
( inverse(multiply(inverse(least_upper_bound(X_124,identity)),X_23)) != multiply(inverse(X_23),least_upper_bound(X_124,identity))
| inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)) = multiply(inverse(X_23),least_upper_bound(X_124,identity)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_124,identity)),inverse(least_upper_bound(identity,X_124))) )],[refute_0_670,refute_0_2141]) ).
cnf(refute_0_2143,plain,
inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)) = multiply(inverse(X_23),least_upper_bound(X_124,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_124,identity)),X_23)),multiply(inverse(X_23),least_upper_bound(X_124,identity))) )],[refute_0_2140,refute_0_2142]) ).
cnf(refute_0_2144,plain,
inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)) = multiply(inverse(X_23),least_upper_bound(identity,X_124)),
inference(subst,[],[refute_0_538:[bind(X,$fot(least_upper_bound(identity,X_124)))]]) ).
cnf(refute_0_2145,plain,
( inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)) != multiply(inverse(X_23),least_upper_bound(X_124,identity))
| inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)) != multiply(inverse(X_23),least_upper_bound(identity,X_124))
| multiply(inverse(X_23),least_upper_bound(identity,X_124)) = multiply(inverse(X_23),least_upper_bound(X_124,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)),multiply(inverse(X_23),least_upper_bound(X_124,identity))) ),[0],$fot(multiply(inverse(X_23),least_upper_bound(identity,X_124)))]]) ).
cnf(refute_0_2146,plain,
( inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)) != multiply(inverse(X_23),least_upper_bound(X_124,identity))
| multiply(inverse(X_23),least_upper_bound(identity,X_124)) = multiply(inverse(X_23),least_upper_bound(X_124,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)),multiply(inverse(X_23),least_upper_bound(identity,X_124))) )],[refute_0_2144,refute_0_2145]) ).
cnf(refute_0_2147,plain,
multiply(inverse(X_23),least_upper_bound(identity,X_124)) = multiply(inverse(X_23),least_upper_bound(X_124,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,X_124)),X_23)),multiply(inverse(X_23),least_upper_bound(X_124,identity))) )],[refute_0_2143,refute_0_2146]) ).
cnf(refute_0_2148,plain,
( multiply(inverse(X_23),least_upper_bound(identity,X_124)) != multiply(inverse(X_23),least_upper_bound(X_124,identity))
| multiply(inverse(X_23),least_upper_bound(X_124,identity)) = multiply(inverse(X_23),least_upper_bound(identity,X_124)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(X_23),least_upper_bound(identity,X_124)))),bind(Y0,$fot(multiply(inverse(X_23),least_upper_bound(X_124,identity))))]]) ).
cnf(refute_0_2149,plain,
multiply(inverse(X_23),least_upper_bound(X_124,identity)) = multiply(inverse(X_23),least_upper_bound(identity,X_124)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_23),least_upper_bound(identity,X_124)),multiply(inverse(X_23),least_upper_bound(X_124,identity))) )],[refute_0_2147,refute_0_2148]) ).
cnf(refute_0_2150,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))),
inference(subst,[],[refute_0_2149:[bind(X_124,$fot(least_upper_bound(identity,multiply(X_141,X_140)))),bind(X_23,$fot(least_upper_bound(X_141,inverse(X_140))))]]) ).
cnf(refute_0_2151,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) != X_140
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) != multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))))
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = X_140 ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))))),bind(Z0,$fot(X_140))]]) ).
cnf(refute_0_2152,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))) != X_140
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = X_140 ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)),multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140))))) )],[refute_0_2150,refute_0_2151]) ).
cnf(refute_0_2153,plain,
multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) = X_140,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_141,X_140)))),X_140) )],[refute_0_2139,refute_0_2152]) ).
cnf(refute_0_2154,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) != X_140
| multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) != least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)
| X_140 = least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)),least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)) ),[0],$fot(X_140)]]) ).
cnf(refute_0_2155,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) != least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)
| X_140 = least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)),X_140) )],[refute_0_2153,refute_0_2154]) ).
cnf(refute_0_2156,plain,
least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140) = least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140)))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_140)),bind(Y,$fot(inverse(least_upper_bound(X_141,inverse(X_140)))))]]) ).
cnf(refute_0_2157,plain,
( X_140 != least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)
| least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140) != least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140))))
| X_140 = least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_140,least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140))))) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140))]]) ).
cnf(refute_0_2158,plain,
( X_140 != least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)
| X_140 = least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140),least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140))))) )],[refute_0_2156,refute_0_2157]) ).
cnf(refute_0_2159,plain,
( multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)) != least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)
| X_140 = least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140)))) ),
inference(resolve,[$cnf( $equal(X_140,least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)) )],[refute_0_2155,refute_0_2158]) ).
cnf(refute_0_2160,plain,
X_140 = least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_141,inverse(X_140))),least_upper_bound(least_upper_bound(identity,multiply(X_141,X_140)),identity)),least_upper_bound(inverse(least_upper_bound(X_141,inverse(X_140))),X_140)) )],[refute_0_2131,refute_0_2159]) ).
cnf(refute_0_2161,plain,
( X_140 != least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140))))
| least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140)))) = X_140 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_140)),bind(Y0,$fot(least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140))))))]]) ).
cnf(refute_0_2162,plain,
least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140)))) = X_140,
inference(resolve,[$cnf( $equal(X_140,least_upper_bound(X_140,inverse(least_upper_bound(X_141,inverse(X_140))))) )],[refute_0_2160,refute_0_2161]) ).
cnf(refute_0_2163,plain,
least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))) = X_135,
inference(subst,[],[refute_0_2162:[bind(X_140,$fot(X_135)),bind(X_141,$fot(X_76))]]) ).
cnf(refute_0_2164,plain,
inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))) = inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))))]]) ).
cnf(refute_0_2165,plain,
( inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))) != inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))))
| least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))) != X_135
| inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))) = inverse(X_135) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))))) ),[1,0],$fot(X_135)]]) ).
cnf(refute_0_2166,plain,
( least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))) != X_135
| inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))) = inverse(X_135) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))))) )],[refute_0_2164,refute_0_2165]) ).
cnf(refute_0_2167,plain,
inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))) = inverse(X_135),
inference(resolve,[$cnf( $equal(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135)))),X_135) )],[refute_0_2163,refute_0_2166]) ).
cnf(refute_0_2168,plain,
multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) = multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))))]]) ).
cnf(refute_0_2169,plain,
( multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))
| inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))) != inverse(X_135)
| multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) = multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))) ),[1,0],$fot(inverse(X_135))]]) ).
cnf(refute_0_2170,plain,
( inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))) != inverse(X_135)
| multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) = multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))) )],[refute_0_2168,refute_0_2169]) ).
cnf(refute_0_2171,plain,
multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) = multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),inverse(X_135)) )],[refute_0_2167,refute_0_2170]) ).
cnf(refute_0_2172,plain,
( multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) != least_upper_bound(inverse(X_135),X_76)
| multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) != multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76)))
| multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(inverse(X_135),X_76) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))))),bind(Y0,$fot(multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))))),bind(Z0,$fot(least_upper_bound(inverse(X_135),X_76)))]]) ).
cnf(refute_0_2173,plain,
( multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))) != least_upper_bound(inverse(X_135),X_76)
| multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(inverse(X_135),X_76) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76)))) )],[refute_0_2171,refute_0_2172]) ).
cnf(refute_0_2174,plain,
multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) = least_upper_bound(inverse(X_135),X_76),
inference(resolve,[$cnf( $equal(multiply(inverse(X_135),least_upper_bound(identity,multiply(X_135,X_76))),least_upper_bound(inverse(X_135),X_76)) )],[refute_0_2124,refute_0_2173]) ).
cnf(refute_0_2175,plain,
( multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))) != least_upper_bound(inverse(X_135),X_76)
| least_upper_bound(X_76,inverse(X_135)) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))
| least_upper_bound(X_76,inverse(X_135)) = least_upper_bound(inverse(X_135),X_76) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_76,inverse(X_135)),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))) ),[1],$fot(least_upper_bound(inverse(X_135),X_76))]]) ).
cnf(refute_0_2176,plain,
( least_upper_bound(X_76,inverse(X_135)) != multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))
| least_upper_bound(X_76,inverse(X_135)) = least_upper_bound(inverse(X_135),X_76) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76))),least_upper_bound(inverse(X_135),X_76)) )],[refute_0_2174,refute_0_2175]) ).
cnf(refute_0_2177,plain,
least_upper_bound(X_76,inverse(X_135)) = least_upper_bound(inverse(X_135),X_76),
inference(resolve,[$cnf( $equal(least_upper_bound(X_76,inverse(X_135)),multiply(inverse(least_upper_bound(X_135,inverse(least_upper_bound(X_76,inverse(X_135))))),least_upper_bound(identity,multiply(X_135,X_76)))) )],[refute_0_2111,refute_0_2176]) ).
cnf(refute_0_2178,plain,
( least_upper_bound(X_76,inverse(X_135)) != least_upper_bound(inverse(X_135),X_76)
| least_upper_bound(inverse(X_135),X_76) = least_upper_bound(X_76,inverse(X_135)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X_76,inverse(X_135)))),bind(Y0,$fot(least_upper_bound(inverse(X_135),X_76)))]]) ).
cnf(refute_0_2179,plain,
least_upper_bound(inverse(X_135),X_76) = least_upper_bound(X_76,inverse(X_135)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_76,inverse(X_135)),least_upper_bound(inverse(X_135),X_76)) )],[refute_0_2177,refute_0_2178]) ).
cnf(refute_0_2180,plain,
least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234) = least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234)))),
inference(subst,[],[refute_0_2179:[bind(X_135,$fot(greatest_lower_bound(X_233,inverse(X_234)))),bind(X_76,$fot(X_234))]]) ).
cnf(refute_0_2181,plain,
( inverse(greatest_lower_bound(X_233,inverse(X_234))) != least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)
| least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234) != least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234))))
| inverse(greatest_lower_bound(X_233,inverse(X_234))) = least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234))))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234))]]) ).
cnf(refute_0_2182,plain,
( inverse(greatest_lower_bound(X_233,inverse(X_234))) != least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)
| inverse(greatest_lower_bound(X_233,inverse(X_234))) = least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234),least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234))))) )],[refute_0_2180,refute_0_2181]) ).
cnf(refute_0_2183,plain,
( multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)) != least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)
| inverse(greatest_lower_bound(X_233,inverse(X_234))) = least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)) )],[refute_0_2090,refute_0_2182]) ).
cnf(refute_0_2184,plain,
inverse(greatest_lower_bound(X_233,inverse(X_234))) = least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(greatest_lower_bound(identity,multiply(X_233,X_234)),identity)),least_upper_bound(inverse(greatest_lower_bound(X_233,inverse(X_234))),X_234)) )],[refute_0_2061,refute_0_2183]) ).
cnf(refute_0_2185,plain,
( inverse(greatest_lower_bound(X_233,inverse(X_234))) != least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234))))
| least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234)))) = inverse(greatest_lower_bound(X_233,inverse(X_234))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(X_233,inverse(X_234))))),bind(Y0,$fot(least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234))))))]]) ).
cnf(refute_0_2186,plain,
least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234)))) = inverse(greatest_lower_bound(X_233,inverse(X_234))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_233,inverse(X_234))),least_upper_bound(X_234,inverse(greatest_lower_bound(X_233,inverse(X_234))))) )],[refute_0_2184,refute_0_2185]) ).
cnf(refute_0_2187,plain,
least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))) = inverse(greatest_lower_bound(identity,inverse(X_386))),
inference(subst,[],[refute_0_2186:[bind(X_233,$fot(identity)),bind(X_234,$fot(X_386))]]) ).
cnf(refute_0_2188,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(subst,[],[refute_0_487:[bind(X_95,$fot(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_2189,plain,
least_upper_bound(identity,greatest_lower_bound(identity,Y)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_2190,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,greatest_lower_bound(identity,Y)) != identity
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_2191,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,Y)),identity) )],[refute_0_2189,refute_0_2190]) ).
cnf(refute_0_2192,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_2188,refute_0_2191]) ).
cnf(refute_0_2193,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = inverse(greatest_lower_bound(identity,Y)),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_2194,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != inverse(greatest_lower_bound(identity,Y))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_2195,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_2193,refute_0_2194]) ).
cnf(refute_0_2196,plain,
inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_2192,refute_0_2195]) ).
cnf(refute_0_2197,plain,
( inverse(greatest_lower_bound(identity,Y)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))))]]) ).
cnf(refute_0_2198,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_2196,refute_0_2197]) ).
cnf(refute_0_2199,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))) = inverse(greatest_lower_bound(identity,inverse(X_386))),
inference(subst,[],[refute_0_2198:[bind(Y,$fot(inverse(X_386)))]]) ).
cnf(refute_0_2200,plain,
least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) = least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))))]]) ).
cnf(refute_0_2201,plain,
( least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) != least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) = least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))),least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_386))))]]) ).
cnf(refute_0_2202,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) = least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))),least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))))) )],[refute_0_2200,refute_0_2201]) ).
cnf(refute_0_2203,plain,
least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) = least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))),inverse(greatest_lower_bound(identity,inverse(X_386)))) )],[refute_0_2199,refute_0_2202]) ).
cnf(refute_0_2204,plain,
( least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) != least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386))))
| least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) = inverse(greatest_lower_bound(identity,inverse(X_386))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))))),bind(Y0,$fot(least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X_386)))))]]) ).
cnf(refute_0_2205,plain,
( least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) = inverse(greatest_lower_bound(identity,inverse(X_386))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))),least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386))))) )],[refute_0_2203,refute_0_2204]) ).
cnf(refute_0_2206,plain,
least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) = inverse(greatest_lower_bound(identity,inverse(X_386))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_386,inverse(greatest_lower_bound(identity,inverse(X_386)))),inverse(greatest_lower_bound(identity,inverse(X_386)))) )],[refute_0_2187,refute_0_2205]) ).
cnf(refute_0_2207,plain,
least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))),
inference(subst,[],[refute_0_210:[bind(X,$fot(X_386)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(greatest_lower_bound(identity,inverse(X_386)))))]]) ).
cnf(refute_0_2208,plain,
( least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) != least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))))
| least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = inverse(greatest_lower_bound(identity,inverse(X_386))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))))),bind(Y0,$fot(least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X_386)))))]]) ).
cnf(refute_0_2209,plain,
( least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = inverse(greatest_lower_bound(identity,inverse(X_386))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))),least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386)))))) )],[refute_0_2207,refute_0_2208]) ).
cnf(refute_0_2210,plain,
least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) = inverse(greatest_lower_bound(identity,inverse(X_386))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_386,least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(X_386))))),inverse(greatest_lower_bound(identity,inverse(X_386)))) )],[refute_0_2206,refute_0_2209]) ).
cnf(refute_0_2211,plain,
( least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) != inverse(greatest_lower_bound(identity,inverse(X_386)))
| least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) != least_upper_bound(X_386,identity)
| inverse(greatest_lower_bound(identity,inverse(X_386))) = least_upper_bound(X_386,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))),least_upper_bound(X_386,identity)) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(X_386))))]]) ).
cnf(refute_0_2212,plain,
( least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))) != least_upper_bound(X_386,identity)
| inverse(greatest_lower_bound(identity,inverse(X_386))) = least_upper_bound(X_386,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))),inverse(greatest_lower_bound(identity,inverse(X_386)))) )],[refute_0_2210,refute_0_2211]) ).
cnf(refute_0_2213,plain,
inverse(greatest_lower_bound(identity,inverse(X_386))) = least_upper_bound(X_386,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_386,identity),inverse(greatest_lower_bound(identity,inverse(X_386)))),least_upper_bound(X_386,identity)) )],[refute_0_2040,refute_0_2212]) ).
cnf(refute_0_2214,plain,
inverse(greatest_lower_bound(identity,inverse(inverse(X)))) = least_upper_bound(inverse(X),identity),
inference(subst,[],[refute_0_2213:[bind(X_386,$fot(inverse(X)))]]) ).
cnf(refute_0_2215,plain,
( inverse(greatest_lower_bound(identity,inverse(inverse(X)))) != least_upper_bound(inverse(X),identity)
| least_upper_bound(inverse(X),identity) != least_upper_bound(identity,inverse(X))
| inverse(greatest_lower_bound(identity,inverse(inverse(X)))) = least_upper_bound(identity,inverse(X)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X)))))),bind(Y0,$fot(least_upper_bound(inverse(X),identity))),bind(Z0,$fot(least_upper_bound(identity,inverse(X))))]]) ).
cnf(refute_0_2216,plain,
( least_upper_bound(inverse(X),identity) != least_upper_bound(identity,inverse(X))
| inverse(greatest_lower_bound(identity,inverse(inverse(X)))) = least_upper_bound(identity,inverse(X)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X)))),least_upper_bound(inverse(X),identity)) )],[refute_0_2214,refute_0_2215]) ).
cnf(refute_0_2217,plain,
inverse(greatest_lower_bound(identity,inverse(inverse(X)))) = least_upper_bound(identity,inverse(X)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),identity),least_upper_bound(identity,inverse(X))) )],[refute_0_2033,refute_0_2216]) ).
cnf(refute_0_2218,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)))),
inference(subst,[],[refute_0_1849:[bind(X_35,$fot(inverse(greatest_lower_bound(identity,inverse(X))))),bind(X_79,$fot(greatest_lower_bound(identity,X)))]]) ).
cnf(refute_0_2219,plain,
inverse(inverse(X)) = multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))),
inference(subst,[],[refute_0_1723:[bind(X_106,$fot(inverse(X)))]]) ).
cnf(refute_0_2220,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X))))
| X = multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X))))) ),[0],$fot(X)]]) ).
cnf(refute_0_2221,plain,
( inverse(inverse(X)) != multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X))))
| X = multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_2220]) ).
cnf(refute_0_2222,plain,
X = multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X))))) )],[refute_0_2219,refute_0_2221]) ).
cnf(refute_0_2223,plain,
greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,inverse(inverse(X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X))))]]) ).
cnf(refute_0_2224,plain,
( greatest_lower_bound(identity,inverse(inverse(X))) != greatest_lower_bound(identity,inverse(inverse(X)))
| inverse(inverse(X)) != X
| greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,X) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_2225,plain,
( inverse(inverse(X)) != X
| greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) )],[refute_0_2223,refute_0_2224]) ).
cnf(refute_0_2226,plain,
greatest_lower_bound(identity,inverse(inverse(X))) = greatest_lower_bound(identity,X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p20x_2,refute_0_2225]) ).
cnf(refute_0_2227,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))))]]) ).
cnf(refute_0_2228,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X))))
| greatest_lower_bound(identity,inverse(inverse(X))) != greatest_lower_bound(identity,X)
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X))))) ),[1,1],$fot(greatest_lower_bound(identity,X))]]) ).
cnf(refute_0_2229,plain,
( greatest_lower_bound(identity,inverse(inverse(X))) != greatest_lower_bound(identity,X)
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X))))) )],[refute_0_2227,refute_0_2228]) ).
cnf(refute_0_2230,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X))),greatest_lower_bound(identity,X)) )],[refute_0_2226,refute_0_2229]) ).
cnf(refute_0_2231,plain,
inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) = multiply(inverse(greatest_lower_bound(X_128,identity)),X),
inference(subst,[],[refute_0_538:[bind(X_23,$fot(greatest_lower_bound(X_128,identity)))]]) ).
cnf(refute_0_2232,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(identity),X_127))) = multiply(inverse(greatest_lower_bound(identity,X_127)),identity),
inference(subst,[],[refute_0_1772:[bind(X_40,$fot(identity)),bind(X_41,$fot(X_127))]]) ).
cnf(refute_0_2233,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(identity),X_127))) != multiply(inverse(greatest_lower_bound(identity,X_127)),identity)
| inverse(identity) != identity
| inverse(greatest_lower_bound(identity,multiply(identity,X_127))) = multiply(inverse(greatest_lower_bound(identity,X_127)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(identity),X_127))),multiply(inverse(greatest_lower_bound(identity,X_127)),identity)) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_2234,plain,
( inverse(greatest_lower_bound(identity,multiply(inverse(identity),X_127))) != multiply(inverse(greatest_lower_bound(identity,X_127)),identity)
| inverse(greatest_lower_bound(identity,multiply(identity,X_127))) = multiply(inverse(greatest_lower_bound(identity,X_127)),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p20x_1,refute_0_2233]) ).
cnf(refute_0_2235,plain,
inverse(greatest_lower_bound(identity,multiply(identity,X_127))) = multiply(inverse(greatest_lower_bound(identity,X_127)),identity),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(identity),X_127))),multiply(inverse(greatest_lower_bound(identity,X_127)),identity)) )],[refute_0_2232,refute_0_2234]) ).
cnf(refute_0_2236,plain,
multiply(identity,greatest_lower_bound(X_127,identity)) = greatest_lower_bound(X_127,identity),
inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_127,identity)))]]) ).
cnf(refute_0_2237,plain,
greatest_lower_bound(identity,multiply(identity,X_127)) = multiply(identity,greatest_lower_bound(X_127,identity)),
inference(subst,[],[refute_0_337:[bind(X_35,$fot(identity)),bind(X_36,$fot(X_127))]]) ).
cnf(refute_0_2238,plain,
( multiply(identity,greatest_lower_bound(X_127,identity)) != greatest_lower_bound(X_127,identity)
| greatest_lower_bound(identity,multiply(identity,X_127)) != multiply(identity,greatest_lower_bound(X_127,identity))
| greatest_lower_bound(identity,multiply(identity,X_127)) = greatest_lower_bound(X_127,identity) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,X_127)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_127,identity)))),bind(Z0,$fot(greatest_lower_bound(X_127,identity)))]]) ).
cnf(refute_0_2239,plain,
( multiply(identity,greatest_lower_bound(X_127,identity)) != greatest_lower_bound(X_127,identity)
| greatest_lower_bound(identity,multiply(identity,X_127)) = greatest_lower_bound(X_127,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_127)),multiply(identity,greatest_lower_bound(X_127,identity))) )],[refute_0_2237,refute_0_2238]) ).
cnf(refute_0_2240,plain,
greatest_lower_bound(identity,multiply(identity,X_127)) = greatest_lower_bound(X_127,identity),
inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_127,identity)),greatest_lower_bound(X_127,identity)) )],[refute_0_2236,refute_0_2239]) ).
cnf(refute_0_2241,plain,
inverse(greatest_lower_bound(identity,multiply(identity,X_127))) = inverse(greatest_lower_bound(identity,multiply(identity,X_127))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(identity,X_127))))]]) ).
cnf(refute_0_2242,plain,
( greatest_lower_bound(identity,multiply(identity,X_127)) != greatest_lower_bound(X_127,identity)
| inverse(greatest_lower_bound(identity,multiply(identity,X_127))) != inverse(greatest_lower_bound(identity,multiply(identity,X_127)))
| inverse(greatest_lower_bound(identity,multiply(identity,X_127))) = inverse(greatest_lower_bound(X_127,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,X_127))),inverse(greatest_lower_bound(identity,multiply(identity,X_127)))) ),[1,0],$fot(greatest_lower_bound(X_127,identity))]]) ).
cnf(refute_0_2243,plain,
( greatest_lower_bound(identity,multiply(identity,X_127)) != greatest_lower_bound(X_127,identity)
| inverse(greatest_lower_bound(identity,multiply(identity,X_127))) = inverse(greatest_lower_bound(X_127,identity)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,X_127))),inverse(greatest_lower_bound(identity,multiply(identity,X_127)))) )],[refute_0_2241,refute_0_2242]) ).
cnf(refute_0_2244,plain,
inverse(greatest_lower_bound(identity,multiply(identity,X_127))) = inverse(greatest_lower_bound(X_127,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_127)),greatest_lower_bound(X_127,identity)) )],[refute_0_2240,refute_0_2243]) ).
cnf(refute_0_2245,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,X_127))) != multiply(inverse(greatest_lower_bound(identity,X_127)),identity)
| inverse(greatest_lower_bound(identity,multiply(identity,X_127))) != inverse(greatest_lower_bound(X_127,identity))
| inverse(greatest_lower_bound(X_127,identity)) = multiply(inverse(greatest_lower_bound(identity,X_127)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,X_127))),multiply(inverse(greatest_lower_bound(identity,X_127)),identity)) ),[0],$fot(inverse(greatest_lower_bound(X_127,identity)))]]) ).
cnf(refute_0_2246,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,X_127))) != multiply(inverse(greatest_lower_bound(identity,X_127)),identity)
| inverse(greatest_lower_bound(X_127,identity)) = multiply(inverse(greatest_lower_bound(identity,X_127)),identity) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,X_127))),inverse(greatest_lower_bound(X_127,identity))) )],[refute_0_2244,refute_0_2245]) ).
cnf(refute_0_2247,plain,
multiply(inverse(greatest_lower_bound(identity,X_127)),identity) = inverse(greatest_lower_bound(identity,X_127)),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_127))))]]) ).
cnf(refute_0_2248,plain,
( multiply(inverse(greatest_lower_bound(identity,X_127)),identity) != inverse(greatest_lower_bound(identity,X_127))
| inverse(greatest_lower_bound(X_127,identity)) != multiply(inverse(greatest_lower_bound(identity,X_127)),identity)
| inverse(greatest_lower_bound(X_127,identity)) = inverse(greatest_lower_bound(identity,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_127,identity)),multiply(inverse(greatest_lower_bound(identity,X_127)),identity)) ),[1],$fot(inverse(greatest_lower_bound(identity,X_127)))]]) ).
cnf(refute_0_2249,plain,
( inverse(greatest_lower_bound(X_127,identity)) != multiply(inverse(greatest_lower_bound(identity,X_127)),identity)
| inverse(greatest_lower_bound(X_127,identity)) = inverse(greatest_lower_bound(identity,X_127)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_127)),identity),inverse(greatest_lower_bound(identity,X_127))) )],[refute_0_2247,refute_0_2248]) ).
cnf(refute_0_2250,plain,
( inverse(greatest_lower_bound(identity,multiply(identity,X_127))) != multiply(inverse(greatest_lower_bound(identity,X_127)),identity)
| inverse(greatest_lower_bound(X_127,identity)) = inverse(greatest_lower_bound(identity,X_127)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_127,identity)),multiply(inverse(greatest_lower_bound(identity,X_127)),identity)) )],[refute_0_2246,refute_0_2249]) ).
cnf(refute_0_2251,plain,
inverse(greatest_lower_bound(X_127,identity)) = inverse(greatest_lower_bound(identity,X_127)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(identity,X_127))),multiply(inverse(greatest_lower_bound(identity,X_127)),identity)) )],[refute_0_2235,refute_0_2250]) ).
cnf(refute_0_2252,plain,
inverse(greatest_lower_bound(X_128,identity)) = inverse(greatest_lower_bound(identity,X_128)),
inference(subst,[],[refute_0_2251:[bind(X_127,$fot(X_128))]]) ).
cnf(refute_0_2253,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) != multiply(inverse(greatest_lower_bound(X_128,identity)),X)
| inverse(greatest_lower_bound(X_128,identity)) != inverse(greatest_lower_bound(identity,X_128))
| inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) = multiply(inverse(greatest_lower_bound(identity,X_128)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))),multiply(inverse(greatest_lower_bound(X_128,identity)),X)) ),[1,0],$fot(inverse(greatest_lower_bound(identity,X_128)))]]) ).
cnf(refute_0_2254,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) != multiply(inverse(greatest_lower_bound(X_128,identity)),X)
| inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) = multiply(inverse(greatest_lower_bound(identity,X_128)),X) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_128,identity)),inverse(greatest_lower_bound(identity,X_128))) )],[refute_0_2252,refute_0_2253]) ).
cnf(refute_0_2255,plain,
inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) = multiply(inverse(greatest_lower_bound(identity,X_128)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))),multiply(inverse(greatest_lower_bound(X_128,identity)),X)) )],[refute_0_2231,refute_0_2254]) ).
cnf(refute_0_2256,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) != multiply(inverse(greatest_lower_bound(X_128,identity)),X)
| inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) != multiply(inverse(greatest_lower_bound(identity,X_128)),X)
| multiply(inverse(greatest_lower_bound(X_128,identity)),X) = multiply(inverse(greatest_lower_bound(identity,X_128)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))),multiply(inverse(greatest_lower_bound(identity,X_128)),X)) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_128,identity)),X))]]) ).
cnf(refute_0_2257,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))) != multiply(inverse(greatest_lower_bound(identity,X_128)),X)
| multiply(inverse(greatest_lower_bound(X_128,identity)),X) = multiply(inverse(greatest_lower_bound(identity,X_128)),X) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))),multiply(inverse(greatest_lower_bound(X_128,identity)),X)) )],[refute_0_2231,refute_0_2256]) ).
cnf(refute_0_2258,plain,
multiply(inverse(greatest_lower_bound(X_128,identity)),X) = multiply(inverse(greatest_lower_bound(identity,X_128)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_128,identity))),multiply(inverse(greatest_lower_bound(identity,X_128)),X)) )],[refute_0_2255,refute_0_2257]) ).
cnf(refute_0_2259,plain,
multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))),
inference(subst,[],[refute_0_2258:[bind(X,$fot(greatest_lower_bound(identity,inverse(inverse(X))))),bind(X_128,$fot(inverse(X)))]]) ).
cnf(refute_0_2260,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))
| multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X))))
| multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))]]) ).
cnf(refute_0_2261,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))
| multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X))))) )],[refute_0_2259,refute_0_2260]) ).
cnf(refute_0_2262,plain,
multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))) )],[refute_0_2230,refute_0_2261]) ).
cnf(refute_0_2263,plain,
( X != multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X))))
| multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))
| X = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))))]]) ).
cnf(refute_0_2264,plain,
( X != multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X))))
| X = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X)))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))) )],[refute_0_2262,refute_0_2263]) ).
cnf(refute_0_2265,plain,
X = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)),
inference(resolve,[$cnf( $equal(X,multiply(inverse(greatest_lower_bound(inverse(X),identity)),greatest_lower_bound(identity,inverse(inverse(X))))) )],[refute_0_2222,refute_0_2264]) ).
cnf(refute_0_2266,plain,
( X != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) = X ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))]]) ).
cnf(refute_0_2267,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) = X,
inference(resolve,[$cnf( $equal(X,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))) )],[refute_0_2265,refute_0_2266]) ).
cnf(refute_0_2268,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)) != X
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))) ),[1,1,1],$fot(X)]]) ).
cnf(refute_0_2269,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)),X) )],[refute_0_2267,refute_0_2268]) ).
cnf(refute_0_2270,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))) )],[refute_0_2218,refute_0_2269]) ).
cnf(refute_0_2271,plain,
inverse(multiply(X,identity)) = inverse(multiply(X,identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(X,identity)))]]) ).
cnf(refute_0_2272,plain,
( multiply(X,identity) != X
| inverse(multiply(X,identity)) != inverse(multiply(X,identity))
| inverse(multiply(X,identity)) = inverse(X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,identity)),inverse(multiply(X,identity))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_2273,plain,
( multiply(X,identity) != X
| inverse(multiply(X,identity)) = inverse(X) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X,identity)),inverse(multiply(X,identity))) )],[refute_0_2271,refute_0_2272]) ).
cnf(refute_0_2274,plain,
inverse(multiply(X,identity)) = inverse(X),
inference(resolve,[$cnf( $equal(multiply(X,identity),X) )],[refute_0_561,refute_0_2273]) ).
cnf(refute_0_2275,plain,
greatest_lower_bound(identity,inverse(multiply(X,identity))) = greatest_lower_bound(identity,inverse(multiply(X,identity))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(X,identity))))]]) ).
cnf(refute_0_2276,plain,
( greatest_lower_bound(identity,inverse(multiply(X,identity))) != greatest_lower_bound(identity,inverse(multiply(X,identity)))
| inverse(multiply(X,identity)) != inverse(X)
| greatest_lower_bound(identity,inverse(multiply(X,identity))) = greatest_lower_bound(identity,inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X,identity))),greatest_lower_bound(identity,inverse(multiply(X,identity)))) ),[1,1],$fot(inverse(X))]]) ).
cnf(refute_0_2277,plain,
( inverse(multiply(X,identity)) != inverse(X)
| greatest_lower_bound(identity,inverse(multiply(X,identity))) = greatest_lower_bound(identity,inverse(X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X,identity))),greatest_lower_bound(identity,inverse(multiply(X,identity)))) )],[refute_0_2275,refute_0_2276]) ).
cnf(refute_0_2278,plain,
greatest_lower_bound(identity,inverse(multiply(X,identity))) = greatest_lower_bound(identity,inverse(X)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,identity)),inverse(X)) )],[refute_0_2274,refute_0_2277]) ).
cnf(refute_0_2279,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))) = inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))))]]) ).
cnf(refute_0_2280,plain,
( greatest_lower_bound(identity,inverse(multiply(X,identity))) != greatest_lower_bound(identity,inverse(X))
| inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))) != inverse(greatest_lower_bound(identity,inverse(multiply(X,identity))))
| inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))) = inverse(greatest_lower_bound(identity,inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))),inverse(greatest_lower_bound(identity,inverse(multiply(X,identity))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X)))]]) ).
cnf(refute_0_2281,plain,
( greatest_lower_bound(identity,inverse(multiply(X,identity))) != greatest_lower_bound(identity,inverse(X))
| inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))),inverse(greatest_lower_bound(identity,inverse(multiply(X,identity))))) )],[refute_0_2279,refute_0_2280]) ).
cnf(refute_0_2282,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X,identity))),greatest_lower_bound(identity,inverse(X))) )],[refute_0_2278,refute_0_2281]) ).
cnf(refute_0_2283,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) = inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))),
inference(subst,[],[refute_0_1781:[bind(X_126,$fot(identity))]]) ).
cnf(refute_0_2284,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) != inverse(greatest_lower_bound(identity,inverse(multiply(X,identity))))
| inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))) != inverse(greatest_lower_bound(identity,inverse(X)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_2285,plain,
( inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))) != inverse(greatest_lower_bound(identity,inverse(X)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity),inverse(greatest_lower_bound(identity,inverse(multiply(X,identity))))) )],[refute_0_2283,refute_0_2284]) ).
cnf(refute_0_2286,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X,identity)))),inverse(greatest_lower_bound(identity,inverse(X)))) )],[refute_0_2282,refute_0_2285]) ).
cnf(refute_0_2287,plain,
greatest_lower_bound(identity,least_upper_bound(identity,inverse(X))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_2288,plain,
multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = greatest_lower_bound(X_55,multiply(X_55,greatest_lower_bound(inverse(X_55),X_37))),
inference(subst,[],[refute_0_182:[bind(X_35,$fot(X_55)),bind(X_36,$fot(greatest_lower_bound(inverse(X_55),X_37)))]]) ).
cnf(refute_0_2289,plain,
multiply(X_55,greatest_lower_bound(inverse(X_55),X_37)) = greatest_lower_bound(identity,multiply(X_55,X_37)),
inference(subst,[],[refute_0_1893:[bind(X_35,$fot(X_55))]]) ).
cnf(refute_0_2290,plain,
( multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) != greatest_lower_bound(X_55,multiply(X_55,greatest_lower_bound(inverse(X_55),X_37)))
| multiply(X_55,greatest_lower_bound(inverse(X_55),X_37)) != greatest_lower_bound(identity,multiply(X_55,X_37))
| multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)),greatest_lower_bound(X_55,multiply(X_55,greatest_lower_bound(inverse(X_55),X_37)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_55,X_37)))]]) ).
cnf(refute_0_2291,plain,
( multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) != greatest_lower_bound(X_55,multiply(X_55,greatest_lower_bound(inverse(X_55),X_37)))
| multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37))) ),
inference(resolve,[$cnf( $equal(multiply(X_55,greatest_lower_bound(inverse(X_55),X_37)),greatest_lower_bound(identity,multiply(X_55,X_37))) )],[refute_0_2289,refute_0_2290]) ).
cnf(refute_0_2292,plain,
multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37))),
inference(resolve,[$cnf( $equal(multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)),greatest_lower_bound(X_55,multiply(X_55,greatest_lower_bound(inverse(X_55),X_37)))) )],[refute_0_2288,refute_0_2291]) ).
cnf(refute_0_2293,plain,
multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37))) = greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))),
inference(subst,[],[refute_0_1956:[bind(X,$fot(X_55)),bind(Y,$fot(identity)),bind(X_39,$fot(X_37))]]) ).
cnf(refute_0_2294,plain,
multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37))),
inference(subst,[],[refute_0_361:[bind(X_27,$fot(X_55)),bind(X_56,$fot(greatest_lower_bound(inverse(X_55),X_37)))]]) ).
cnf(refute_0_2295,plain,
( multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) != multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37)))
| multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37))) != greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37)))
| multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)))),bind(Y0,$fot(multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37)))))]]) ).
cnf(refute_0_2296,plain,
( multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37))) != greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37)))
| multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))) ),
inference(resolve,[$cnf( $equal(multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)),multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37)))) )],[refute_0_2294,refute_0_2295]) ).
cnf(refute_0_2297,plain,
multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) = greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))),
inference(resolve,[$cnf( $equal(multiply(X_55,greatest_lower_bound(identity,greatest_lower_bound(inverse(X_55),X_37))),greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37)))) )],[refute_0_2293,refute_0_2296]) ).
cnf(refute_0_2298,plain,
( multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) != greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37)))
| multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) != greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37)))
| greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))) = greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)),greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37)))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))))]]) ).
cnf(refute_0_2299,plain,
( multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)) != greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37)))
| greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))) = greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37))) ),
inference(resolve,[$cnf( $equal(multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)),greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37)))) )],[refute_0_2297,refute_0_2298]) ).
cnf(refute_0_2300,plain,
greatest_lower_bound(identity,multiply(X_55,greatest_lower_bound(identity,X_37))) = greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37))),
inference(resolve,[$cnf( $equal(multiply(X_55,greatest_lower_bound(greatest_lower_bound(inverse(X_55),X_37),identity)),greatest_lower_bound(X_55,greatest_lower_bound(identity,multiply(X_55,X_37)))) )],[refute_0_2292,refute_0_2299]) ).
cnf(refute_0_2301,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) = greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),X_150))),
inference(subst,[],[refute_0_2300:[bind(X_37,$fot(X_150)),bind(X_55,$fot(least_upper_bound(X_81,inverse(X_150))))]]) ).
cnf(refute_0_2302,plain,
multiply(least_upper_bound(X_81,inverse(X_150)),X_150) = least_upper_bound(identity,multiply(X_81,X_150)),
inference(subst,[],[refute_0_721:[bind(X_80,$fot(X_150))]]) ).
cnf(refute_0_2303,plain,
( multiply(least_upper_bound(X_81,inverse(X_150)),X_150) != least_upper_bound(identity,multiply(X_81,X_150))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) != greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),X_150)))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) = greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))),greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),X_150)))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(X_81,X_150)))]]) ).
cnf(refute_0_2304,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) != greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),X_150)))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) = greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_81,inverse(X_150)),X_150),least_upper_bound(identity,multiply(X_81,X_150))) )],[refute_0_2302,refute_0_2303]) ).
cnf(refute_0_2305,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) = greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))),greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),X_150)))) )],[refute_0_2301,refute_0_2304]) ).
cnf(refute_0_2306,plain,
greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))),
inference(subst,[],[refute_0_811:[bind(X_56,$fot(least_upper_bound(X_81,inverse(X_150))))]]) ).
cnf(refute_0_2307,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity),
inference(subst,[],[refute_0_1287:[bind(Y,$fot(multiply(X_81,X_150))),bind(X_46,$fot(least_upper_bound(X_81,inverse(X_150)))),bind(X_47,$fot(identity))]]) ).
cnf(refute_0_2308,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))) != greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity)
| greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity) != greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity))),bind(Z0,$fot(greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))))]]) ).
cnf(refute_0_2309,plain,
( greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity) != greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))
| greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))),greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity)) )],[refute_0_2307,refute_0_2308]) ).
cnf(refute_0_2310,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),identity),greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))) )],[refute_0_2306,refute_0_2309]) ).
cnf(refute_0_2311,plain,
greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28))),
inference(subst,[],[refute_0_132:[bind(X,$fot(greatest_lower_bound(X_47,X_28))),bind(X_26,$fot(X_46)),bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_2312,plain,
greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28)) = greatest_lower_bound(X_47,X_28),
inference(subst,[],[refute_0_71:[bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_2313,plain,
( greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28)) != greatest_lower_bound(X_47,X_28)
| greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28)))
| greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28)))) ),[1,1],$fot(greatest_lower_bound(X_47,X_28))]]) ).
cnf(refute_0_2314,plain,
( greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28)))
| greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28)),greatest_lower_bound(X_47,X_28)) )],[refute_0_2312,refute_0_2313]) ).
cnf(refute_0_2315,plain,
greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,greatest_lower_bound(X_47,X_28)))) )],[refute_0_2311,refute_0_2314]) ).
cnf(refute_0_2316,plain,
greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)),
inference(subst,[],[refute_0_1174:[bind(X,$fot(X_47)),bind(Z,$fot(X_28)),bind(X_31,$fot(X_46))]]) ).
cnf(refute_0_2317,plain,
greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))),
inference(subst,[],[refute_0_145:[bind(X_45,$fot(X_47)),bind(X_46,$fot(greatest_lower_bound(X_47,X_28))),bind(X_47,$fot(X_46))]]) ).
cnf(refute_0_2318,plain,
( greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))) != greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28))
| greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)))
| greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)))),bind(Y0,$fot(greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))))),bind(Z0,$fot(greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28))))]]) ).
cnf(refute_0_2319,plain,
( greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))) != greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28))
| greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)))) )],[refute_0_2317,refute_0_2318]) ).
cnf(refute_0_2320,plain,
greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_47,greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))),greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28))) )],[refute_0_2316,refute_0_2319]) ).
cnf(refute_0_2321,plain,
( greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))
| greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28))
| greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))) ),[0],$fot(greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)))]]) ).
cnf(refute_0_2322,plain,
( greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))
| greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28))) )],[refute_0_2320,refute_0_2321]) ).
cnf(refute_0_2323,plain,
greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)) = greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_47,X_28),greatest_lower_bound(X_46,X_47)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))) )],[refute_0_2315,refute_0_2322]) ).
cnf(refute_0_2324,plain,
( greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)) != greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))
| greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)))),bind(Y0,$fot(greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))))]]) ).
cnf(refute_0_2325,plain,
greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28)) = greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_47,greatest_lower_bound(X_46,X_28)),greatest_lower_bound(X_46,greatest_lower_bound(X_47,X_28))) )],[refute_0_2323,refute_0_2324]) ).
cnf(refute_0_2326,plain,
greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))),
inference(subst,[],[refute_0_2325:[bind(X_28,$fot(least_upper_bound(identity,multiply(X_81,X_150)))),bind(X_46,$fot(least_upper_bound(X_81,inverse(X_150)))),bind(X_47,$fot(identity))]]) ).
cnf(refute_0_2327,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))) != greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))
| greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150))))
| greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))))),bind(Z0,$fot(greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))))]]) ).
cnf(refute_0_2328,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))) != greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))
| greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150))))) )],[refute_0_2326,refute_0_2327]) ).
cnf(refute_0_2329,plain,
greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),least_upper_bound(identity,multiply(X_81,X_150)))),greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))) )],[refute_0_2310,refute_0_2328]) ).
cnf(refute_0_2330,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) != greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150))))
| greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))) != greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))),greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))))]]) ).
cnf(refute_0_2331,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) != greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150))))
| greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150)))),greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150)))) )],[refute_0_2329,refute_0_2330]) ).
cnf(refute_0_2332,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))) = greatest_lower_bound(identity,least_upper_bound(X_81,inverse(X_150))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,X_150))),greatest_lower_bound(least_upper_bound(X_81,inverse(X_150)),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_81,X_150))))) )],[refute_0_2305,refute_0_2331]) ).
cnf(refute_0_2333,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) = greatest_lower_bound(identity,least_upper_bound(identity,inverse(X))),
inference(subst,[],[refute_0_2332:[bind(X_150,$fot(X)),bind(X_81,$fot(identity))]]) ).
cnf(refute_0_2334,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) != greatest_lower_bound(identity,least_upper_bound(identity,inverse(X)))
| greatest_lower_bound(identity,least_upper_bound(identity,inverse(X))) != identity
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2335,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,inverse(X))) != identity
| greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))),greatest_lower_bound(identity,least_upper_bound(identity,inverse(X)))) )],[refute_0_2333,refute_0_2334]) ).
cnf(refute_0_2336,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X))),identity) )],[refute_0_2287,refute_0_2335]) ).
cnf(refute_0_2337,plain,
multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) = least_upper_bound(greatest_lower_bound(identity,X_89),multiply(inverse(X_89),greatest_lower_bound(identity,X_89))),
inference(subst,[],[refute_0_613:[bind(X_80,$fot(greatest_lower_bound(identity,X_89))),bind(X_81,$fot(inverse(X_89)))]]) ).
cnf(refute_0_2338,plain,
multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = greatest_lower_bound(inverse(X_89),multiply(inverse(X_89),greatest_lower_bound(X_89,identity))),
inference(subst,[],[refute_0_182:[bind(X_35,$fot(inverse(X_89))),bind(X_36,$fot(greatest_lower_bound(X_89,identity)))]]) ).
cnf(refute_0_2339,plain,
multiply(inverse(X_89),greatest_lower_bound(X_89,identity)) = greatest_lower_bound(identity,inverse(X_89)),
inference(subst,[],[refute_0_772:[bind(X_40,$fot(X_89))]]) ).
cnf(refute_0_2340,plain,
( multiply(inverse(X_89),greatest_lower_bound(X_89,identity)) != greatest_lower_bound(identity,inverse(X_89))
| multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) != greatest_lower_bound(inverse(X_89),multiply(inverse(X_89),greatest_lower_bound(X_89,identity)))
| multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)),greatest_lower_bound(inverse(X_89),multiply(inverse(X_89),greatest_lower_bound(X_89,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_89)))]]) ).
cnf(refute_0_2341,plain,
( multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) != greatest_lower_bound(inverse(X_89),multiply(inverse(X_89),greatest_lower_bound(X_89,identity)))
| multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(X_89,identity)),greatest_lower_bound(identity,inverse(X_89))) )],[refute_0_2339,refute_0_2340]) ).
cnf(refute_0_2342,plain,
multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)),greatest_lower_bound(inverse(X_89),multiply(inverse(X_89),greatest_lower_bound(X_89,identity)))) )],[refute_0_2338,refute_0_2341]) ).
cnf(refute_0_2343,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)) = greatest_lower_bound(identity,X_89),
inference(subst,[],[refute_0_96:[bind(Y,$fot(X_89)),bind(X_21,$fot(identity))]]) ).
cnf(refute_0_2344,plain,
multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))) = multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))))]]) ).
cnf(refute_0_2345,plain,
( multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))) != multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)) != greatest_lower_bound(identity,X_89)
| multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))) = multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))),multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_89))]]) ).
cnf(refute_0_2346,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)) != greatest_lower_bound(identity,X_89)
| multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))) = multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))),multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)))) )],[refute_0_2344,refute_0_2345]) ).
cnf(refute_0_2347,plain,
multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))) = multiply(inverse(X_89),greatest_lower_bound(identity,X_89)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)),greatest_lower_bound(identity,X_89)) )],[refute_0_2343,refute_0_2346]) ).
cnf(refute_0_2348,plain,
multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))),
inference(subst,[],[refute_0_361:[bind(X_27,$fot(inverse(X_89))),bind(X_56,$fot(greatest_lower_bound(X_89,identity)))]]) ).
cnf(refute_0_2349,plain,
( multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) != multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)))
| multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))) != multiply(inverse(X_89),greatest_lower_bound(identity,X_89))
| multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)))),bind(Y0,$fot(multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))))),bind(Z0,$fot(multiply(inverse(X_89),greatest_lower_bound(identity,X_89))))]]) ).
cnf(refute_0_2350,plain,
( multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))) != multiply(inverse(X_89),greatest_lower_bound(identity,X_89))
| multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)),multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity)))) )],[refute_0_2348,refute_0_2349]) ).
cnf(refute_0_2351,plain,
multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) = multiply(inverse(X_89),greatest_lower_bound(identity,X_89)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(identity,greatest_lower_bound(X_89,identity))),multiply(inverse(X_89),greatest_lower_bound(identity,X_89))) )],[refute_0_2347,refute_0_2350]) ).
cnf(refute_0_2352,plain,
( multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) != multiply(inverse(X_89),greatest_lower_bound(identity,X_89))
| multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) != greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))
| multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) = greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)),greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))) ),[0],$fot(multiply(inverse(X_89),greatest_lower_bound(identity,X_89)))]]) ).
cnf(refute_0_2353,plain,
( multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) != greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))
| multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) = greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)),multiply(inverse(X_89),greatest_lower_bound(identity,X_89))) )],[refute_0_2351,refute_0_2352]) ).
cnf(refute_0_2354,plain,
greatest_lower_bound(inverse(X_89),inverse(X_89)) = inverse(X_89),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(inverse(X_89)))]]) ).
cnf(refute_0_2355,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))))]]) ).
cnf(refute_0_2356,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89)))
| greatest_lower_bound(inverse(X_89),inverse(X_89)) != inverse(X_89)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))) = greatest_lower_bound(identity,inverse(X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89)))) ),[1,1],$fot(inverse(X_89))]]) ).
cnf(refute_0_2357,plain,
( greatest_lower_bound(inverse(X_89),inverse(X_89)) != inverse(X_89)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))) = greatest_lower_bound(identity,inverse(X_89)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89)))) )],[refute_0_2355,refute_0_2356]) ).
cnf(refute_0_2358,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))) = greatest_lower_bound(identity,inverse(X_89)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_89),inverse(X_89)),inverse(X_89)) )],[refute_0_2354,refute_0_2357]) ).
cnf(refute_0_2359,plain,
greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))),
inference(subst,[],[refute_0_2325:[bind(X_28,$fot(inverse(X_89))),bind(X_46,$fot(inverse(X_89))),bind(X_47,$fot(identity))]]) ).
cnf(refute_0_2360,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))) != greatest_lower_bound(identity,inverse(X_89))
| greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89)))
| greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(identity,inverse(X_89)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_2361,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))) != greatest_lower_bound(identity,inverse(X_89))
| greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(identity,inverse(X_89)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89)))) )],[refute_0_2359,refute_0_2360]) ).
cnf(refute_0_2362,plain,
greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) = greatest_lower_bound(identity,inverse(X_89)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_89),inverse(X_89))),greatest_lower_bound(identity,inverse(X_89))) )],[refute_0_2358,refute_0_2361]) ).
cnf(refute_0_2363,plain,
( multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) != greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))
| greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))) != greatest_lower_bound(identity,inverse(X_89))
| multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) = greatest_lower_bound(identity,inverse(X_89)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_89),greatest_lower_bound(identity,X_89)),greatest_lower_bound(identity,inverse(X_89))) ),[0],$fot(greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))))]]) ).
cnf(refute_0_2364,plain,
( multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) != greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))
| multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) = greatest_lower_bound(identity,inverse(X_89)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89))),greatest_lower_bound(identity,inverse(X_89))) )],[refute_0_2362,refute_0_2363]) ).
cnf(refute_0_2365,plain,
( multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)) != greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))
| multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) = greatest_lower_bound(identity,inverse(X_89)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(identity,X_89)),greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_2353,refute_0_2364]) ).
cnf(refute_0_2366,plain,
multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) = greatest_lower_bound(identity,inverse(X_89)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(greatest_lower_bound(X_89,identity),identity)),greatest_lower_bound(inverse(X_89),greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_2342,refute_0_2365]) ).
cnf(refute_0_2367,plain,
( multiply(inverse(X_89),greatest_lower_bound(identity,X_89)) != greatest_lower_bound(identity,inverse(X_89))
| multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) != least_upper_bound(greatest_lower_bound(identity,X_89),multiply(inverse(X_89),greatest_lower_bound(identity,X_89)))
| multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) = least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)),least_upper_bound(greatest_lower_bound(identity,X_89),multiply(inverse(X_89),greatest_lower_bound(identity,X_89)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_89)))]]) ).
cnf(refute_0_2368,plain,
( multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) != least_upper_bound(greatest_lower_bound(identity,X_89),multiply(inverse(X_89),greatest_lower_bound(identity,X_89)))
| multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) = least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_89),greatest_lower_bound(identity,X_89)),greatest_lower_bound(identity,inverse(X_89))) )],[refute_0_2366,refute_0_2367]) ).
cnf(refute_0_2369,plain,
multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) = least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)),least_upper_bound(greatest_lower_bound(identity,X_89),multiply(inverse(X_89),greatest_lower_bound(identity,X_89)))) )],[refute_0_2337,refute_0_2368]) ).
cnf(refute_0_2370,plain,
multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) = multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)),
inference(subst,[],[refute_0_1659:[bind(X_17,$fot(greatest_lower_bound(identity,X_89))),bind(X_223,$fot(inverse(X_89)))]]) ).
cnf(refute_0_2371,plain,
( multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) != multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89))
| multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) != least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89)))
| multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)) = least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)),least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)))]]) ).
cnf(refute_0_2372,plain,
( multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)) != least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89)))
| multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)) = least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)),multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89))) )],[refute_0_2370,refute_0_2371]) ).
cnf(refute_0_2373,plain,
multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)) = least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_89),identity),greatest_lower_bound(identity,X_89)),least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_2369,refute_0_2372]) ).
cnf(refute_0_2374,plain,
( multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)) != least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89)))
| least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))) = multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89)))))]]) ).
cnf(refute_0_2375,plain,
least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89))) = multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_89)),greatest_lower_bound(identity,X_89)),least_upper_bound(greatest_lower_bound(identity,X_89),greatest_lower_bound(identity,inverse(X_89)))) )],[refute_0_2373,refute_0_2374]) ).
cnf(refute_0_2376,plain,
least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))) = multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)),
inference(subst,[],[refute_0_2375:[bind(X_89,$fot(X))]]) ).
cnf(refute_0_2377,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_2378,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) != greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))
| least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))) != multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) ),[1,1],$fot(multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)))]]) ).
cnf(refute_0_2379,plain,
( least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))) != multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) )],[refute_0_2377,refute_0_2378]) ).
cnf(refute_0_2380,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))),multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) )],[refute_0_2376,refute_0_2379]) ).
cnf(refute_0_2381,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) != identity
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2382,plain,
( greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))) != identity
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X)))) )],[refute_0_2380,refute_0_2381]) ).
cnf(refute_0_2383,plain,
greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(X)),greatest_lower_bound(identity,X))),identity) )],[refute_0_2336,refute_0_2382]) ).
cnf(refute_0_2384,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))))]]) ).
cnf(refute_0_2385,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))
| greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) != identity
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2386,plain,
( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))) != identity
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))) )],[refute_0_2384,refute_0_2385]) ).
cnf(refute_0_2387,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))),identity) )],[refute_0_2383,refute_0_2386]) ).
cnf(refute_0_2388,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity)
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) != inverse(greatest_lower_bound(identity,inverse(X)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_2389,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity) != inverse(greatest_lower_bound(identity,inverse(X)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity)) )],[refute_0_2387,refute_0_2388]) ).
cnf(refute_0_2390,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),identity),inverse(greatest_lower_bound(identity,inverse(X)))) )],[refute_0_2286,refute_0_2389]) ).
cnf(refute_0_2391,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))),
inference(subst,[],[refute_0_1839:[bind(X_120,$fot(greatest_lower_bound(identity,inverse(X)))),bind(X_121,$fot(greatest_lower_bound(identity,X)))]]) ).
cnf(refute_0_2392,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))))]]) ).
cnf(refute_0_2393,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X))))) )],[refute_0_2218,refute_0_2392]) ).
cnf(refute_0_2394,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,X)))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))) )],[refute_0_2391,refute_0_2393]) ).
cnf(refute_0_2395,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) != inverse(greatest_lower_bound(identity,inverse(X)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_2396,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))) != inverse(greatest_lower_bound(identity,inverse(X)))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))),multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X)))))) )],[refute_0_2394,refute_0_2395]) ).
cnf(refute_0_2397,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(identity,inverse(X))))),inverse(greatest_lower_bound(identity,inverse(X)))) )],[refute_0_2390,refute_0_2396]) ).
cnf(refute_0_2398,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))
| multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != inverse(greatest_lower_bound(identity,inverse(X)))
| inverse(greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(X))))]]) ).
cnf(refute_0_2399,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))
| inverse(greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))),inverse(greatest_lower_bound(identity,inverse(X)))) )],[refute_0_2397,refute_0_2398]) ).
cnf(refute_0_2400,plain,
greatest_lower_bound(X_36,X_37) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)))),
inference(subst,[],[refute_0_2055:[bind(X_232,$fot(inverse(X_37))),bind(X_59,$fot(greatest_lower_bound(X_36,X_37)))]]) ).
cnf(refute_0_2401,plain,
( multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(identity,multiply(inverse(X_37),X_36))
| greatest_lower_bound(X_36,X_37) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),greatest_lower_bound(X_36,X_37))))
| greatest_lower_bound(X_36,X_37) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,X_37),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),greatest_lower_bound(X_36,X_37))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))]]) ).
cnf(refute_0_2402,plain,
( greatest_lower_bound(X_36,X_37) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),greatest_lower_bound(X_36,X_37))))
| greatest_lower_bound(X_36,X_37) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) )],[refute_0_920,refute_0_2401]) ).
cnf(refute_0_2403,plain,
greatest_lower_bound(X_36,X_37) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_37),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),greatest_lower_bound(X_36,X_37))))) )],[refute_0_2400,refute_0_2402]) ).
cnf(refute_0_2404,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(identity,multiply(inverse(X_37),X_36)),
inference(subst,[],[refute_0_71:[bind(X_27,$fot(identity)),bind(X_28,$fot(multiply(inverse(X_37),X_36)))]]) ).
cnf(refute_0_2405,plain,
multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))))]]) ).
cnf(refute_0_2406,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))
| greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != greatest_lower_bound(identity,multiply(inverse(X_37),X_36))
| multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))]]) ).
cnf(refute_0_2407,plain,
( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != greatest_lower_bound(identity,multiply(inverse(X_37),X_36))
| multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))) )],[refute_0_2405,refute_0_2406]) ).
cnf(refute_0_2408,plain,
multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) )],[refute_0_2404,refute_0_2407]) ).
cnf(refute_0_2409,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))
| greatest_lower_bound(X_36,X_37) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))
| greatest_lower_bound(X_36,X_37) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,X_37),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))) ),[1],$fot(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))]]) ).
cnf(refute_0_2410,plain,
( greatest_lower_bound(X_36,X_37) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))
| greatest_lower_bound(X_36,X_37) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) )],[refute_0_2408,refute_0_2409]) ).
cnf(refute_0_2411,plain,
greatest_lower_bound(X_36,X_37) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_37),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))) )],[refute_0_2403,refute_0_2410]) ).
cnf(refute_0_2412,plain,
multiply(X_37,identity) = X_37,
inference(subst,[],[refute_0_561:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_2413,plain,
greatest_lower_bound(multiply(X_37,identity),X_36) = greatest_lower_bound(multiply(X_37,identity),X_36),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X_37,identity),X_36))]]) ).
cnf(refute_0_2414,plain,
( multiply(X_37,identity) != X_37
| greatest_lower_bound(multiply(X_37,identity),X_36) != greatest_lower_bound(multiply(X_37,identity),X_36)
| greatest_lower_bound(multiply(X_37,identity),X_36) = greatest_lower_bound(X_37,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_37,identity),X_36),greatest_lower_bound(multiply(X_37,identity),X_36)) ),[1,0],$fot(X_37)]]) ).
cnf(refute_0_2415,plain,
( multiply(X_37,identity) != X_37
| greatest_lower_bound(multiply(X_37,identity),X_36) = greatest_lower_bound(X_37,X_36) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_37,identity),X_36),greatest_lower_bound(multiply(X_37,identity),X_36)) )],[refute_0_2413,refute_0_2414]) ).
cnf(refute_0_2416,plain,
greatest_lower_bound(multiply(X_37,identity),X_36) = greatest_lower_bound(X_37,X_36),
inference(resolve,[$cnf( $equal(multiply(X_37,identity),X_37) )],[refute_0_2412,refute_0_2415]) ).
cnf(refute_0_2417,plain,
multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(multiply(X_37,identity),X_36),
inference(subst,[],[refute_0_1246:[bind(X,$fot(X_37)),bind(Y,$fot(identity)),bind(X_63,$fot(X_36))]]) ).
cnf(refute_0_2418,plain,
( multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != greatest_lower_bound(multiply(X_37,identity),X_36)
| greatest_lower_bound(multiply(X_37,identity),X_36) != greatest_lower_bound(X_37,X_36)
| multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(X_37,X_36) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_37,identity),X_36))),bind(Z0,$fot(greatest_lower_bound(X_37,X_36)))]]) ).
cnf(refute_0_2419,plain,
( greatest_lower_bound(multiply(X_37,identity),X_36) != greatest_lower_bound(X_37,X_36)
| multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(X_37,X_36) ),
inference(resolve,[$cnf( $equal(multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),greatest_lower_bound(multiply(X_37,identity),X_36)) )],[refute_0_2417,refute_0_2418]) ).
cnf(refute_0_2420,plain,
multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(X_37,X_36),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_37,identity),X_36),greatest_lower_bound(X_37,X_36)) )],[refute_0_2416,refute_0_2419]) ).
cnf(refute_0_2421,plain,
X_234 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234))),
inference(subst,[],[refute_0_2055:[bind(X_232,$fot(inverse(greatest_lower_bound(X_100,X_234)))),bind(X_59,$fot(X_234))]]) ).
cnf(refute_0_2422,plain,
identity = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)),
inference(subst,[],[refute_0_1477:[bind(X_101,$fot(X_234))]]) ).
cnf(refute_0_2423,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234))))]]) ).
cnf(refute_0_2424,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234))) )],[refute_0_2422,refute_0_2423]) ).
cnf(refute_0_2425,plain,
( X_234 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)) != identity
| X_234 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_234,multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_2426,plain,
( X_234 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)))
| X_234 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)),identity) )],[refute_0_2424,refute_0_2425]) ).
cnf(refute_0_2427,plain,
X_234 = multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity),
inference(resolve,[$cnf( $equal(X_234,multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_100,X_234)),X_234)))) )],[refute_0_2421,refute_0_2426]) ).
cnf(refute_0_2428,plain,
multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity) = inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),
inference(subst,[],[refute_0_561:[bind(X,$fot(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))))]]) ).
cnf(refute_0_2429,plain,
inverse(multiply(inverse(X),greatest_lower_bound(X_230,X_229))) = multiply(inverse(greatest_lower_bound(X_230,X_229)),X),
inference(subst,[],[refute_0_538:[bind(X_23,$fot(greatest_lower_bound(X_230,X_229)))]]) ).
cnf(refute_0_2430,plain,
multiply(inverse(X),greatest_lower_bound(X_230,X_229)) = multiply(inverse(X),greatest_lower_bound(X_229,X_230)),
inference(subst,[],[refute_0_332:[bind(X_35,$fot(inverse(X))),bind(X_36,$fot(X_229)),bind(X_37,$fot(X_230))]]) ).
cnf(refute_0_2431,plain,
( multiply(inverse(X),greatest_lower_bound(X_230,X_229)) != multiply(inverse(X),greatest_lower_bound(X_229,X_230))
| inverse(multiply(inverse(X),greatest_lower_bound(X_230,X_229))) != multiply(inverse(greatest_lower_bound(X_230,X_229)),X)
| inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))) = multiply(inverse(greatest_lower_bound(X_230,X_229)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_230,X_229))),multiply(inverse(greatest_lower_bound(X_230,X_229)),X)) ),[0,0],$fot(multiply(inverse(X),greatest_lower_bound(X_229,X_230)))]]) ).
cnf(refute_0_2432,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_230,X_229))) != multiply(inverse(greatest_lower_bound(X_230,X_229)),X)
| inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))) = multiply(inverse(greatest_lower_bound(X_230,X_229)),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),greatest_lower_bound(X_230,X_229)),multiply(inverse(X),greatest_lower_bound(X_229,X_230))) )],[refute_0_2430,refute_0_2431]) ).
cnf(refute_0_2433,plain,
inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))) = multiply(inverse(greatest_lower_bound(X_230,X_229)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_230,X_229))),multiply(inverse(greatest_lower_bound(X_230,X_229)),X)) )],[refute_0_2429,refute_0_2432]) ).
cnf(refute_0_2434,plain,
inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))) = multiply(inverse(greatest_lower_bound(X_229,X_230)),X),
inference(subst,[],[refute_0_538:[bind(X_23,$fot(greatest_lower_bound(X_229,X_230)))]]) ).
cnf(refute_0_2435,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))) != multiply(inverse(greatest_lower_bound(X_229,X_230)),X)
| inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))) != multiply(inverse(greatest_lower_bound(X_230,X_229)),X)
| multiply(inverse(greatest_lower_bound(X_229,X_230)),X) = multiply(inverse(greatest_lower_bound(X_230,X_229)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))),multiply(inverse(greatest_lower_bound(X_230,X_229)),X)) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_229,X_230)),X))]]) ).
cnf(refute_0_2436,plain,
( inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))) != multiply(inverse(greatest_lower_bound(X_230,X_229)),X)
| multiply(inverse(greatest_lower_bound(X_229,X_230)),X) = multiply(inverse(greatest_lower_bound(X_230,X_229)),X) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))),multiply(inverse(greatest_lower_bound(X_229,X_230)),X)) )],[refute_0_2434,refute_0_2435]) ).
cnf(refute_0_2437,plain,
multiply(inverse(greatest_lower_bound(X_229,X_230)),X) = multiply(inverse(greatest_lower_bound(X_230,X_229)),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_229,X_230))),multiply(inverse(greatest_lower_bound(X_230,X_229)),X)) )],[refute_0_2433,refute_0_2436]) ).
cnf(refute_0_2438,plain,
( multiply(inverse(greatest_lower_bound(X_229,X_230)),X) != multiply(inverse(greatest_lower_bound(X_230,X_229)),X)
| multiply(inverse(greatest_lower_bound(X_230,X_229)),X) = multiply(inverse(greatest_lower_bound(X_229,X_230)),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_229,X_230)),X))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_230,X_229)),X)))]]) ).
cnf(refute_0_2439,plain,
multiply(inverse(greatest_lower_bound(X_230,X_229)),X) = multiply(inverse(greatest_lower_bound(X_229,X_230)),X),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_229,X_230)),X),multiply(inverse(greatest_lower_bound(X_230,X_229)),X)) )],[refute_0_2437,refute_0_2438]) ).
cnf(refute_0_2440,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) = multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity),
inference(subst,[],[refute_0_2439:[bind(X,$fot(identity)),bind(X_229,$fot(inverse(X_234))),bind(X_230,$fot(inverse(greatest_lower_bound(X_100,X_234))))]]) ).
cnf(refute_0_2441,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity) != inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) != multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity)
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) = inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))))]]) ).
cnf(refute_0_2442,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity) != inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) = inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity),multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity)) )],[refute_0_2440,refute_0_2441]) ).
cnf(refute_0_2443,plain,
multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) = inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),identity),inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))) )],[refute_0_2428,refute_0_2442]) ).
cnf(refute_0_2444,plain,
( X_234 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity)
| multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity) != inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))
| X_234 = inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_234,inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity))]]) ).
cnf(refute_0_2445,plain,
( X_234 != multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity)
| X_234 = inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity),inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))) )],[refute_0_2443,refute_0_2444]) ).
cnf(refute_0_2446,plain,
X_234 = inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))),
inference(resolve,[$cnf( $equal(X_234,multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_100,X_234)),inverse(X_234))),identity)) )],[refute_0_2427,refute_0_2445]) ).
cnf(refute_0_2447,plain,
( X_234 != inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))
| inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))) = X_234 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_234)),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))))]]) ).
cnf(refute_0_2448,plain,
inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234)))) = X_234,
inference(resolve,[$cnf( $equal(X_234,inverse(greatest_lower_bound(inverse(X_234),inverse(greatest_lower_bound(X_100,X_234))))) )],[refute_0_2446,refute_0_2447]) ).
cnf(refute_0_2449,plain,
inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))) = X_37,
inference(subst,[],[refute_0_2448:[bind(X_100,$fot(X_36)),bind(X_234,$fot(X_37))]]) ).
cnf(refute_0_2450,plain,
multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))]]) ).
cnf(refute_0_2451,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))
| inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))) != X_37
| multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) ),[1,0],$fot(X_37)]]) ).
cnf(refute_0_2452,plain,
( inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))) != X_37
| multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) )],[refute_0_2450,refute_0_2451]) ).
cnf(refute_0_2453,plain,
multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),X_37) )],[refute_0_2449,refute_0_2452]) ).
cnf(refute_0_2454,plain,
( multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != greatest_lower_bound(X_37,X_36)
| multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))
| multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(X_37,X_36) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))),bind(Y0,$fot(multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))))),bind(Z0,$fot(greatest_lower_bound(X_37,X_36)))]]) ).
cnf(refute_0_2455,plain,
( multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != greatest_lower_bound(X_37,X_36)
| multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(X_37,X_36) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) )],[refute_0_2453,refute_0_2454]) ).
cnf(refute_0_2456,plain,
multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) = greatest_lower_bound(X_37,X_36),
inference(resolve,[$cnf( $equal(multiply(X_37,greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),greatest_lower_bound(X_37,X_36)) )],[refute_0_2420,refute_0_2455]) ).
cnf(refute_0_2457,plain,
( multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))) != greatest_lower_bound(X_37,X_36)
| greatest_lower_bound(X_36,X_37) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))
| greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,X_37),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) ),[1],$fot(greatest_lower_bound(X_37,X_36))]]) ).
cnf(refute_0_2458,plain,
( greatest_lower_bound(X_36,X_37) != multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))
| greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,X_36) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36))),greatest_lower_bound(X_37,X_36)) )],[refute_0_2456,refute_0_2457]) ).
cnf(refute_0_2459,plain,
greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,X_36),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_37),multiply(inverse(greatest_lower_bound(inverse(X_37),inverse(greatest_lower_bound(X_36,X_37)))),greatest_lower_bound(identity,multiply(inverse(X_37),X_36)))) )],[refute_0_2411,refute_0_2458]) ).
cnf(refute_0_2460,plain,
( greatest_lower_bound(X_36,X_37) != greatest_lower_bound(X_37,X_36)
| greatest_lower_bound(X_37,X_36) = greatest_lower_bound(X_36,X_37) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_36,X_37))),bind(Y0,$fot(greatest_lower_bound(X_37,X_36)))]]) ).
cnf(refute_0_2461,plain,
greatest_lower_bound(X_37,X_36) = greatest_lower_bound(X_36,X_37),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_37,X_36)) )],[refute_0_2459,refute_0_2460]) ).
cnf(refute_0_2462,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)) = greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))),
inference(subst,[],[refute_0_2461:[bind(X_36,$fot(least_upper_bound(identity,X))),bind(X_37,$fot(inverse(greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_2463,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)) != greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X))))
| inverse(greatest_lower_bound(identity,inverse(X))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))
| inverse(greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))) ),[1],$fot(greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))))]]) ).
cnf(refute_0_2464,plain,
( inverse(greatest_lower_bound(identity,inverse(X))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))
| inverse(greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)),greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X))))) )],[refute_0_2462,refute_0_2463]) ).
cnf(refute_0_2465,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))
| inverse(greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))) )],[refute_0_2399,refute_0_2464]) ).
cnf(refute_0_2466,plain,
inverse(greatest_lower_bound(identity,inverse(X))) = greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X),inverse(inverse(greatest_lower_bound(identity,inverse(X))))))),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X))) )],[refute_0_2270,refute_0_2465]) ).
cnf(refute_0_2467,plain,
( inverse(greatest_lower_bound(identity,inverse(X))) != greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X))))
| greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))) = inverse(greatest_lower_bound(identity,inverse(X))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X))))))]]) ).
cnf(refute_0_2468,plain,
greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X)))) = inverse(greatest_lower_bound(identity,inverse(X))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(least_upper_bound(identity,X),inverse(greatest_lower_bound(identity,inverse(X))))) )],[refute_0_2466,refute_0_2467]) ).
cnf(refute_0_2469,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = inverse(greatest_lower_bound(identity,inverse(inverse(X)))),
inference(subst,[],[refute_0_2468:[bind(X,$fot(inverse(X)))]]) ).
cnf(refute_0_2470,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) != inverse(greatest_lower_bound(identity,inverse(inverse(X))))
| inverse(greatest_lower_bound(identity,inverse(inverse(X)))) != least_upper_bound(identity,inverse(X))
| greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = least_upper_bound(identity,inverse(X)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X)))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X))))]]) ).
cnf(refute_0_2471,plain,
( inverse(greatest_lower_bound(identity,inverse(inverse(X)))) != least_upper_bound(identity,inverse(X))
| greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = least_upper_bound(identity,inverse(X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) )],[refute_0_2469,refute_0_2470]) ).
cnf(refute_0_2472,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = least_upper_bound(identity,inverse(X)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X)))),least_upper_bound(identity,inverse(X))) )],[refute_0_2217,refute_0_2471]) ).
cnf(refute_0_2473,plain,
greatest_lower_bound(least_upper_bound(X_289,X_290),Y) = greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(least_upper_bound(X_289,X_290)))]]) ).
cnf(refute_0_2474,plain,
( greatest_lower_bound(Y,least_upper_bound(X_289,X_290)) != greatest_lower_bound(least_upper_bound(X_290,X_289),Y)
| greatest_lower_bound(least_upper_bound(X_289,X_290),Y) != greatest_lower_bound(Y,least_upper_bound(X_289,X_290))
| greatest_lower_bound(least_upper_bound(X_289,X_290),Y) = greatest_lower_bound(least_upper_bound(X_290,X_289),Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_289,X_290),Y),greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) ),[1],$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),Y))]]) ).
cnf(refute_0_2475,plain,
( greatest_lower_bound(least_upper_bound(X_289,X_290),Y) != greatest_lower_bound(Y,least_upper_bound(X_289,X_290))
| greatest_lower_bound(least_upper_bound(X_289,X_290),Y) = greatest_lower_bound(least_upper_bound(X_290,X_289),Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,least_upper_bound(X_289,X_290)),greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) )],[refute_0_1513,refute_0_2474]) ).
cnf(refute_0_2476,plain,
greatest_lower_bound(least_upper_bound(X_289,X_290),Y) = greatest_lower_bound(least_upper_bound(X_290,X_289),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_289,X_290),Y),greatest_lower_bound(Y,least_upper_bound(X_289,X_290))) )],[refute_0_2473,refute_0_2475]) ).
cnf(refute_0_2477,plain,
( greatest_lower_bound(least_upper_bound(X_289,X_290),Y) != greatest_lower_bound(least_upper_bound(X_290,X_289),Y)
| greatest_lower_bound(least_upper_bound(X_290,X_289),Y) = greatest_lower_bound(least_upper_bound(X_289,X_290),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_289,X_290),Y))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_290,X_289),Y)))]]) ).
cnf(refute_0_2478,plain,
greatest_lower_bound(least_upper_bound(X_290,X_289),Y) = greatest_lower_bound(least_upper_bound(X_289,X_290),Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_289,X_290),Y),greatest_lower_bound(least_upper_bound(X_290,X_289),Y)) )],[refute_0_2476,refute_0_2477]) ).
cnf(refute_0_2479,plain,
greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))),
inference(subst,[],[refute_0_2478:[bind(Y,$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X)))))),bind(X_289,$fot(identity)),bind(X_290,$fot(inverse(X)))]]) ).
cnf(refute_0_2480,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) != least_upper_bound(identity,inverse(X))
| greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) != greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))
| greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = least_upper_bound(identity,inverse(X)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X))))]]) ).
cnf(refute_0_2481,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) != least_upper_bound(identity,inverse(X))
| greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = least_upper_bound(identity,inverse(X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))),greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))) )],[refute_0_2479,refute_0_2480]) ).
cnf(refute_0_2482,plain,
greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) = least_upper_bound(identity,inverse(X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(identity,inverse(inverse(X))))),least_upper_bound(identity,inverse(X))) )],[refute_0_2472,refute_0_2481]) ).
cnf(refute_0_2483,plain,
( greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))) != least_upper_bound(identity,inverse(X))
| inverse(greatest_lower_bound(identity,X)) != greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))
| inverse(greatest_lower_bound(identity,X)) = least_upper_bound(identity,inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X)),greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))) ),[1],$fot(least_upper_bound(identity,inverse(X)))]]) ).
cnf(refute_0_2484,plain,
( inverse(greatest_lower_bound(identity,X)) != greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))
| inverse(greatest_lower_bound(identity,X)) = least_upper_bound(identity,inverse(X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X))))),least_upper_bound(identity,inverse(X))) )],[refute_0_2482,refute_0_2483]) ).
cnf(refute_0_2485,plain,
inverse(greatest_lower_bound(identity,X)) = least_upper_bound(identity,inverse(X)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X)),greatest_lower_bound(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(identity,inverse(inverse(X)))))) )],[refute_0_1886,refute_0_2484]) ).
cnf(refute_0_2486,plain,
( inverse(greatest_lower_bound(identity,X)) != least_upper_bound(identity,inverse(X))
| least_upper_bound(identity,inverse(X)) = inverse(greatest_lower_bound(identity,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X))))]]) ).
cnf(refute_0_2487,plain,
least_upper_bound(identity,inverse(X)) = inverse(greatest_lower_bound(identity,X)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X)),least_upper_bound(identity,inverse(X))) )],[refute_0_2485,refute_0_2486]) ).
cnf(refute_0_2488,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),
inference(subst,[],[refute_0_2487:[bind(X,$fot(greatest_lower_bound(X_350,least_upper_bound(identity,X_76))))]]) ).
cnf(refute_0_2489,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != inverse(greatest_lower_bound(X_350,identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(X_350,identity)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_350,identity))))]]) ).
cnf(refute_0_2490,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != inverse(greatest_lower_bound(X_350,identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(X_350,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76))))) )],[refute_0_2488,refute_0_2489]) ).
cnf(refute_0_2491,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) = inverse(greatest_lower_bound(X_350,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),inverse(greatest_lower_bound(X_350,identity))) )],[refute_0_1717,refute_0_2490]) ).
cnf(refute_0_2492,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != inverse(greatest_lower_bound(X_350,identity))
| least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| inverse(greatest_lower_bound(X_350,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) ),[0],$fot(inverse(greatest_lower_bound(X_350,identity)))]]) ).
cnf(refute_0_2493,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| inverse(greatest_lower_bound(X_350,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),inverse(greatest_lower_bound(X_350,identity))) )],[refute_0_2491,refute_0_2492]) ).
cnf(refute_0_2494,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)) = greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)),X_28),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_26)),bind(Y,$fot(least_upper_bound(X_13,X_26))),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_2495,plain,
greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)) = X_26,
inference(subst,[],[refute_0_85:[bind(X_12,$fot(X_26))]]) ).
cnf(refute_0_2496,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)),X_28)
| greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)) != X_26
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)) = greatest_lower_bound(X_26,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)),greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)),X_28)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_2497,plain,
( greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)) != greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)),X_28)
| greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)) = greatest_lower_bound(X_26,X_28) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)),X_26) )],[refute_0_2495,refute_0_2496]) ).
cnf(refute_0_2498,plain,
greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)) = greatest_lower_bound(X_26,X_28),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,greatest_lower_bound(least_upper_bound(X_13,X_26),X_28)),greatest_lower_bound(greatest_lower_bound(X_26,least_upper_bound(X_13,X_26)),X_28)) )],[refute_0_2494,refute_0_2497]) ).
cnf(refute_0_2499,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)) = greatest_lower_bound(identity,X_350),
inference(subst,[],[refute_0_2498:[bind(X_13,$fot(X_76)),bind(X_26,$fot(identity)),bind(X_28,$fot(X_350))]]) ).
cnf(refute_0_2500,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))))]]) ).
cnf(refute_0_2501,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)) != greatest_lower_bound(identity,X_350)
| inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,X_350)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) ),[1,0],$fot(greatest_lower_bound(identity,X_350))]]) ).
cnf(refute_0_2502,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)) != greatest_lower_bound(identity,X_350)
| inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,X_350)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) )],[refute_0_2500,refute_0_2501]) ).
cnf(refute_0_2503,plain,
inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,X_350)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)),greatest_lower_bound(identity,X_350)) )],[refute_0_2499,refute_0_2502]) ).
cnf(refute_0_2504,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),
inference(subst,[],[refute_0_2487:[bind(X,$fot(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))]]) ).
cnf(refute_0_2505,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) != inverse(greatest_lower_bound(identity,X_350))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,X_350)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_350))))]]) ).
cnf(refute_0_2506,plain,
( inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) != inverse(greatest_lower_bound(identity,X_350))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,X_350)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) )],[refute_0_2504,refute_0_2505]) ).
cnf(refute_0_2507,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) = inverse(greatest_lower_bound(identity,X_350)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),inverse(greatest_lower_bound(identity,X_350))) )],[refute_0_2503,refute_0_2506]) ).
cnf(refute_0_2508,plain,
( inverse(greatest_lower_bound(X_350,identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))) != inverse(greatest_lower_bound(identity,X_350))
| inverse(greatest_lower_bound(X_350,identity)) = inverse(greatest_lower_bound(identity,X_350)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_350,identity)),inverse(greatest_lower_bound(identity,X_350))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))))]]) ).
cnf(refute_0_2509,plain,
( inverse(greatest_lower_bound(X_350,identity)) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| inverse(greatest_lower_bound(X_350,identity)) = inverse(greatest_lower_bound(identity,X_350)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350))),inverse(greatest_lower_bound(identity,X_350))) )],[refute_0_2507,refute_0_2508]) ).
cnf(refute_0_2510,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))) != least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))
| inverse(greatest_lower_bound(X_350,identity)) = inverse(greatest_lower_bound(identity,X_350)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_350,identity)),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) )],[refute_0_2493,refute_0_2509]) ).
cnf(refute_0_2511,plain,
inverse(greatest_lower_bound(X_350,identity)) = inverse(greatest_lower_bound(identity,X_350)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_350,least_upper_bound(identity,X_76)))),least_upper_bound(identity,inverse(greatest_lower_bound(least_upper_bound(X_76,identity),X_350)))) )],[refute_0_1712,refute_0_2510]) ).
cnf(refute_0_2512,plain,
( inverse(greatest_lower_bound(X_350,identity)) != inverse(greatest_lower_bound(identity,X_350))
| inverse(greatest_lower_bound(identity,X_350)) = inverse(greatest_lower_bound(X_350,identity)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(greatest_lower_bound(X_350,identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,X_350))))]]) ).
cnf(refute_0_2513,plain,
inverse(greatest_lower_bound(identity,X_350)) = inverse(greatest_lower_bound(X_350,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_350,identity)),inverse(greatest_lower_bound(identity,X_350))) )],[refute_0_2511,refute_0_2512]) ).
cnf(refute_0_2514,plain,
inverse(greatest_lower_bound(identity,a)) = inverse(greatest_lower_bound(a,identity)),
inference(subst,[],[refute_0_2513:[bind(X_350,$fot(a))]]) ).
cnf(refute_0_2515,plain,
least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(identity,a)),
inference(subst,[],[refute_0_2487:[bind(X,$fot(a))]]) ).
cnf(refute_0_2516,plain,
( inverse(greatest_lower_bound(identity,a)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(identity,a))
| least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(least_upper_bound(identity,inverse(a)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,a)))),bind(Z0,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).
cnf(refute_0_2517,plain,
( inverse(greatest_lower_bound(identity,a)) != inverse(greatest_lower_bound(a,identity))
| least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(identity,a))) )],[refute_0_2515,refute_0_2516]) ).
cnf(refute_0_2518,plain,
least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2514,refute_0_2517]) ).
cnf(refute_0_2519,plain,
multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))))]]) ).
cnf(refute_0_2520,plain,
( multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) != multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a)))
| least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
| multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a)))) ),[1,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).
cnf(refute_0_2521,plain,
( least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
| multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a)))) )],[refute_0_2519,refute_0_2520]) ).
cnf(refute_0_2522,plain,
multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2518,refute_0_2521]) ).
cnf(refute_0_2523,plain,
( multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity
| multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) != multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity)))
| multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))))),bind(Y0,$fot(multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_2524,plain,
( multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity
| multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity)))) )],[refute_0_2522,refute_0_2523]) ).
cnf(refute_0_2525,plain,
multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))),identity) )],[refute_0_1340,refute_0_2524]) ).
cnf(refute_0_2526,plain,
( multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity
| identity != identity
| multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),identity) ),[0],$fot(identity)]]) ).
cnf(refute_0_2527,plain,
( identity != identity
| multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))) = identity ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),identity) )],[refute_0_2525,refute_0_2526]) ).
cnf(refute_0_2528,plain,
identity != identity,
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),least_upper_bound(identity,inverse(a))),identity) )],[refute_0_2527,refute_0_1339]) ).
cnf(refute_0_2529,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_2530,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_2529,refute_0_2528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP183-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 04:18:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.00/30.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.00/30.18
% 30.00/30.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.33/30.51
%------------------------------------------------------------------------------