TSTP Solution File: GRP190-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP190-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 10:37:54 EDT 2022
% Result : Unsatisfiable 5.12s 5.33s
% Output : CNFRefutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 78
% Syntax : Number of clauses : 335 ( 183 unt; 0 nHn; 161 RR)
% Number of literals : 552 ( 551 equ; 218 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 679 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p39a_1,hypothesis,
least_upper_bound(a,b) = a ).
cnf(prove_p39a,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b) ).
cnf(refute_0_0,plain,
greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))) = inverse(inverse(X_120)),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(inverse(inverse(X_120))))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_66),X_66),X_67) = multiply(inverse(X_66),multiply(X_66,X_67)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_66))),bind(Y,$fot(X_66)),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_66),X_66) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_66),X_66),X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| multiply(inverse(X_66),X_66) != identity
| multiply(identity,X_67) = multiply(inverse(X_66),multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_66),X_66),X_67),multiply(inverse(X_66),multiply(X_66,X_67))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_66),X_66),X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| multiply(identity,X_67) = multiply(inverse(X_66),multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),X_66),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_67) = multiply(inverse(X_66),multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_66),X_66),X_67),multiply(inverse(X_66),multiply(X_66,X_67))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_67) = X_67,
inference(subst,[],[left_identity:[bind(X,$fot(X_67))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_67) != X_67
| multiply(identity,X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| X_67 = multiply(inverse(X_66),multiply(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_67),multiply(inverse(X_66),multiply(X_66,X_67))) ),[0],$fot(X_67)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_67) != multiply(inverse(X_66),multiply(X_66,X_67))
| X_67 = multiply(inverse(X_66),multiply(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_67),X_67) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_67 = multiply(inverse(X_66),multiply(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(identity,X_67),multiply(inverse(X_66),multiply(X_66,X_67))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(X_99,X_100) = multiply(inverse(inverse(X_100)),multiply(inverse(X_100),greatest_lower_bound(X_99,X_100))),
inference(subst,[],[refute_0_9:[bind(X_66,$fot(inverse(X_100))),bind(X_67,$fot(greatest_lower_bound(X_99,X_100)))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_84))),bind(Y,$fot(X_83)),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_12,plain,
multiply(inverse(X_84),X_84) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_84))]]) ).
cnf(refute_0_13,plain,
( multiply(inverse(X_84),X_84) != identity
| multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))
| multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(multiply(inverse(X_84),X_83),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_14,plain,
( multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))
| multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(multiply(inverse(X_84),X_83),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),X_84),identity) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(multiply(inverse(X_84),X_83),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(multiply(inverse(X_84),X_83),multiply(inverse(X_84),X_84))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_20,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_19]) ).
cnf(refute_0_21,plain,
greatest_lower_bound(multiply(inverse(X_84),X_83),identity) = greatest_lower_bound(identity,multiply(inverse(X_84),X_83)),
inference(subst,[],[refute_0_20:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_84),X_83)))]]) ).
cnf(refute_0_22,plain,
( multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(multiply(inverse(X_84),X_83),identity)
| greatest_lower_bound(multiply(inverse(X_84),X_83),identity) != greatest_lower_bound(identity,multiply(inverse(X_84),X_83))
| multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(identity,multiply(inverse(X_84),X_83))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_84),X_83),identity))]]) ).
cnf(refute_0_23,plain,
( multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(multiply(inverse(X_84),X_83),identity)
| multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(identity,multiply(inverse(X_84),X_83)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_84),X_83),identity),greatest_lower_bound(identity,multiply(inverse(X_84),X_83))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(identity,multiply(inverse(X_84),X_83)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(multiply(inverse(X_84),X_83),identity)) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(inverse(X_100),greatest_lower_bound(X_99,X_100)) = greatest_lower_bound(identity,multiply(inverse(X_100),X_99)),
inference(subst,[],[refute_0_24:[bind(X_83,$fot(X_99)),bind(X_84,$fot(X_100))]]) ).
cnf(refute_0_26,plain,
( multiply(inverse(X_100),greatest_lower_bound(X_99,X_100)) != greatest_lower_bound(identity,multiply(inverse(X_100),X_99))
| greatest_lower_bound(X_99,X_100) != multiply(inverse(inverse(X_100)),multiply(inverse(X_100),greatest_lower_bound(X_99,X_100)))
| greatest_lower_bound(X_99,X_100) = multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_99,X_100),multiply(inverse(inverse(X_100)),multiply(inverse(X_100),greatest_lower_bound(X_99,X_100)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_100),X_99)))]]) ).
cnf(refute_0_27,plain,
( greatest_lower_bound(X_99,X_100) != multiply(inverse(inverse(X_100)),multiply(inverse(X_100),greatest_lower_bound(X_99,X_100)))
| greatest_lower_bound(X_99,X_100) = multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_100),greatest_lower_bound(X_99,X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
greatest_lower_bound(X_99,X_100) = multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_99,X_100),multiply(inverse(inverse(X_100)),multiply(inverse(X_100),greatest_lower_bound(X_99,X_100)))) )],[refute_0_10,refute_0_27]) ).
cnf(refute_0_29,plain,
X_70 = multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70)),
inference(subst,[],[refute_0_9:[bind(X_66,$fot(inverse(X_70))),bind(X_67,$fot(X_70))]]) ).
cnf(refute_0_30,plain,
multiply(inverse(X_70),X_70) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_70))]]) ).
cnf(refute_0_31,plain,
( X_70 != multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))
| multiply(inverse(X_70),X_70) != identity
| X_70 = multiply(inverse(inverse(X_70)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_32,plain,
( X_70 != multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))
| X_70 = multiply(inverse(inverse(X_70)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_70),X_70),identity) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
X_70 = multiply(inverse(inverse(X_70)),identity),
inference(resolve,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),multiply(inverse(X_70),X_70))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70))),
inference(subst,[],[refute_0_9:[bind(X_66,$fot(inverse(X_69))),bind(X_67,$fot(multiply(X_69,X_70)))]]) ).
cnf(refute_0_35,plain,
X_70 = multiply(inverse(X_69),multiply(X_69,X_70)),
inference(subst,[],[refute_0_9:[bind(X_66,$fot(X_69)),bind(X_67,$fot(X_70))]]) ).
cnf(refute_0_36,plain,
( X_70 != multiply(inverse(X_69),multiply(X_69,X_70))
| multiply(inverse(X_69),multiply(X_69,X_70)) = X_70 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_70)),bind(Y0,$fot(multiply(inverse(X_69),multiply(X_69,X_70))))]]) ).
cnf(refute_0_37,plain,
multiply(inverse(X_69),multiply(X_69,X_70)) = X_70,
inference(resolve,[$cnf( $equal(X_70,multiply(inverse(X_69),multiply(X_69,X_70))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))
| multiply(inverse(X_69),multiply(X_69,X_70)) != X_70
| multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))) ),[1,1],$fot(X_70)]]) ).
cnf(refute_0_39,plain,
( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))
| multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_69),multiply(X_69,X_70)),X_70) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_69,X_70) = multiply(inverse(inverse(X_69)),X_70),
inference(resolve,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),multiply(inverse(X_69),multiply(X_69,X_70)))) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(X_69,X_70) != multiply(inverse(inverse(X_69)),X_70)
| multiply(inverse(inverse(X_69)),X_70) = multiply(X_69,X_70) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_69,X_70))),bind(Y0,$fot(multiply(inverse(inverse(X_69)),X_70)))]]) ).
cnf(refute_0_42,plain,
multiply(inverse(inverse(X_69)),X_70) = multiply(X_69,X_70),
inference(resolve,[$cnf( $equal(multiply(X_69,X_70),multiply(inverse(inverse(X_69)),X_70)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(inverse(inverse(X_70)),identity) = multiply(X_70,identity),
inference(subst,[],[refute_0_42:[bind(X_69,$fot(X_70)),bind(X_70,$fot(identity))]]) ).
cnf(refute_0_44,plain,
( X_70 != multiply(inverse(inverse(X_70)),identity)
| multiply(inverse(inverse(X_70)),identity) != multiply(X_70,identity)
| X_70 = multiply(X_70,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_70,multiply(X_70,identity)) ),[0],$fot(multiply(inverse(inverse(X_70)),identity))]]) ).
cnf(refute_0_45,plain,
( X_70 != multiply(inverse(inverse(X_70)),identity)
| X_70 = multiply(X_70,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_70)),identity),multiply(X_70,identity)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
X_70 = multiply(X_70,identity),
inference(resolve,[$cnf( $equal(X_70,multiply(inverse(inverse(X_70)),identity)) )],[refute_0_33,refute_0_45]) ).
cnf(refute_0_47,plain,
( X_70 != multiply(X_70,identity)
| multiply(X_70,identity) = X_70 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_70)),bind(Y0,$fot(multiply(X_70,identity)))]]) ).
cnf(refute_0_48,plain,
multiply(X_70,identity) = X_70,
inference(resolve,[$cnf( $equal(X_70,multiply(X_70,identity)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(inverse(inverse(X_100)),identity) = inverse(inverse(X_100)),
inference(subst,[],[refute_0_48:[bind(X_70,$fot(inverse(inverse(X_100))))]]) ).
cnf(refute_0_50,plain,
greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99) = greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99))]]) ).
cnf(refute_0_51,plain,
( multiply(inverse(inverse(X_100)),identity) != inverse(inverse(X_100))
| greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99) != greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99)
| greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99) = greatest_lower_bound(inverse(inverse(X_100)),X_99) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99),greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99)) ),[1,0],$fot(inverse(inverse(X_100)))]]) ).
cnf(refute_0_52,plain,
( multiply(inverse(inverse(X_100)),identity) != inverse(inverse(X_100))
| greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99) = greatest_lower_bound(inverse(inverse(X_100)),X_99) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99),greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99) = greatest_lower_bound(inverse(inverse(X_100)),X_99),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_100)),identity),inverse(inverse(X_100))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))) = greatest_lower_bound(multiply(inverse(X_66),X_83),multiply(inverse(X_66),multiply(X_66,X_67))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_66))),bind(Y,$fot(X_83)),bind(Z,$fot(multiply(X_66,X_67)))]]) ).
cnf(refute_0_55,plain,
( X_67 != multiply(inverse(X_66),multiply(X_66,X_67))
| multiply(inverse(X_66),multiply(X_66,X_67)) = X_67 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_67)),bind(Y0,$fot(multiply(inverse(X_66),multiply(X_66,X_67))))]]) ).
cnf(refute_0_56,plain,
multiply(inverse(X_66),multiply(X_66,X_67)) = X_67,
inference(resolve,[$cnf( $equal(X_67,multiply(inverse(X_66),multiply(X_66,X_67))) )],[refute_0_9,refute_0_55]) ).
cnf(refute_0_57,plain,
( multiply(inverse(X_66),multiply(X_66,X_67)) != X_67
| multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))) != greatest_lower_bound(multiply(inverse(X_66),X_83),multiply(inverse(X_66),multiply(X_66,X_67)))
| multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))) = greatest_lower_bound(multiply(inverse(X_66),X_83),X_67) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))),greatest_lower_bound(multiply(inverse(X_66),X_83),multiply(inverse(X_66),multiply(X_66,X_67)))) ),[1,1],$fot(X_67)]]) ).
cnf(refute_0_58,plain,
( multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))) != greatest_lower_bound(multiply(inverse(X_66),X_83),multiply(inverse(X_66),multiply(X_66,X_67)))
| multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))) = greatest_lower_bound(multiply(inverse(X_66),X_83),X_67) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),multiply(X_66,X_67)),X_67) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))) = greatest_lower_bound(multiply(inverse(X_66),X_83),X_67),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),greatest_lower_bound(X_83,multiply(X_66,X_67))),greatest_lower_bound(multiply(inverse(X_66),X_83),multiply(inverse(X_66),multiply(X_66,X_67)))) )],[refute_0_54,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) = greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99),
inference(subst,[],[refute_0_59:[bind(X_66,$fot(inverse(X_100))),bind(X_67,$fot(X_99)),bind(X_83,$fot(identity))]]) ).
cnf(refute_0_61,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_62,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_18,refute_0_61]) ).
cnf(refute_0_63,plain,
( multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) != greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99)
| greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99) != greatest_lower_bound(inverse(inverse(X_100)),X_99)
| multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) = greatest_lower_bound(inverse(inverse(X_100)),X_99) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99))),bind(Z0,$fot(greatest_lower_bound(inverse(inverse(X_100)),X_99)))]]) ).
cnf(refute_0_64,plain,
( greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99) != greatest_lower_bound(inverse(inverse(X_100)),X_99)
| multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) = greatest_lower_bound(inverse(inverse(X_100)),X_99) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))),greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99)) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) = greatest_lower_bound(inverse(inverse(X_100)),X_99),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(inverse(X_100)),identity),X_99),greatest_lower_bound(inverse(inverse(X_100)),X_99)) )],[refute_0_53,refute_0_64]) ).
cnf(refute_0_66,plain,
( multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))) != greatest_lower_bound(inverse(inverse(X_100)),X_99)
| greatest_lower_bound(X_99,X_100) != multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99)))
| greatest_lower_bound(X_99,X_100) = greatest_lower_bound(inverse(inverse(X_100)),X_99) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_99,X_100),multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99)))) ),[1],$fot(greatest_lower_bound(inverse(inverse(X_100)),X_99))]]) ).
cnf(refute_0_67,plain,
( greatest_lower_bound(X_99,X_100) != multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99)))
| greatest_lower_bound(X_99,X_100) = greatest_lower_bound(inverse(inverse(X_100)),X_99) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99))),greatest_lower_bound(inverse(inverse(X_100)),X_99)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
greatest_lower_bound(X_99,X_100) = greatest_lower_bound(inverse(inverse(X_100)),X_99),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_99,X_100),multiply(inverse(inverse(X_100)),greatest_lower_bound(identity,multiply(inverse(X_100),X_99)))) )],[refute_0_28,refute_0_67]) ).
cnf(refute_0_69,plain,
greatest_lower_bound(inverse(inverse(X_120)),X_120) = greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))),
inference(subst,[],[refute_0_68:[bind(X_100,$fot(X_120)),bind(X_99,$fot(inverse(inverse(X_120))))]]) ).
cnf(refute_0_70,plain,
( greatest_lower_bound(inverse(inverse(X_120)),X_120) != greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120)))
| greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))) = greatest_lower_bound(inverse(inverse(X_120)),X_120) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(inverse(inverse(X_120)),X_120))),bind(Y0,$fot(greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120)))))]]) ).
cnf(refute_0_71,plain,
greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))) = greatest_lower_bound(inverse(inverse(X_120)),X_120),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),X_120),greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))) != greatest_lower_bound(inverse(inverse(X_120)),X_120)
| greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))) != inverse(inverse(X_120))
| greatest_lower_bound(inverse(inverse(X_120)),X_120) = inverse(inverse(X_120)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))),inverse(inverse(X_120))) ),[0],$fot(greatest_lower_bound(inverse(inverse(X_120)),X_120))]]) ).
cnf(refute_0_73,plain,
( greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))) != inverse(inverse(X_120))
| greatest_lower_bound(inverse(inverse(X_120)),X_120) = inverse(inverse(X_120)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))),greatest_lower_bound(inverse(inverse(X_120)),X_120)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
greatest_lower_bound(inverse(inverse(X_120)),X_120) = inverse(inverse(X_120)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),inverse(inverse(X_120))),inverse(inverse(X_120))) )],[refute_0_0,refute_0_73]) ).
cnf(refute_0_75,plain,
greatest_lower_bound(X_120,X_120) = X_120,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_120))]]) ).
cnf(refute_0_76,plain,
( greatest_lower_bound(X_99,X_100) != greatest_lower_bound(inverse(inverse(X_100)),X_99)
| greatest_lower_bound(inverse(inverse(X_100)),X_99) = greatest_lower_bound(X_99,X_100) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_99,X_100))),bind(Y0,$fot(greatest_lower_bound(inverse(inverse(X_100)),X_99)))]]) ).
cnf(refute_0_77,plain,
greatest_lower_bound(inverse(inverse(X_100)),X_99) = greatest_lower_bound(X_99,X_100),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_99,X_100),greatest_lower_bound(inverse(inverse(X_100)),X_99)) )],[refute_0_68,refute_0_76]) ).
cnf(refute_0_78,plain,
greatest_lower_bound(inverse(inverse(X_120)),X_120) = greatest_lower_bound(X_120,X_120),
inference(subst,[],[refute_0_77:[bind(X_100,$fot(X_120)),bind(X_99,$fot(X_120))]]) ).
cnf(refute_0_79,plain,
( greatest_lower_bound(X_120,X_120) != X_120
| greatest_lower_bound(inverse(inverse(X_120)),X_120) != greatest_lower_bound(X_120,X_120)
| greatest_lower_bound(inverse(inverse(X_120)),X_120) = X_120 ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(greatest_lower_bound(inverse(inverse(X_120)),X_120))),bind(Y0,$fot(greatest_lower_bound(X_120,X_120))),bind(Z0,$fot(X_120))]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(X_120,X_120) != X_120
| greatest_lower_bound(inverse(inverse(X_120)),X_120) = X_120 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),X_120),greatest_lower_bound(X_120,X_120)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
greatest_lower_bound(inverse(inverse(X_120)),X_120) = X_120,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,X_120),X_120) )],[refute_0_75,refute_0_80]) ).
cnf(refute_0_82,plain,
( greatest_lower_bound(inverse(inverse(X_120)),X_120) != X_120
| greatest_lower_bound(inverse(inverse(X_120)),X_120) != inverse(inverse(X_120))
| X_120 = inverse(inverse(X_120)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),X_120),inverse(inverse(X_120))) ),[0],$fot(X_120)]]) ).
cnf(refute_0_83,plain,
( greatest_lower_bound(inverse(inverse(X_120)),X_120) != inverse(inverse(X_120))
| X_120 = inverse(inverse(X_120)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),X_120),X_120) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
X_120 = inverse(inverse(X_120)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X_120)),X_120),inverse(inverse(X_120))) )],[refute_0_74,refute_0_83]) ).
cnf(refute_0_85,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(inverse(least_upper_bound(inverse(a),inverse(b)))),
inference(subst,[],[refute_0_84:[bind(X_120,$fot(least_upper_bound(inverse(a),inverse(b))))]]) ).
cnf(refute_0_86,plain,
X_67 = multiply(inverse(least_upper_bound(inverse(X_67),X_125)),multiply(least_upper_bound(inverse(X_67),X_125),X_67)),
inference(subst,[],[refute_0_9:[bind(X_66,$fot(least_upper_bound(inverse(X_67),X_125)))]]) ).
cnf(refute_0_87,plain,
multiply(least_upper_bound(inverse(X_42),X_44),X_42) = least_upper_bound(multiply(inverse(X_42),X_42),multiply(X_44,X_42)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_42)),bind(Y,$fot(inverse(X_42))),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_88,plain,
multiply(inverse(X_42),X_42) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_89,plain,
( multiply(inverse(X_42),X_42) != identity
| multiply(least_upper_bound(inverse(X_42),X_44),X_42) != least_upper_bound(multiply(inverse(X_42),X_42),multiply(X_44,X_42))
| multiply(least_upper_bound(inverse(X_42),X_44),X_42) = least_upper_bound(identity,multiply(X_44,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_42),X_44),X_42),least_upper_bound(multiply(inverse(X_42),X_42),multiply(X_44,X_42))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_90,plain,
( multiply(least_upper_bound(inverse(X_42),X_44),X_42) != least_upper_bound(multiply(inverse(X_42),X_42),multiply(X_44,X_42))
| multiply(least_upper_bound(inverse(X_42),X_44),X_42) = least_upper_bound(identity,multiply(X_44,X_42)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_42),X_42),identity) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(least_upper_bound(inverse(X_42),X_44),X_42) = least_upper_bound(identity,multiply(X_44,X_42)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_42),X_44),X_42),least_upper_bound(multiply(inverse(X_42),X_42),multiply(X_44,X_42))) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(least_upper_bound(inverse(X_67),X_125),X_67) = least_upper_bound(identity,multiply(X_125,X_67)),
inference(subst,[],[refute_0_91:[bind(X_42,$fot(X_67)),bind(X_44,$fot(X_125))]]) ).
cnf(refute_0_93,plain,
( X_67 != multiply(inverse(least_upper_bound(inverse(X_67),X_125)),multiply(least_upper_bound(inverse(X_67),X_125),X_67))
| multiply(least_upper_bound(inverse(X_67),X_125),X_67) != least_upper_bound(identity,multiply(X_125,X_67))
| X_67 = multiply(inverse(least_upper_bound(inverse(X_67),X_125)),least_upper_bound(identity,multiply(X_125,X_67))) ),
introduced(tautology,[equality,[$cnf( $equal(X_67,multiply(inverse(least_upper_bound(inverse(X_67),X_125)),multiply(least_upper_bound(inverse(X_67),X_125),X_67))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_125,X_67)))]]) ).
cnf(refute_0_94,plain,
( X_67 != multiply(inverse(least_upper_bound(inverse(X_67),X_125)),multiply(least_upper_bound(inverse(X_67),X_125),X_67))
| X_67 = multiply(inverse(least_upper_bound(inverse(X_67),X_125)),least_upper_bound(identity,multiply(X_125,X_67))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_67),X_125),X_67),least_upper_bound(identity,multiply(X_125,X_67))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
X_67 = multiply(inverse(least_upper_bound(inverse(X_67),X_125)),least_upper_bound(identity,multiply(X_125,X_67))),
inference(resolve,[$cnf( $equal(X_67,multiply(inverse(least_upper_bound(inverse(X_67),X_125)),multiply(least_upper_bound(inverse(X_67),X_125),X_67))) )],[refute_0_86,refute_0_94]) ).
cnf(refute_0_96,plain,
b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b))),
inference(subst,[],[refute_0_95:[bind(X_125,$fot(inverse(least_upper_bound(a,X_251)))),bind(X_67,$fot(b))]]) ).
cnf(refute_0_97,plain,
multiply(inverse(least_upper_bound(X_116,X_115)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))),
inference(subst,[],[refute_0_24:[bind(X_83,$fot(least_upper_bound(X_115,X_116))),bind(X_84,$fot(least_upper_bound(X_116,X_115)))]]) ).
cnf(refute_0_98,plain,
greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) = X_8,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_99,plain,
least_upper_bound(X_9,X_8) = least_upper_bound(X_8,X_9),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_100,plain,
( least_upper_bound(X_9,X_8) != least_upper_bound(X_8,X_9)
| least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_9,X_8))),bind(Y0,$fot(least_upper_bound(X_8,X_9)))]]) ).
cnf(refute_0_101,plain,
least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_8),least_upper_bound(X_8,X_9)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,X_9) != least_upper_bound(X_9,X_8)
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) ),[0,1],$fot(least_upper_bound(X_9,X_8))]]) ).
cnf(refute_0_103,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,X_9),least_upper_bound(X_9,X_8)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))) = least_upper_bound(X_16,X_9),
inference(subst,[],[refute_0_104:[bind(X_8,$fot(least_upper_bound(X_16,X_9)))]]) ).
cnf(refute_0_106,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_107,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_108,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_109,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_111,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_106,refute_0_111]) ).
cnf(refute_0_113,plain,
least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))) = least_upper_bound(X_15,Y),
inference(subst,[],[refute_0_112:[bind(X_10,$fot(least_upper_bound(X_15,Y))),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_114,plain,
greatest_lower_bound(X_15,least_upper_bound(X_15,Y)) = X_15,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_115,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_116,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( $equal(greatest_lower_bound(X_15,least_upper_bound(X_15,Y)),X_15) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),greatest_lower_bound(X_15,least_upper_bound(X_15,Y))),least_upper_bound(X_15,Y)) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_119,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_118]) ).
cnf(refute_0_120,plain,
least_upper_bound(least_upper_bound(X_15,Y),X_15) = least_upper_bound(X_15,least_upper_bound(Y,X_15)),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_121,plain,
( least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,Y)
| least_upper_bound(least_upper_bound(X_15,Y),X_15) != least_upper_bound(X_15,least_upper_bound(Y,X_15))
| least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y) ),
introduced(tautology,[equality,[$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_122,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( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,least_upper_bound(Y,X_15))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
least_upper_bound(X_15,least_upper_bound(Y,X_15)) = least_upper_bound(X_15,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,Y),X_15),least_upper_bound(X_15,Y)) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
least_upper_bound(X_9,least_upper_bound(X_16,X_9)) = least_upper_bound(X_9,X_16),
inference(subst,[],[refute_0_123:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_9))]]) ).
cnf(refute_0_125,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))) != least_upper_bound(X_16,X_9)
| least_upper_bound(X_9,least_upper_bound(X_16,X_9)) != least_upper_bound(X_9,X_16)
| greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,X_16)) = least_upper_bound(X_16,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))),least_upper_bound(X_16,X_9)) ),[0,1],$fot(least_upper_bound(X_9,X_16))]]) ).
cnf(refute_0_126,plain,
( greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))) != least_upper_bound(X_16,X_9)
| greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,X_16)) = least_upper_bound(X_16,X_9) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,least_upper_bound(X_16,X_9)),least_upper_bound(X_9,X_16)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,X_16)) = least_upper_bound(X_16,X_9),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_16,X_9),least_upper_bound(X_9,least_upper_bound(X_16,X_9))),least_upper_bound(X_16,X_9)) )],[refute_0_105,refute_0_126]) ).
cnf(refute_0_128,plain,
greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115)) = least_upper_bound(X_115,X_116),
inference(subst,[],[refute_0_127:[bind(X_16,$fot(X_115)),bind(X_9,$fot(X_116))]]) ).
cnf(refute_0_129,plain,
( multiply(inverse(least_upper_bound(X_116,X_115)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)))
| greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115)) != least_upper_bound(X_115,X_116)
| multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_116,X_115)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)))) ),[0,1],$fot(least_upper_bound(X_115,X_116))]]) ).
cnf(refute_0_130,plain,
( multiply(inverse(least_upper_bound(X_116,X_115)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)))
| multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_116,X_115)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)))) )],[refute_0_97,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_83))),bind(Y,$fot(X_83)),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_133,plain,
multiply(inverse(X_83),X_83) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_134,plain,
( multiply(inverse(X_83),X_83) != identity
| multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))
| multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(identity,multiply(inverse(X_83),X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_135,plain,
( multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)) != greatest_lower_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))
| multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(identity,multiply(inverse(X_83),X_84)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_83),X_83),identity) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)) = greatest_lower_bound(identity,multiply(inverse(X_83),X_84)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_83),greatest_lower_bound(X_83,X_84)),greatest_lower_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(inverse(least_upper_bound(X_115,X_116)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))),
inference(subst,[],[refute_0_136:[bind(X_83,$fot(least_upper_bound(X_115,X_116))),bind(X_84,$fot(least_upper_bound(X_116,X_115)))]]) ).
cnf(refute_0_138,plain,
( multiply(inverse(least_upper_bound(X_115,X_116)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))
| greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115)) != least_upper_bound(X_115,X_116)
| multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_115,X_116)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))) ),[0,1],$fot(least_upper_bound(X_115,X_116))]]) ).
cnf(refute_0_139,plain,
( multiply(inverse(least_upper_bound(X_115,X_116)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))
| multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) )],[refute_0_128,refute_0_138]) ).
cnf(refute_0_140,plain,
multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_115,X_116)),greatest_lower_bound(least_upper_bound(X_115,X_116),least_upper_bound(X_116,X_115))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))) )],[refute_0_137,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_115,X_116)))]]) ).
cnf(refute_0_142,plain,
( multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))
| multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)) != identity
| identity = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_143,plain,
( multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))
| identity = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)),identity) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
identity = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_115,X_116)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
( identity != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))) = identity ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))))]]) ).
cnf(refute_0_146,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_115,X_116)),least_upper_bound(X_116,X_115)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))) = identity,
inference(subst,[],[refute_0_146:[bind(X_115,$fot(X_116)),bind(X_116,$fot(X_115))]]) ).
cnf(refute_0_148,plain,
( multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))) != identity
| multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))))]]) ).
cnf(refute_0_149,plain,
( multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)))
| multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116))),identity) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_116,X_115)),least_upper_bound(X_115,X_116)))) )],[refute_0_131,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_24))),least_upper_bound(least_upper_bound(b,X_24),a)) = identity,
inference(subst,[],[refute_0_150:[bind(X_115,$fot(least_upper_bound(b,X_24))),bind(X_116,$fot(a))]]) ).
cnf(refute_0_152,plain,
least_upper_bound(a,least_upper_bound(b,X_24)) = least_upper_bound(least_upper_bound(a,b),X_24),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_153,plain,
( least_upper_bound(a,b) != a
| least_upper_bound(a,least_upper_bound(b,X_24)) != least_upper_bound(least_upper_bound(a,b),X_24)
| least_upper_bound(a,least_upper_bound(b,X_24)) = least_upper_bound(a,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_24)),least_upper_bound(least_upper_bound(a,b),X_24)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_154,plain,
( least_upper_bound(a,least_upper_bound(b,X_24)) != least_upper_bound(least_upper_bound(a,b),X_24)
| least_upper_bound(a,least_upper_bound(b,X_24)) = least_upper_bound(a,X_24) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),a) )],[p39a_1,refute_0_153]) ).
cnf(refute_0_155,plain,
least_upper_bound(a,least_upper_bound(b,X_24)) = least_upper_bound(a,X_24),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_24)),least_upper_bound(least_upper_bound(a,b),X_24)) )],[refute_0_152,refute_0_154]) ).
cnf(refute_0_156,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_24))),least_upper_bound(least_upper_bound(b,X_24),a)) != identity
| least_upper_bound(a,least_upper_bound(b,X_24)) != least_upper_bound(a,X_24)
| multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_24))),least_upper_bound(least_upper_bound(b,X_24),a)),identity) ),[0,0,0],$fot(least_upper_bound(a,X_24))]]) ).
cnf(refute_0_157,plain,
( multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_24))),least_upper_bound(least_upper_bound(b,X_24),a)) != identity
| multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_24)),least_upper_bound(a,X_24)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_24))),least_upper_bound(least_upper_bound(b,X_24),a)),identity) )],[refute_0_151,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(inverse(X_39),least_upper_bound(X_38,X_39)) = least_upper_bound(multiply(inverse(X_39),X_38),multiply(inverse(X_39),X_39)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_39))),bind(Y,$fot(X_38)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_160,plain,
multiply(inverse(X_39),X_39) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_161,plain,
( multiply(inverse(X_39),X_39) != identity
| multiply(inverse(X_39),least_upper_bound(X_38,X_39)) != least_upper_bound(multiply(inverse(X_39),X_38),multiply(inverse(X_39),X_39))
| multiply(inverse(X_39),least_upper_bound(X_38,X_39)) = least_upper_bound(multiply(inverse(X_39),X_38),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_39),least_upper_bound(X_38,X_39)),least_upper_bound(multiply(inverse(X_39),X_38),multiply(inverse(X_39),X_39))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_162,plain,
( multiply(inverse(X_39),least_upper_bound(X_38,X_39)) != least_upper_bound(multiply(inverse(X_39),X_38),multiply(inverse(X_39),X_39))
| multiply(inverse(X_39),least_upper_bound(X_38,X_39)) = least_upper_bound(multiply(inverse(X_39),X_38),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_39),X_39),identity) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
multiply(inverse(X_39),least_upper_bound(X_38,X_39)) = least_upper_bound(multiply(inverse(X_39),X_38),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_39),least_upper_bound(X_38,X_39)),least_upper_bound(multiply(inverse(X_39),X_38),multiply(inverse(X_39),X_39))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_165,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_164]) ).
cnf(refute_0_166,plain,
least_upper_bound(multiply(inverse(X_39),X_38),identity) = least_upper_bound(identity,multiply(inverse(X_39),X_38)),
inference(subst,[],[refute_0_165:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_39),X_38)))]]) ).
cnf(refute_0_167,plain,
( multiply(inverse(X_39),least_upper_bound(X_38,X_39)) != least_upper_bound(multiply(inverse(X_39),X_38),identity)
| least_upper_bound(multiply(inverse(X_39),X_38),identity) != least_upper_bound(identity,multiply(inverse(X_39),X_38))
| multiply(inverse(X_39),least_upper_bound(X_38,X_39)) = least_upper_bound(identity,multiply(inverse(X_39),X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_39),least_upper_bound(X_38,X_39)),least_upper_bound(identity,multiply(inverse(X_39),X_38))) ),[0],$fot(least_upper_bound(multiply(inverse(X_39),X_38),identity))]]) ).
cnf(refute_0_168,plain,
( multiply(inverse(X_39),least_upper_bound(X_38,X_39)) != least_upper_bound(multiply(inverse(X_39),X_38),identity)
| multiply(inverse(X_39),least_upper_bound(X_38,X_39)) = least_upper_bound(identity,multiply(inverse(X_39),X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_39),X_38),identity),least_upper_bound(identity,multiply(inverse(X_39),X_38))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(inverse(X_39),least_upper_bound(X_38,X_39)) = least_upper_bound(identity,multiply(inverse(X_39),X_38)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_39),least_upper_bound(X_38,X_39)),least_upper_bound(multiply(inverse(X_39),X_38),identity)) )],[refute_0_163,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_38,least_upper_bound(X_54,X_55))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38)),
inference(subst,[],[refute_0_169:[bind(X_39,$fot(least_upper_bound(X_54,X_55)))]]) ).
cnf(refute_0_171,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,least_upper_bound(Y,X_22)),X_24),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(least_upper_bound(Y,X_22))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_172,plain,
least_upper_bound(X_22,least_upper_bound(Y,X_22)) = least_upper_bound(X_22,Y),
inference(subst,[],[refute_0_123:[bind(X_15,$fot(X_22))]]) ).
cnf(refute_0_173,plain,
( least_upper_bound(X_22,least_upper_bound(Y,X_22)) != least_upper_bound(X_22,Y)
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,least_upper_bound(Y,X_22)),X_24)
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,Y),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,least_upper_bound(Y,X_22)),X_24)) ),[1,0],$fot(least_upper_bound(X_22,Y))]]) ).
cnf(refute_0_174,plain,
( least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,least_upper_bound(Y,X_22)),X_24)
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,Y),X_24) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(Y,X_22)),least_upper_bound(X_22,Y)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,Y),X_24),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,least_upper_bound(Y,X_22)),X_24)) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(Y,X_23))) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(least_upper_bound(Y,X_23)))]]) ).
cnf(refute_0_177,plain,
least_upper_bound(X_23,least_upper_bound(Y,X_23)) = least_upper_bound(X_23,Y),
inference(subst,[],[refute_0_123:[bind(X_15,$fot(X_23))]]) ).
cnf(refute_0_178,plain,
( least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(Y,X_23))) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23))
| least_upper_bound(X_23,least_upper_bound(Y,X_23)) != least_upper_bound(X_23,Y)
| least_upper_bound(X_22,least_upper_bound(X_23,Y)) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(Y,X_23))),least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23))) ),[0,1],$fot(least_upper_bound(X_23,Y))]]) ).
cnf(refute_0_179,plain,
( least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(Y,X_23))) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23))
| least_upper_bound(X_22,least_upper_bound(X_23,Y)) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(Y,X_23)),least_upper_bound(X_23,Y)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
least_upper_bound(X_22,least_upper_bound(X_23,Y)) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(Y,X_23))),least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23))) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
least_upper_bound(least_upper_bound(X_22,X_23),Y) = least_upper_bound(X_22,least_upper_bound(X_23,Y)),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_182,plain,
least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)) = least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)))]]) ).
cnf(refute_0_183,plain,
( least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)) != least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y))
| least_upper_bound(least_upper_bound(X_22,X_23),Y) != least_upper_bound(X_22,least_upper_bound(X_23,Y))
| least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)),least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y))) ),[1,1],$fot(least_upper_bound(X_22,least_upper_bound(X_23,Y)))]]) ).
cnf(refute_0_184,plain,
( least_upper_bound(least_upper_bound(X_22,X_23),Y) != least_upper_bound(X_22,least_upper_bound(X_23,Y))
| least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)),least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),Y),least_upper_bound(X_22,least_upper_bound(X_23,Y))) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(least_upper_bound(X_22,X_23),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_22,X_23)))]]) ).
cnf(refute_0_187,plain,
least_upper_bound(X_22,least_upper_bound(X_23,X)) = least_upper_bound(least_upper_bound(X_22,X_23),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X))]]) ).
cnf(refute_0_188,plain,
( least_upper_bound(X_22,least_upper_bound(X_23,X)) != least_upper_bound(least_upper_bound(X_22,X_23),X)
| least_upper_bound(least_upper_bound(X_22,X_23),X) = least_upper_bound(X_22,least_upper_bound(X_23,X)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_23,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_22,X_23),X)))]]) ).
cnf(refute_0_189,plain,
least_upper_bound(least_upper_bound(X_22,X_23),X) = least_upper_bound(X_22,least_upper_bound(X_23,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X)),least_upper_bound(least_upper_bound(X_22,X_23),X)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
( least_upper_bound(X,least_upper_bound(X_22,X_23)) != least_upper_bound(least_upper_bound(X_22,X_23),X)
| least_upper_bound(least_upper_bound(X_22,X_23),X) != least_upper_bound(X_22,least_upper_bound(X_23,X))
| least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_22,X_23)),least_upper_bound(X_22,least_upper_bound(X_23,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,X_23),X))]]) ).
cnf(refute_0_191,plain,
( least_upper_bound(X,least_upper_bound(X_22,X_23)) != least_upper_bound(least_upper_bound(X_22,X_23),X)
| least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),X),least_upper_bound(X_22,least_upper_bound(X_23,X))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_22,X_23)),least_upper_bound(least_upper_bound(X_22,X_23),X)) )],[refute_0_186,refute_0_191]) ).
cnf(refute_0_193,plain,
( least_upper_bound(X,least_upper_bound(X_22,X_23)) != least_upper_bound(X_22,least_upper_bound(X_23,X))
| least_upper_bound(X_22,least_upper_bound(X_23,X)) = least_upper_bound(X,least_upper_bound(X_22,X_23)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_22,X_23)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_23,X))))]]) ).
cnf(refute_0_194,plain,
least_upper_bound(X_22,least_upper_bound(X_23,X)) = least_upper_bound(X,least_upper_bound(X_22,X_23)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_22,X_23)),least_upper_bound(X_22,least_upper_bound(X_23,X))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) = least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)),
inference(subst,[],[refute_0_194:[bind(X,$fot(X_23)),bind(X_22,$fot(least_upper_bound(X_22,X_23))),bind(X_23,$fot(Y))]]) ).
cnf(refute_0_196,plain,
( least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))
| least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) != least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y))
| least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)))),bind(Y0,$fot(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)))),bind(Z0,$fot(least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))))]]) ).
cnf(refute_0_197,plain,
( least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))
| least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)),least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),Y)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))) )],[refute_0_185,refute_0_197]) ).
cnf(refute_0_199,plain,
( least_upper_bound(X_22,least_upper_bound(X_23,Y)) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23))
| least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))
| least_upper_bound(X_22,least_upper_bound(X_23,Y)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_22,least_upper_bound(X_23,Y)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)))]]) ).
cnf(refute_0_200,plain,
( least_upper_bound(X_22,least_upper_bound(X_23,Y)) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23))
| least_upper_bound(X_22,least_upper_bound(X_23,Y)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
least_upper_bound(X_22,least_upper_bound(X_23,Y)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,Y)),least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(Y,X_23))) )],[refute_0_180,refute_0_200]) ).
cnf(refute_0_202,plain,
( least_upper_bound(X_22,least_upper_bound(X_23,Y)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))
| least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) = least_upper_bound(X_22,least_upper_bound(X_23,Y)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_23,Y)))),bind(Y0,$fot(least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))))]]) ).
cnf(refute_0_203,plain,
least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y))) = least_upper_bound(X_22,least_upper_bound(X_23,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,Y)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,Y)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))) = least_upper_bound(Y,least_upper_bound(X_22,X_24)),
inference(subst,[],[refute_0_203:[bind(Y,$fot(X_24)),bind(X_22,$fot(Y)),bind(X_23,$fot(X_22))]]) ).
cnf(refute_0_205,plain,
least_upper_bound(least_upper_bound(Y,X_22),X_24) = least_upper_bound(Y,least_upper_bound(X_22,X_24)),
inference(subst,[],[refute_0_119:[bind(X,$fot(Y)),bind(Y,$fot(X_22)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_206,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)))]]) ).
cnf(refute_0_207,plain,
( least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24))
| least_upper_bound(least_upper_bound(Y,X_22),X_24) != least_upper_bound(Y,least_upper_bound(X_22,X_24))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_22,X_24)))]]) ).
cnf(refute_0_208,plain,
( least_upper_bound(least_upper_bound(Y,X_22),X_24) != least_upper_bound(Y,least_upper_bound(X_22,X_24))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_22),X_24),least_upper_bound(Y,least_upper_bound(X_22,X_24))) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
( least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))) != least_upper_bound(Y,least_upper_bound(X_22,X_24))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24)))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(Y,least_upper_bound(X_22,X_24)) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_22,X_24))))]]) ).
cnf(refute_0_211,plain,
( least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))) != least_upper_bound(Y,least_upper_bound(X_22,X_24))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(Y,least_upper_bound(X_22,X_24)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24)))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) = least_upper_bound(Y,least_upper_bound(X_22,X_24)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(Y,least_upper_bound(X_22,X_24))),least_upper_bound(Y,least_upper_bound(X_22,X_24))) )],[refute_0_204,refute_0_211]) ).
cnf(refute_0_213,plain,
( least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(Y,least_upper_bound(X_22,X_24))
| least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,Y),X_24)
| least_upper_bound(Y,least_upper_bound(X_22,X_24)) = least_upper_bound(least_upper_bound(X_22,Y),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,Y),X_24)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_22,X_24)))]]) ).
cnf(refute_0_214,plain,
( least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,Y),X_24)
| least_upper_bound(Y,least_upper_bound(X_22,X_24)) = least_upper_bound(least_upper_bound(X_22,Y),X_24) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(Y,least_upper_bound(X_22,X_24))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
least_upper_bound(least_upper_bound(X_22,Y),X_24) = least_upper_bound(X_22,least_upper_bound(Y,X_24)),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_22)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_216,plain,
( least_upper_bound(Y,least_upper_bound(X_22,X_24)) != least_upper_bound(least_upper_bound(X_22,Y),X_24)
| least_upper_bound(least_upper_bound(X_22,Y),X_24) != least_upper_bound(X_22,least_upper_bound(Y,X_24))
| least_upper_bound(Y,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(Y,X_24)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_22,X_24)),least_upper_bound(X_22,least_upper_bound(Y,X_24))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,Y),X_24))]]) ).
cnf(refute_0_217,plain,
( least_upper_bound(Y,least_upper_bound(X_22,X_24)) != least_upper_bound(least_upper_bound(X_22,Y),X_24)
| least_upper_bound(Y,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(Y,X_24)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,Y),X_24),least_upper_bound(X_22,least_upper_bound(Y,X_24))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
( least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,Y),X_24)
| least_upper_bound(Y,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(Y,X_24)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_22,X_24)),least_upper_bound(least_upper_bound(X_22,Y),X_24)) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
least_upper_bound(Y,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(Y,X_24)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(Y,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,Y),X_24)) )],[refute_0_175,refute_0_218]) ).
cnf(refute_0_220,plain,
least_upper_bound(X_38,least_upper_bound(X_54,X_55)) = least_upper_bound(X_54,least_upper_bound(X_38,X_55)),
inference(subst,[],[refute_0_219:[bind(Y,$fot(X_38)),bind(X_22,$fot(X_54)),bind(X_24,$fot(X_55))]]) ).
cnf(refute_0_221,plain,
( multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_38,least_upper_bound(X_54,X_55))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38))
| least_upper_bound(X_38,least_upper_bound(X_54,X_55)) != least_upper_bound(X_54,least_upper_bound(X_38,X_55))
| multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_54,least_upper_bound(X_38,X_55))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_38,least_upper_bound(X_54,X_55))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38))) ),[0,1],$fot(least_upper_bound(X_54,least_upper_bound(X_38,X_55)))]]) ).
cnf(refute_0_222,plain,
( multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_38,least_upper_bound(X_54,X_55))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38))
| multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_54,least_upper_bound(X_38,X_55))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,least_upper_bound(X_54,X_55)),least_upper_bound(X_54,least_upper_bound(X_38,X_55))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_54,least_upper_bound(X_38,X_55))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_54,X_55)),least_upper_bound(X_38,least_upper_bound(X_54,X_55))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_54,X_55)),X_38))) )],[refute_0_170,refute_0_222]) ).
cnf(refute_0_224,plain,
multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)),
inference(subst,[],[refute_0_223:[bind(X_38,$fot(b)),bind(X_54,$fot(a)),bind(X_55,$fot(X_24))]]) ).
cnf(refute_0_225,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_127:[bind(X_16,$fot(multiply(X,Z))),bind(X_9,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_226,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_18:[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_227,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_226]) ).
cnf(refute_0_228,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_229,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_225,refute_0_229]) ).
cnf(refute_0_231,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_127:[bind(X_16,$fot(Y)),bind(X_9,$fot(Z))]]) ).
cnf(refute_0_232,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_233,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_234,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_237,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_236]) ).
cnf(refute_0_238,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
inference(subst,[],[refute_0_237:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_239,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_240,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_235,refute_0_240]) ).
cnf(refute_0_242,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_227:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_243,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_244,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_245,plain,
( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_248,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_241,refute_0_248]) ).
cnf(refute_0_250,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_20:[bind(X,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_251,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_252,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_249,refute_0_252]) ).
cnf(refute_0_254,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_255,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_257,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_242,refute_0_256]) ).
cnf(refute_0_258,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_255,refute_0_257]) ).
cnf(refute_0_259,plain,
multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_230,refute_0_258]) ).
cnf(refute_0_260,plain,
( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_261,plain,
multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) = multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24))),
inference(subst,[],[refute_0_261:[bind(X,$fot(inverse(least_upper_bound(a,X_24)))),bind(Y,$fot(a)),bind(Z,$fot(least_upper_bound(b,X_24)))]]) ).
cnf(refute_0_263,plain,
( multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b))
| multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) != multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24)))
| multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b))))]]) ).
cnf(refute_0_264,plain,
( multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b))
| multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)),multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24)))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(a,least_upper_bound(b,X_24))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b))) )],[refute_0_224,refute_0_264]) ).
cnf(refute_0_266,plain,
( multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) != identity
| multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)),identity) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)))]]) ).
cnf(refute_0_267,plain,
( multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)) != identity
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_24)),b)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,X_24)),least_upper_bound(least_upper_bound(b,X_24),a)),identity) )],[refute_0_158,refute_0_267]) ).
cnf(refute_0_269,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b)) = identity,
inference(subst,[],[refute_0_268:[bind(X_24,$fot(X_251))]]) ).
cnf(refute_0_270,plain,
( b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b)) != identity
| b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_271,plain,
( b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b)))
| b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b)),identity) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_251)),b)))) )],[refute_0_96,refute_0_271]) ).
cnf(refute_0_273,plain,
multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),
inference(subst,[],[refute_0_48:[bind(X_70,$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251))))))]]) ).
cnf(refute_0_274,plain,
( multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251))))
| b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity)) ),[1],$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))))]]) ).
cnf(refute_0_275,plain,
( b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity),inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251))))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,X_251)))),identity)) )],[refute_0_272,refute_0_275]) ).
cnf(refute_0_277,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a)))))),
inference(subst,[],[refute_0_276:[bind(X_251,$fot(greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))))]]) ).
cnf(refute_0_278,plain,
least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)) = X_10,
inference(subst,[],[refute_0_112:[bind(X_11,$fot(greatest_lower_bound(X_28,X_29)))]]) ).
cnf(refute_0_279,plain,
greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10)) = greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_28)),bind(Y,$fot(X_29)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_280,plain,
( greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10)) != greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)
| greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10) = greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)))]]) ).
cnf(refute_0_281,plain,
greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10) = greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10)),greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
( greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10) != greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10))
| least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)),X_10) ),[0,1],$fot(greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10)))]]) ).
cnf(refute_0_283,plain,
( least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10))) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10),greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
least_upper_bound(X_10,greatest_lower_bound(X_28,greatest_lower_bound(X_29,X_10))) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(greatest_lower_bound(X_28,X_29),X_10)),X_10) )],[refute_0_278,refute_0_283]) ).
cnf(refute_0_285,plain,
least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))) = a,
inference(subst,[],[refute_0_284:[bind(X_10,$fot(a))]]) ).
cnf(refute_0_286,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))))))
| least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))) != a
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))))))) ),[1,0,1,0],$fot(a)]]) ).
cnf(refute_0_287,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))))))
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))),a) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
b = inverse(least_upper_bound(inverse(b),inverse(a))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,greatest_lower_bound(X_28,greatest_lower_bound(X_29,a))))))) )],[refute_0_277,refute_0_287]) ).
cnf(refute_0_289,plain,
least_upper_bound(X_117,X_118) = multiply(inverse(inverse(least_upper_bound(X_118,X_117))),multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118))),
inference(subst,[],[refute_0_9:[bind(X_66,$fot(inverse(least_upper_bound(X_118,X_117)))),bind(X_67,$fot(least_upper_bound(X_117,X_118)))]]) ).
cnf(refute_0_290,plain,
multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118)) = identity,
inference(subst,[],[refute_0_150:[bind(X_115,$fot(X_117)),bind(X_116,$fot(X_118))]]) ).
cnf(refute_0_291,plain,
( multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118)) != identity
| least_upper_bound(X_117,X_118) != multiply(inverse(inverse(least_upper_bound(X_118,X_117))),multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118)))
| least_upper_bound(X_117,X_118) = multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_117,X_118),multiply(inverse(inverse(least_upper_bound(X_118,X_117))),multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_292,plain,
( least_upper_bound(X_117,X_118) != multiply(inverse(inverse(least_upper_bound(X_118,X_117))),multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118)))
| least_upper_bound(X_117,X_118) = multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118)),identity) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
least_upper_bound(X_117,X_118) = multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity),
inference(resolve,[$cnf( $equal(least_upper_bound(X_117,X_118),multiply(inverse(inverse(least_upper_bound(X_118,X_117))),multiply(inverse(least_upper_bound(X_118,X_117)),least_upper_bound(X_117,X_118)))) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity) = inverse(inverse(least_upper_bound(X_118,X_117))),
inference(subst,[],[refute_0_48:[bind(X_70,$fot(inverse(inverse(least_upper_bound(X_118,X_117)))))]]) ).
cnf(refute_0_295,plain,
( multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity) != inverse(inverse(least_upper_bound(X_118,X_117)))
| least_upper_bound(X_117,X_118) != multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity)
| least_upper_bound(X_117,X_118) = inverse(inverse(least_upper_bound(X_118,X_117))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_117,X_118),multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity)) ),[1],$fot(inverse(inverse(least_upper_bound(X_118,X_117))))]]) ).
cnf(refute_0_296,plain,
( least_upper_bound(X_117,X_118) != multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity)
| least_upper_bound(X_117,X_118) = inverse(inverse(least_upper_bound(X_118,X_117))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity),inverse(inverse(least_upper_bound(X_118,X_117)))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
least_upper_bound(X_117,X_118) = inverse(inverse(least_upper_bound(X_118,X_117))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_117,X_118),multiply(inverse(inverse(least_upper_bound(X_118,X_117))),identity)) )],[refute_0_293,refute_0_296]) ).
cnf(refute_0_298,plain,
( X_120 != inverse(inverse(X_120))
| inverse(inverse(X_120)) = X_120 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_120)),bind(Y0,$fot(inverse(inverse(X_120))))]]) ).
cnf(refute_0_299,plain,
inverse(inverse(X_120)) = X_120,
inference(resolve,[$cnf( $equal(X_120,inverse(inverse(X_120))) )],[refute_0_84,refute_0_298]) ).
cnf(refute_0_300,plain,
inverse(inverse(least_upper_bound(X_118,X_117))) = least_upper_bound(X_118,X_117),
inference(subst,[],[refute_0_299:[bind(X_120,$fot(least_upper_bound(X_118,X_117)))]]) ).
cnf(refute_0_301,plain,
( inverse(inverse(least_upper_bound(X_118,X_117))) != least_upper_bound(X_118,X_117)
| least_upper_bound(X_117,X_118) != inverse(inverse(least_upper_bound(X_118,X_117)))
| least_upper_bound(X_117,X_118) = least_upper_bound(X_118,X_117) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_117,X_118),inverse(inverse(least_upper_bound(X_118,X_117)))) ),[1],$fot(least_upper_bound(X_118,X_117))]]) ).
cnf(refute_0_302,plain,
( least_upper_bound(X_117,X_118) != inverse(inverse(least_upper_bound(X_118,X_117)))
| least_upper_bound(X_117,X_118) = least_upper_bound(X_118,X_117) ),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_118,X_117))),least_upper_bound(X_118,X_117)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
least_upper_bound(X_117,X_118) = least_upper_bound(X_118,X_117),
inference(resolve,[$cnf( $equal(least_upper_bound(X_117,X_118),inverse(inverse(least_upper_bound(X_118,X_117)))) )],[refute_0_297,refute_0_302]) ).
cnf(refute_0_304,plain,
( least_upper_bound(X_117,X_118) != least_upper_bound(X_118,X_117)
| least_upper_bound(X_118,X_117) = least_upper_bound(X_117,X_118) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_117,X_118))),bind(Y0,$fot(least_upper_bound(X_118,X_117)))]]) ).
cnf(refute_0_305,plain,
least_upper_bound(X_118,X_117) = least_upper_bound(X_117,X_118),
inference(resolve,[$cnf( $equal(least_upper_bound(X_117,X_118),least_upper_bound(X_118,X_117)) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
least_upper_bound(inverse(b),inverse(a)) = least_upper_bound(inverse(a),inverse(b)),
inference(subst,[],[refute_0_305:[bind(X_117,$fot(inverse(a))),bind(X_118,$fot(inverse(b)))]]) ).
cnf(refute_0_307,plain,
inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(b),inverse(a))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(b),inverse(a))))]]) ).
cnf(refute_0_308,plain,
( inverse(least_upper_bound(inverse(b),inverse(a))) != inverse(least_upper_bound(inverse(b),inverse(a)))
| least_upper_bound(inverse(b),inverse(a)) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(b),inverse(a)))) ),[1,0],$fot(least_upper_bound(inverse(a),inverse(b)))]]) ).
cnf(refute_0_309,plain,
( least_upper_bound(inverse(b),inverse(a)) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(b),inverse(a)))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(a)),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_306,refute_0_309]) ).
cnf(refute_0_311,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| inverse(least_upper_bound(inverse(b),inverse(a))) != inverse(least_upper_bound(inverse(a),inverse(b)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) ),[0],$fot(inverse(least_upper_bound(inverse(b),inverse(a))))]]) ).
cnf(refute_0_312,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
b = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(a)))) )],[refute_0_288,refute_0_312]) ).
cnf(refute_0_314,plain,
( b != inverse(least_upper_bound(inverse(a),inverse(b)))
| inverse(least_upper_bound(inverse(a),inverse(b))) = b ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(least_upper_bound(inverse(a),inverse(b)))))]]) ).
cnf(refute_0_315,plain,
inverse(least_upper_bound(inverse(a),inverse(b))) = b,
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
( inverse(least_upper_bound(inverse(a),inverse(b))) != b
| least_upper_bound(inverse(a),inverse(b)) != inverse(inverse(least_upper_bound(inverse(a),inverse(b))))
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(inverse(least_upper_bound(inverse(a),inverse(b))))) ),[1,0],$fot(b)]]) ).
cnf(refute_0_317,plain,
( least_upper_bound(inverse(a),inverse(b)) != inverse(inverse(least_upper_bound(inverse(a),inverse(b))))
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(a),inverse(b))),b) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(inverse(least_upper_bound(inverse(a),inverse(b))))) )],[refute_0_85,refute_0_317]) ).
cnf(refute_0_319,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)) )],[refute_0_318,prove_p39a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP190-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 12:58:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.12/5.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.12/5.33
% 5.12/5.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.19/5.37
%------------------------------------------------------------------------------