TSTP Solution File: GRP167-5 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 10:37:14 EDT 2022
% Result : Unsatisfiable 0.90s 1.14s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 101
% Syntax : Number of clauses : 410 ( 218 unt; 0 nHn; 196 RR)
% Number of literals : 683 ( 682 equ; 275 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 667 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p10,axiom,
inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)) ).
cnf(lat4_1,axiom,
positive_part(X) = least_upper_bound(X,identity) ).
cnf(lat4_2,axiom,
negative_part(X) = greatest_lower_bound(X,identity) ).
cnf(lat4_3,axiom,
least_upper_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)) ).
cnf(prove_lat4,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)) ).
cnf(refute_0_0,plain,
multiply(multiply(inverse(X_108),X_108),X_109) = multiply(inverse(X_108),multiply(X_108,X_109)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_108))),bind(Y,$fot(X_108)),bind(Z,$fot(X_109))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_108),X_108) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_108))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(inverse(X_108),X_108),X_109) != multiply(inverse(X_108),multiply(X_108,X_109))
| multiply(inverse(X_108),X_108) != identity
| multiply(identity,X_109) = multiply(inverse(X_108),multiply(X_108,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_108),X_108),X_109),multiply(inverse(X_108),multiply(X_108,X_109))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_108),X_108),X_109) != multiply(inverse(X_108),multiply(X_108,X_109))
| multiply(identity,X_109) = multiply(inverse(X_108),multiply(X_108,X_109)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_108),X_108),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_109) = multiply(inverse(X_108),multiply(X_108,X_109)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_108),X_108),X_109),multiply(inverse(X_108),multiply(X_108,X_109))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_109) = X_109,
inference(subst,[],[left_identity:[bind(X,$fot(X_109))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_109) != X_109
| multiply(identity,X_109) != multiply(inverse(X_108),multiply(X_108,X_109))
| X_109 = multiply(inverse(X_108),multiply(X_108,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_109),multiply(inverse(X_108),multiply(X_108,X_109))) ),[0],$fot(X_109)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_109) != multiply(inverse(X_108),multiply(X_108,X_109))
| X_109 = multiply(inverse(X_108),multiply(X_108,X_109)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_109),X_109) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_109 = multiply(inverse(X_108),multiply(X_108,X_109)),
inference(resolve,[$cnf( $equal(multiply(identity,X_109),multiply(inverse(X_108),multiply(X_108,X_109))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
X_109 = multiply(inverse(inverse(positive_part(X_109))),multiply(inverse(positive_part(X_109)),X_109)),
inference(subst,[],[refute_0_8:[bind(X_108,$fot(inverse(positive_part(X_109))))]]) ).
cnf(refute_0_10,plain,
multiply(greatest_lower_bound(X_159,identity),X_158) = greatest_lower_bound(multiply(X_159,X_158),multiply(identity,X_158)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_158)),bind(Y,$fot(X_159)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_11,plain,
multiply(identity,X_158) = X_158,
inference(subst,[],[left_identity:[bind(X,$fot(X_158))]]) ).
cnf(refute_0_12,plain,
( multiply(greatest_lower_bound(X_159,identity),X_158) != greatest_lower_bound(multiply(X_159,X_158),multiply(identity,X_158))
| multiply(identity,X_158) != X_158
| multiply(greatest_lower_bound(X_159,identity),X_158) = greatest_lower_bound(multiply(X_159,X_158),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_159,identity),X_158),greatest_lower_bound(multiply(X_159,X_158),multiply(identity,X_158))) ),[1,1],$fot(X_158)]]) ).
cnf(refute_0_13,plain,
( multiply(greatest_lower_bound(X_159,identity),X_158) != greatest_lower_bound(multiply(X_159,X_158),multiply(identity,X_158))
| multiply(greatest_lower_bound(X_159,identity),X_158) = greatest_lower_bound(multiply(X_159,X_158),X_158) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_158),X_158) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(greatest_lower_bound(X_159,identity),X_158) = greatest_lower_bound(multiply(X_159,X_158),X_158),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_159,identity),X_158),greatest_lower_bound(multiply(X_159,X_158),multiply(identity,X_158))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_17,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( negative_part(X) != greatest_lower_bound(X,identity)
| greatest_lower_bound(X,identity) = negative_part(X) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(greatest_lower_bound(X,identity)))]]) ).
cnf(refute_0_19,plain,
greatest_lower_bound(X,identity) = negative_part(X),
inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) )],[lat4_2,refute_0_18]) ).
cnf(refute_0_20,plain,
greatest_lower_bound(X_159,identity) = negative_part(X_159),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_159))]]) ).
cnf(refute_0_21,plain,
multiply(greatest_lower_bound(X_159,identity),X_158) = multiply(greatest_lower_bound(X_159,identity),X_158),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_159,identity),X_158))]]) ).
cnf(refute_0_22,plain,
( multiply(greatest_lower_bound(X_159,identity),X_158) != multiply(greatest_lower_bound(X_159,identity),X_158)
| greatest_lower_bound(X_159,identity) != negative_part(X_159)
| multiply(greatest_lower_bound(X_159,identity),X_158) = multiply(negative_part(X_159),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_159,identity),X_158),multiply(greatest_lower_bound(X_159,identity),X_158)) ),[1,0],$fot(negative_part(X_159))]]) ).
cnf(refute_0_23,plain,
( greatest_lower_bound(X_159,identity) != negative_part(X_159)
| multiply(greatest_lower_bound(X_159,identity),X_158) = multiply(negative_part(X_159),X_158) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_159,identity),X_158),multiply(greatest_lower_bound(X_159,identity),X_158)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(greatest_lower_bound(X_159,identity),X_158) = multiply(negative_part(X_159),X_158),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_159,identity),negative_part(X_159)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(greatest_lower_bound(X_159,identity),X_158) != multiply(negative_part(X_159),X_158)
| multiply(greatest_lower_bound(X_159,identity),X_158) != greatest_lower_bound(multiply(X_159,X_158),X_158)
| multiply(negative_part(X_159),X_158) = greatest_lower_bound(multiply(X_159,X_158),X_158) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_159,identity),X_158),greatest_lower_bound(multiply(X_159,X_158),X_158)) ),[0],$fot(multiply(negative_part(X_159),X_158))]]) ).
cnf(refute_0_26,plain,
( multiply(greatest_lower_bound(X_159,identity),X_158) != greatest_lower_bound(multiply(X_159,X_158),X_158)
| multiply(negative_part(X_159),X_158) = greatest_lower_bound(multiply(X_159,X_158),X_158) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_159,identity),X_158),multiply(negative_part(X_159),X_158)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
greatest_lower_bound(X_71,X_70) = greatest_lower_bound(X_70,X_71),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_71)),bind(Y,$fot(X_70))]]) ).
cnf(refute_0_28,plain,
greatest_lower_bound(multiply(X_159,X_158),X_158) = greatest_lower_bound(X_158,multiply(X_159,X_158)),
inference(subst,[],[refute_0_27:[bind(X_70,$fot(X_158)),bind(X_71,$fot(multiply(X_159,X_158)))]]) ).
cnf(refute_0_29,plain,
( multiply(negative_part(X_159),X_158) != greatest_lower_bound(multiply(X_159,X_158),X_158)
| greatest_lower_bound(multiply(X_159,X_158),X_158) != greatest_lower_bound(X_158,multiply(X_159,X_158))
| multiply(negative_part(X_159),X_158) = greatest_lower_bound(X_158,multiply(X_159,X_158)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(X_159),X_158),greatest_lower_bound(X_158,multiply(X_159,X_158))) ),[0],$fot(greatest_lower_bound(multiply(X_159,X_158),X_158))]]) ).
cnf(refute_0_30,plain,
( multiply(negative_part(X_159),X_158) != greatest_lower_bound(multiply(X_159,X_158),X_158)
| multiply(negative_part(X_159),X_158) = greatest_lower_bound(X_158,multiply(X_159,X_158)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_159,X_158),X_158),greatest_lower_bound(X_158,multiply(X_159,X_158))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( multiply(greatest_lower_bound(X_159,identity),X_158) != greatest_lower_bound(multiply(X_159,X_158),X_158)
| multiply(negative_part(X_159),X_158) = greatest_lower_bound(X_158,multiply(X_159,X_158)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_159),X_158),greatest_lower_bound(multiply(X_159,X_158),X_158)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(negative_part(X_159),X_158) = greatest_lower_bound(X_158,multiply(X_159,X_158)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_159,identity),X_158),greatest_lower_bound(multiply(X_159,X_158),X_158)) )],[refute_0_14,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(negative_part(inverse(X_161)),X_161) = greatest_lower_bound(X_161,multiply(inverse(X_161),X_161)),
inference(subst,[],[refute_0_32:[bind(X_158,$fot(X_161)),bind(X_159,$fot(inverse(X_161)))]]) ).
cnf(refute_0_34,plain,
multiply(inverse(X_161),X_161) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_161))]]) ).
cnf(refute_0_35,plain,
( multiply(inverse(X_161),X_161) != identity
| multiply(negative_part(inverse(X_161)),X_161) != greatest_lower_bound(X_161,multiply(inverse(X_161),X_161))
| multiply(negative_part(inverse(X_161)),X_161) = greatest_lower_bound(X_161,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_161)),X_161),greatest_lower_bound(X_161,multiply(inverse(X_161),X_161))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_36,plain,
( multiply(negative_part(inverse(X_161)),X_161) != greatest_lower_bound(X_161,multiply(inverse(X_161),X_161))
| multiply(negative_part(inverse(X_161)),X_161) = greatest_lower_bound(X_161,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_161),X_161),identity) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(negative_part(inverse(X_161)),X_161) = greatest_lower_bound(X_161,identity),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_161)),X_161),greatest_lower_bound(X_161,multiply(inverse(X_161),X_161))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
inverse(least_upper_bound(identity,B)) = greatest_lower_bound(inverse(identity),inverse(B)),
inference(subst,[],[p10:[bind(A,$fot(identity))]]) ).
cnf(refute_0_39,plain,
multiply(inverse(identity),identity) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_40,plain,
X_111 = multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111)),
inference(subst,[],[refute_0_8:[bind(X_108,$fot(inverse(X_111))),bind(X_109,$fot(X_111))]]) ).
cnf(refute_0_41,plain,
multiply(inverse(X_111),X_111) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_111))]]) ).
cnf(refute_0_42,plain,
( X_111 != multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))
| multiply(inverse(X_111),X_111) != identity
| X_111 = multiply(inverse(inverse(X_111)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_111,multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_43,plain,
( X_111 != multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))
| X_111 = multiply(inverse(inverse(X_111)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_111),X_111),identity) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
X_111 = multiply(inverse(inverse(X_111)),identity),
inference(resolve,[$cnf( $equal(X_111,multiply(inverse(inverse(X_111)),multiply(inverse(X_111),X_111))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111))),
inference(subst,[],[refute_0_8:[bind(X_108,$fot(inverse(X_110))),bind(X_109,$fot(multiply(X_110,X_111)))]]) ).
cnf(refute_0_46,plain,
X_111 = multiply(inverse(X_110),multiply(X_110,X_111)),
inference(subst,[],[refute_0_8:[bind(X_108,$fot(X_110)),bind(X_109,$fot(X_111))]]) ).
cnf(refute_0_47,plain,
( X_111 != multiply(inverse(X_110),multiply(X_110,X_111))
| multiply(inverse(X_110),multiply(X_110,X_111)) = X_111 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_111)),bind(Y0,$fot(multiply(inverse(X_110),multiply(X_110,X_111))))]]) ).
cnf(refute_0_48,plain,
multiply(inverse(X_110),multiply(X_110,X_111)) = X_111,
inference(resolve,[$cnf( $equal(X_111,multiply(inverse(X_110),multiply(X_110,X_111))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( multiply(X_110,X_111) != multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))
| multiply(inverse(X_110),multiply(X_110,X_111)) != X_111
| multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),X_111) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_110,X_111),multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))) ),[1,1],$fot(X_111)]]) ).
cnf(refute_0_50,plain,
( multiply(X_110,X_111) != multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))
| multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),X_111) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_110),multiply(X_110,X_111)),X_111) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(X_110,X_111) = multiply(inverse(inverse(X_110)),X_111),
inference(resolve,[$cnf( $equal(multiply(X_110,X_111),multiply(inverse(inverse(X_110)),multiply(inverse(X_110),multiply(X_110,X_111)))) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiply(X_110,X_111) != multiply(inverse(inverse(X_110)),X_111)
| multiply(inverse(inverse(X_110)),X_111) = multiply(X_110,X_111) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(multiply(X_110,X_111))),bind(Y0,$fot(multiply(inverse(inverse(X_110)),X_111)))]]) ).
cnf(refute_0_53,plain,
multiply(inverse(inverse(X_110)),X_111) = multiply(X_110,X_111),
inference(resolve,[$cnf( $equal(multiply(X_110,X_111),multiply(inverse(inverse(X_110)),X_111)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(inverse(inverse(X_111)),identity) = multiply(X_111,identity),
inference(subst,[],[refute_0_53:[bind(X_110,$fot(X_111)),bind(X_111,$fot(identity))]]) ).
cnf(refute_0_55,plain,
( X_111 != multiply(inverse(inverse(X_111)),identity)
| multiply(inverse(inverse(X_111)),identity) != multiply(X_111,identity)
| X_111 = multiply(X_111,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_111,multiply(X_111,identity)) ),[0],$fot(multiply(inverse(inverse(X_111)),identity))]]) ).
cnf(refute_0_56,plain,
( X_111 != multiply(inverse(inverse(X_111)),identity)
| X_111 = multiply(X_111,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_111)),identity),multiply(X_111,identity)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
X_111 = multiply(X_111,identity),
inference(resolve,[$cnf( $equal(X_111,multiply(inverse(inverse(X_111)),identity)) )],[refute_0_44,refute_0_56]) ).
cnf(refute_0_58,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_57:[bind(X_111,$fot(inverse(identity)))]]) ).
cnf(refute_0_59,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_60,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(inverse(identity),identity) != identity
| multiply(inverse(identity),identity) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_62,plain,
( multiply(inverse(identity),identity) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_39,refute_0_62]) ).
cnf(refute_0_64,plain,
( inverse(identity) != identity
| inverse(least_upper_bound(identity,B)) != greatest_lower_bound(inverse(identity),inverse(B))
| inverse(least_upper_bound(identity,B)) = greatest_lower_bound(identity,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,B)),greatest_lower_bound(inverse(identity),inverse(B))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_65,plain,
( inverse(least_upper_bound(identity,B)) != greatest_lower_bound(inverse(identity),inverse(B))
| inverse(least_upper_bound(identity,B)) = greatest_lower_bound(identity,inverse(B)) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
inverse(least_upper_bound(identity,B)) = greatest_lower_bound(identity,inverse(B)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,B)),greatest_lower_bound(inverse(identity),inverse(B))) )],[refute_0_38,refute_0_65]) ).
cnf(refute_0_67,plain,
least_upper_bound(identity,Y) = least_upper_bound(Y,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity))]]) ).
cnf(refute_0_68,plain,
positive_part(Y) = least_upper_bound(Y,identity),
inference(subst,[],[lat4_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_69,plain,
( positive_part(Y) != least_upper_bound(Y,identity)
| least_upper_bound(Y,identity) = positive_part(Y) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(positive_part(Y))),bind(Y0,$fot(least_upper_bound(Y,identity)))]]) ).
cnf(refute_0_70,plain,
least_upper_bound(Y,identity) = positive_part(Y),
inference(resolve,[$cnf( $equal(positive_part(Y),least_upper_bound(Y,identity)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( least_upper_bound(Y,identity) != positive_part(Y)
| least_upper_bound(identity,Y) != least_upper_bound(Y,identity)
| least_upper_bound(identity,Y) = positive_part(Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,Y),least_upper_bound(Y,identity)) ),[1],$fot(positive_part(Y))]]) ).
cnf(refute_0_72,plain,
( least_upper_bound(identity,Y) != least_upper_bound(Y,identity)
| least_upper_bound(identity,Y) = positive_part(Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,identity),positive_part(Y)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
least_upper_bound(identity,Y) = positive_part(Y),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,Y),least_upper_bound(Y,identity)) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
least_upper_bound(identity,B) = positive_part(B),
inference(subst,[],[refute_0_73:[bind(Y,$fot(B))]]) ).
cnf(refute_0_75,plain,
inverse(least_upper_bound(identity,B)) = inverse(least_upper_bound(identity,B)),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,B)))]]) ).
cnf(refute_0_76,plain,
( inverse(least_upper_bound(identity,B)) != inverse(least_upper_bound(identity,B))
| least_upper_bound(identity,B) != positive_part(B)
| inverse(least_upper_bound(identity,B)) = inverse(positive_part(B)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,B)),inverse(least_upper_bound(identity,B))) ),[1,0],$fot(positive_part(B))]]) ).
cnf(refute_0_77,plain,
( least_upper_bound(identity,B) != positive_part(B)
| inverse(least_upper_bound(identity,B)) = inverse(positive_part(B)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,B)),inverse(least_upper_bound(identity,B))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
inverse(least_upper_bound(identity,B)) = inverse(positive_part(B)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,B),positive_part(B)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
( inverse(least_upper_bound(identity,B)) != greatest_lower_bound(identity,inverse(B))
| inverse(least_upper_bound(identity,B)) != inverse(positive_part(B))
| inverse(positive_part(B)) = greatest_lower_bound(identity,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,B)),greatest_lower_bound(identity,inverse(B))) ),[0],$fot(inverse(positive_part(B)))]]) ).
cnf(refute_0_80,plain,
( inverse(least_upper_bound(identity,B)) != greatest_lower_bound(identity,inverse(B))
| inverse(positive_part(B)) = greatest_lower_bound(identity,inverse(B)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,B)),inverse(positive_part(B))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
greatest_lower_bound(X,identity) = greatest_lower_bound(identity,X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_82,plain,
( greatest_lower_bound(X,identity) != greatest_lower_bound(identity,X)
| negative_part(X) != greatest_lower_bound(X,identity)
| negative_part(X) = greatest_lower_bound(identity,X) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) ),[1],$fot(greatest_lower_bound(identity,X))]]) ).
cnf(refute_0_83,plain,
( negative_part(X) != greatest_lower_bound(X,identity)
| negative_part(X) = greatest_lower_bound(identity,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,identity),greatest_lower_bound(identity,X)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
negative_part(X) = greatest_lower_bound(identity,X),
inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) )],[lat4_2,refute_0_83]) ).
cnf(refute_0_85,plain,
( negative_part(X) != greatest_lower_bound(identity,X)
| greatest_lower_bound(identity,X) = negative_part(X) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(greatest_lower_bound(identity,X)))]]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(identity,X) = negative_part(X),
inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(identity,X)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
greatest_lower_bound(identity,inverse(B)) = negative_part(inverse(B)),
inference(subst,[],[refute_0_86:[bind(X,$fot(inverse(B)))]]) ).
cnf(refute_0_88,plain,
( greatest_lower_bound(identity,inverse(B)) != negative_part(inverse(B))
| inverse(positive_part(B)) != greatest_lower_bound(identity,inverse(B))
| inverse(positive_part(B)) = negative_part(inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(positive_part(B)),greatest_lower_bound(identity,inverse(B))) ),[1],$fot(negative_part(inverse(B)))]]) ).
cnf(refute_0_89,plain,
( inverse(positive_part(B)) != greatest_lower_bound(identity,inverse(B))
| inverse(positive_part(B)) = negative_part(inverse(B)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(B)),negative_part(inverse(B))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( inverse(least_upper_bound(identity,B)) != greatest_lower_bound(identity,inverse(B))
| inverse(positive_part(B)) = negative_part(inverse(B)) ),
inference(resolve,[$cnf( $equal(inverse(positive_part(B)),greatest_lower_bound(identity,inverse(B))) )],[refute_0_80,refute_0_89]) ).
cnf(refute_0_91,plain,
inverse(positive_part(B)) = negative_part(inverse(B)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,B)),greatest_lower_bound(identity,inverse(B))) )],[refute_0_66,refute_0_90]) ).
cnf(refute_0_92,plain,
( inverse(positive_part(B)) != negative_part(inverse(B))
| negative_part(inverse(B)) = inverse(positive_part(B)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(positive_part(B)))),bind(Y0,$fot(negative_part(inverse(B))))]]) ).
cnf(refute_0_93,plain,
negative_part(inverse(B)) = inverse(positive_part(B)),
inference(resolve,[$cnf( $equal(inverse(positive_part(B)),negative_part(inverse(B))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
negative_part(inverse(X_161)) = inverse(positive_part(X_161)),
inference(subst,[],[refute_0_93:[bind(B,$fot(X_161))]]) ).
cnf(refute_0_95,plain,
multiply(negative_part(inverse(X_161)),X_161) = multiply(negative_part(inverse(X_161)),X_161),
introduced(tautology,[refl,[$fot(multiply(negative_part(inverse(X_161)),X_161))]]) ).
cnf(refute_0_96,plain,
( multiply(negative_part(inverse(X_161)),X_161) != multiply(negative_part(inverse(X_161)),X_161)
| negative_part(inverse(X_161)) != inverse(positive_part(X_161))
| multiply(negative_part(inverse(X_161)),X_161) = multiply(inverse(positive_part(X_161)),X_161) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_161)),X_161),multiply(negative_part(inverse(X_161)),X_161)) ),[1,0],$fot(inverse(positive_part(X_161)))]]) ).
cnf(refute_0_97,plain,
( negative_part(inverse(X_161)) != inverse(positive_part(X_161))
| multiply(negative_part(inverse(X_161)),X_161) = multiply(inverse(positive_part(X_161)),X_161) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_161)),X_161),multiply(negative_part(inverse(X_161)),X_161)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(negative_part(inverse(X_161)),X_161) = multiply(inverse(positive_part(X_161)),X_161),
inference(resolve,[$cnf( $equal(negative_part(inverse(X_161)),inverse(positive_part(X_161))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( multiply(negative_part(inverse(X_161)),X_161) != multiply(inverse(positive_part(X_161)),X_161)
| multiply(negative_part(inverse(X_161)),X_161) != greatest_lower_bound(X_161,identity)
| multiply(inverse(positive_part(X_161)),X_161) = greatest_lower_bound(X_161,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_161)),X_161),greatest_lower_bound(X_161,identity)) ),[0],$fot(multiply(inverse(positive_part(X_161)),X_161))]]) ).
cnf(refute_0_100,plain,
( multiply(negative_part(inverse(X_161)),X_161) != greatest_lower_bound(X_161,identity)
| multiply(inverse(positive_part(X_161)),X_161) = greatest_lower_bound(X_161,identity) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_161)),X_161),multiply(inverse(positive_part(X_161)),X_161)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
greatest_lower_bound(X_161,identity) = negative_part(X_161),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_161))]]) ).
cnf(refute_0_102,plain,
( multiply(inverse(positive_part(X_161)),X_161) != greatest_lower_bound(X_161,identity)
| greatest_lower_bound(X_161,identity) != negative_part(X_161)
| multiply(inverse(positive_part(X_161)),X_161) = negative_part(X_161) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(positive_part(X_161)),X_161),negative_part(X_161)) ),[0],$fot(greatest_lower_bound(X_161,identity))]]) ).
cnf(refute_0_103,plain,
( multiply(inverse(positive_part(X_161)),X_161) != greatest_lower_bound(X_161,identity)
| multiply(inverse(positive_part(X_161)),X_161) = negative_part(X_161) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_161,identity),negative_part(X_161)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( multiply(negative_part(inverse(X_161)),X_161) != greatest_lower_bound(X_161,identity)
| multiply(inverse(positive_part(X_161)),X_161) = negative_part(X_161) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_161)),X_161),greatest_lower_bound(X_161,identity)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(inverse(positive_part(X_161)),X_161) = negative_part(X_161),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_161)),X_161),greatest_lower_bound(X_161,identity)) )],[refute_0_37,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(inverse(positive_part(X_109)),X_109) = negative_part(X_109),
inference(subst,[],[refute_0_105:[bind(X_161,$fot(X_109))]]) ).
cnf(refute_0_107,plain,
( X_109 != multiply(inverse(inverse(positive_part(X_109))),multiply(inverse(positive_part(X_109)),X_109))
| multiply(inverse(positive_part(X_109)),X_109) != negative_part(X_109)
| X_109 = multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(X_109,multiply(inverse(inverse(positive_part(X_109))),multiply(inverse(positive_part(X_109)),X_109))) ),[1,1],$fot(negative_part(X_109))]]) ).
cnf(refute_0_108,plain,
( X_109 != multiply(inverse(inverse(positive_part(X_109))),multiply(inverse(positive_part(X_109)),X_109))
| X_109 = multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_109)),X_109),negative_part(X_109)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
X_109 = multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)),
inference(resolve,[$cnf( $equal(X_109,multiply(inverse(inverse(positive_part(X_109))),multiply(inverse(positive_part(X_109)),X_109))) )],[refute_0_9,refute_0_108]) ).
cnf(refute_0_110,plain,
multiply(multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)),X_109) = multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(least_upper_bound(X_15,X_16)))),bind(Y,$fot(least_upper_bound(X_16,X_15))),bind(Z,$fot(X_109))]]) ).
cnf(refute_0_111,plain,
multiply(inverse(least_upper_bound(X_16,X_15)),least_upper_bound(X_16,X_15)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_16,X_15)))]]) ).
cnf(refute_0_112,plain,
inverse(least_upper_bound(X_13,X_14)) = greatest_lower_bound(inverse(X_13),inverse(X_14)),
inference(subst,[],[p10:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_113,plain,
least_upper_bound(X_14,X_13) = least_upper_bound(X_13,X_14),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_14)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_114,plain,
( least_upper_bound(X_14,X_13) != least_upper_bound(X_13,X_14)
| least_upper_bound(X_13,X_14) = least_upper_bound(X_14,X_13) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_14,X_13))),bind(Y0,$fot(least_upper_bound(X_13,X_14)))]]) ).
cnf(refute_0_115,plain,
least_upper_bound(X_13,X_14) = least_upper_bound(X_14,X_13),
inference(resolve,[$cnf( $equal(least_upper_bound(X_14,X_13),least_upper_bound(X_13,X_14)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( inverse(least_upper_bound(X_13,X_14)) != greatest_lower_bound(inverse(X_13),inverse(X_14))
| least_upper_bound(X_13,X_14) != least_upper_bound(X_14,X_13)
| inverse(least_upper_bound(X_14,X_13)) = greatest_lower_bound(inverse(X_13),inverse(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_13,X_14)),greatest_lower_bound(inverse(X_13),inverse(X_14))) ),[0,0],$fot(least_upper_bound(X_14,X_13))]]) ).
cnf(refute_0_117,plain,
( inverse(least_upper_bound(X_13,X_14)) != greatest_lower_bound(inverse(X_13),inverse(X_14))
| inverse(least_upper_bound(X_14,X_13)) = greatest_lower_bound(inverse(X_13),inverse(X_14)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,X_14),least_upper_bound(X_14,X_13)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
inverse(least_upper_bound(X_14,X_13)) = greatest_lower_bound(inverse(X_13),inverse(X_14)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_13,X_14)),greatest_lower_bound(inverse(X_13),inverse(X_14))) )],[refute_0_112,refute_0_117]) ).
cnf(refute_0_119,plain,
( inverse(least_upper_bound(A,B)) != greatest_lower_bound(inverse(A),inverse(B))
| greatest_lower_bound(inverse(A),inverse(B)) = inverse(least_upper_bound(A,B)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(A,B)))),bind(Y0,$fot(greatest_lower_bound(inverse(A),inverse(B))))]]) ).
cnf(refute_0_120,plain,
greatest_lower_bound(inverse(A),inverse(B)) = inverse(least_upper_bound(A,B)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(A,B)),greatest_lower_bound(inverse(A),inverse(B))) )],[p10,refute_0_119]) ).
cnf(refute_0_121,plain,
greatest_lower_bound(inverse(X_13),inverse(X_14)) = inverse(least_upper_bound(X_13,X_14)),
inference(subst,[],[refute_0_120:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_122,plain,
( greatest_lower_bound(inverse(X_13),inverse(X_14)) != inverse(least_upper_bound(X_13,X_14))
| inverse(least_upper_bound(X_14,X_13)) != greatest_lower_bound(inverse(X_13),inverse(X_14))
| inverse(least_upper_bound(X_14,X_13)) = inverse(least_upper_bound(X_13,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_14,X_13)),greatest_lower_bound(inverse(X_13),inverse(X_14))) ),[1],$fot(inverse(least_upper_bound(X_13,X_14)))]]) ).
cnf(refute_0_123,plain,
( inverse(least_upper_bound(X_14,X_13)) != greatest_lower_bound(inverse(X_13),inverse(X_14))
| inverse(least_upper_bound(X_14,X_13)) = inverse(least_upper_bound(X_13,X_14)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_13),inverse(X_14)),inverse(least_upper_bound(X_13,X_14))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
inverse(least_upper_bound(X_14,X_13)) = inverse(least_upper_bound(X_13,X_14)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_14,X_13)),greatest_lower_bound(inverse(X_13),inverse(X_14))) )],[refute_0_118,refute_0_123]) ).
cnf(refute_0_125,plain,
inverse(least_upper_bound(X_16,X_15)) = inverse(least_upper_bound(X_15,X_16)),
inference(subst,[],[refute_0_124:[bind(X_13,$fot(X_15)),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_126,plain,
( multiply(inverse(least_upper_bound(X_16,X_15)),least_upper_bound(X_16,X_15)) != identity
| inverse(least_upper_bound(X_16,X_15)) != inverse(least_upper_bound(X_15,X_16))
| multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_15)),least_upper_bound(X_16,X_15)),identity) ),[0,0],$fot(inverse(least_upper_bound(X_15,X_16)))]]) ).
cnf(refute_0_127,plain,
( multiply(inverse(least_upper_bound(X_16,X_15)),least_upper_bound(X_16,X_15)) != identity
| multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)) = identity ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_16,X_15)),inverse(least_upper_bound(X_15,X_16))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_15)),least_upper_bound(X_16,X_15)),identity) )],[refute_0_111,refute_0_127]) ).
cnf(refute_0_129,plain,
( multiply(multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)),X_109) != multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))
| multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)) != identity
| multiply(identity,X_109) = multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)),X_109),multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_130,plain,
( multiply(multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)),X_109) != multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))
| multiply(identity,X_109) = multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)),identity) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(identity,X_109) = multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_15,X_16)),least_upper_bound(X_16,X_15)),X_109),multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))) )],[refute_0_110,refute_0_130]) ).
cnf(refute_0_132,plain,
( multiply(identity,X_109) != X_109
| multiply(identity,X_109) != multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))
| X_109 = multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_109),multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))) ),[0],$fot(X_109)]]) ).
cnf(refute_0_133,plain,
( multiply(identity,X_109) != multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))
| X_109 = multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_109),X_109) )],[refute_0_5,refute_0_132]) ).
cnf(refute_0_134,plain,
X_109 = multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109)),
inference(resolve,[$cnf( $equal(multiply(identity,X_109),multiply(inverse(least_upper_bound(X_15,X_16)),multiply(least_upper_bound(X_16,X_15),X_109))) )],[refute_0_131,refute_0_133]) ).
cnf(refute_0_135,plain,
X_115 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))),X_115)),
inference(subst,[],[refute_0_134:[bind(X_109,$fot(X_115)),bind(X_15,$fot(inverse(least_upper_bound(A,B)))),bind(X_16,$fot(inverse(A)))]]) ).
cnf(refute_0_136,plain,
least_upper_bound(inverse(A),greatest_lower_bound(inverse(A),inverse(B))) = inverse(A),
inference(subst,[],[lub_absorbtion:[bind(X,$fot(inverse(A))),bind(Y,$fot(inverse(B)))]]) ).
cnf(refute_0_137,plain,
( greatest_lower_bound(inverse(A),inverse(B)) != inverse(least_upper_bound(A,B))
| least_upper_bound(inverse(A),greatest_lower_bound(inverse(A),inverse(B))) != inverse(A)
| least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))) = inverse(A) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(A),greatest_lower_bound(inverse(A),inverse(B))),inverse(A)) ),[0,1],$fot(inverse(least_upper_bound(A,B)))]]) ).
cnf(refute_0_138,plain,
( least_upper_bound(inverse(A),greatest_lower_bound(inverse(A),inverse(B))) != inverse(A)
| least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))) = inverse(A) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(A),inverse(B)),inverse(least_upper_bound(A,B))) )],[refute_0_120,refute_0_137]) ).
cnf(refute_0_139,plain,
least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))) = inverse(A),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(A),greatest_lower_bound(inverse(A),inverse(B))),inverse(A)) )],[refute_0_136,refute_0_138]) ).
cnf(refute_0_140,plain,
( X_115 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))),X_115))
| least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))) != inverse(A)
| X_115 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) ),
introduced(tautology,[equality,[$cnf( $equal(X_115,multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))),X_115))) ),[1,1,0],$fot(inverse(A))]]) ).
cnf(refute_0_141,plain,
( X_115 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))),X_115))
| X_115 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))),inverse(A)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
X_115 = multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)),
inference(resolve,[$cnf( $equal(X_115,multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))),X_115))) )],[refute_0_135,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(inverse(inverse(A)),multiply(inverse(A),X_115)) = multiply(A,multiply(inverse(A),X_115)),
inference(subst,[],[refute_0_53:[bind(X_110,$fot(A)),bind(X_111,$fot(multiply(inverse(A),X_115)))]]) ).
cnf(refute_0_144,plain,
inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))))]]) ).
cnf(refute_0_145,plain,
( inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))) != inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))))
| least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))) != inverse(A)
| inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))) = inverse(inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))),inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))))) ),[1,0],$fot(inverse(A))]]) ).
cnf(refute_0_146,plain,
( least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))) != inverse(A)
| inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))) = inverse(inverse(A)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))),inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))) = inverse(inverse(A)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))),inverse(A)) )],[refute_0_139,refute_0_146]) ).
cnf(refute_0_148,plain,
least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = greatest_lower_bound(least_upper_bound(X_50,X_51),least_upper_bound(X_50,identity)),
inference(subst,[],[lat4_3:[bind(X,$fot(X_50)),bind(Y,$fot(X_51)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_149,plain,
positive_part(X_50) = least_upper_bound(X_50,identity),
inference(subst,[],[lat4_1:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_150,plain,
( positive_part(X_50) != least_upper_bound(X_50,identity)
| least_upper_bound(X_50,identity) = positive_part(X_50) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(positive_part(X_50))),bind(Y0,$fot(least_upper_bound(X_50,identity)))]]) ).
cnf(refute_0_151,plain,
least_upper_bound(X_50,identity) = positive_part(X_50),
inference(resolve,[$cnf( $equal(positive_part(X_50),least_upper_bound(X_50,identity)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) != greatest_lower_bound(least_upper_bound(X_50,X_51),least_upper_bound(X_50,identity))
| least_upper_bound(X_50,identity) != positive_part(X_50)
| least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),greatest_lower_bound(least_upper_bound(X_50,X_51),least_upper_bound(X_50,identity))) ),[1,1],$fot(positive_part(X_50))]]) ).
cnf(refute_0_153,plain,
( least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) != greatest_lower_bound(least_upper_bound(X_50,X_51),least_upper_bound(X_50,identity))
| least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,identity),positive_part(X_50)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),greatest_lower_bound(least_upper_bound(X_50,X_51),least_upper_bound(X_50,identity))) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
greatest_lower_bound(X_51,identity) = negative_part(X_51),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_156,plain,
least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)))]]) ).
cnf(refute_0_157,plain,
( greatest_lower_bound(X_51,identity) != negative_part(X_51)
| least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) != least_upper_bound(X_50,greatest_lower_bound(X_51,identity))
| least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = least_upper_bound(X_50,negative_part(X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),least_upper_bound(X_50,greatest_lower_bound(X_51,identity))) ),[1,1],$fot(negative_part(X_51))]]) ).
cnf(refute_0_158,plain,
( greatest_lower_bound(X_51,identity) != negative_part(X_51)
| least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = least_upper_bound(X_50,negative_part(X_51)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),least_upper_bound(X_50,greatest_lower_bound(X_51,identity))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) = least_upper_bound(X_50,negative_part(X_51)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_51,identity),negative_part(X_51)) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
( least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) != greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))
| least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) != least_upper_bound(X_50,negative_part(X_51))
| least_upper_bound(X_50,negative_part(X_51)) = greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))) ),[0],$fot(least_upper_bound(X_50,negative_part(X_51)))]]) ).
cnf(refute_0_161,plain,
( least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) != greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))
| least_upper_bound(X_50,negative_part(X_51)) = greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),least_upper_bound(X_50,negative_part(X_51))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_163,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_162]) ).
cnf(refute_0_164,plain,
greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)) = greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51)),
inference(subst,[],[refute_0_163:[bind(X,$fot(positive_part(X_50))),bind(Y,$fot(least_upper_bound(X_50,X_51)))]]) ).
cnf(refute_0_165,plain,
( greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)) != greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51))
| least_upper_bound(X_50,negative_part(X_51)) != greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))
| least_upper_bound(X_50,negative_part(X_51)) = greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,negative_part(X_51)),greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))) ),[1],$fot(greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51)))]]) ).
cnf(refute_0_166,plain,
( least_upper_bound(X_50,negative_part(X_51)) != greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))
| least_upper_bound(X_50,negative_part(X_51)) = greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50)),greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( least_upper_bound(X_50,greatest_lower_bound(X_51,identity)) != greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))
| least_upper_bound(X_50,negative_part(X_51)) = greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,negative_part(X_51)),greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))) )],[refute_0_161,refute_0_166]) ).
cnf(refute_0_168,plain,
least_upper_bound(X_50,negative_part(X_51)) = greatest_lower_bound(positive_part(X_50),least_upper_bound(X_50,X_51)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,greatest_lower_bound(X_51,identity)),greatest_lower_bound(least_upper_bound(X_50,X_51),positive_part(X_50))) )],[refute_0_154,refute_0_167]) ).
cnf(refute_0_169,plain,
least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) = greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,greatest_lower_bound(X_22,X_53))),
inference(subst,[],[refute_0_168:[bind(X_50,$fot(X_53)),bind(X_51,$fot(greatest_lower_bound(X_22,X_53)))]]) ).
cnf(refute_0_170,plain,
least_upper_bound(X_21,greatest_lower_bound(X_21,X_22)) = X_21,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_21)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_171,plain,
greatest_lower_bound(X_22,X_21) = greatest_lower_bound(X_21,X_22),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_22)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_172,plain,
( greatest_lower_bound(X_22,X_21) != greatest_lower_bound(X_21,X_22)
| greatest_lower_bound(X_21,X_22) = greatest_lower_bound(X_22,X_21) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X_22,X_21))),bind(Y0,$fot(greatest_lower_bound(X_21,X_22)))]]) ).
cnf(refute_0_173,plain,
greatest_lower_bound(X_21,X_22) = greatest_lower_bound(X_22,X_21),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_21),greatest_lower_bound(X_21,X_22)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
( greatest_lower_bound(X_21,X_22) != greatest_lower_bound(X_22,X_21)
| least_upper_bound(X_21,greatest_lower_bound(X_21,X_22)) != X_21
| least_upper_bound(X_21,greatest_lower_bound(X_22,X_21)) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_21,greatest_lower_bound(X_21,X_22)),X_21) ),[0,1],$fot(greatest_lower_bound(X_22,X_21))]]) ).
cnf(refute_0_175,plain,
( least_upper_bound(X_21,greatest_lower_bound(X_21,X_22)) != X_21
| least_upper_bound(X_21,greatest_lower_bound(X_22,X_21)) = X_21 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,X_22),greatest_lower_bound(X_22,X_21)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
least_upper_bound(X_21,greatest_lower_bound(X_22,X_21)) = X_21,
inference(resolve,[$cnf( $equal(least_upper_bound(X_21,greatest_lower_bound(X_21,X_22)),X_21) )],[refute_0_170,refute_0_175]) ).
cnf(refute_0_177,plain,
least_upper_bound(X_53,greatest_lower_bound(X_22,X_53)) = X_53,
inference(subst,[],[refute_0_176:[bind(X_21,$fot(X_53))]]) ).
cnf(refute_0_178,plain,
( least_upper_bound(X_53,greatest_lower_bound(X_22,X_53)) != X_53
| least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) != greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,greatest_lower_bound(X_22,X_53)))
| least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) = greatest_lower_bound(positive_part(X_53),X_53) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))),greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,greatest_lower_bound(X_22,X_53)))) ),[1,1],$fot(X_53)]]) ).
cnf(refute_0_179,plain,
( least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) != greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,greatest_lower_bound(X_22,X_53)))
| least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) = greatest_lower_bound(positive_part(X_53),X_53) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,greatest_lower_bound(X_22,X_53)),X_53) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) = greatest_lower_bound(positive_part(X_53),X_53),
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))),greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,greatest_lower_bound(X_22,X_53)))) )],[refute_0_169,refute_0_179]) ).
cnf(refute_0_181,plain,
greatest_lower_bound(X,least_upper_bound(X,identity)) = X,
inference(subst,[],[glb_absorbtion:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_182,plain,
( positive_part(X) != least_upper_bound(X,identity)
| least_upper_bound(X,identity) = positive_part(X) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(positive_part(X))),bind(Y0,$fot(least_upper_bound(X,identity)))]]) ).
cnf(refute_0_183,plain,
least_upper_bound(X,identity) = positive_part(X),
inference(resolve,[$cnf( $equal(positive_part(X),least_upper_bound(X,identity)) )],[lat4_1,refute_0_182]) ).
cnf(refute_0_184,plain,
( greatest_lower_bound(X,least_upper_bound(X,identity)) != X
| least_upper_bound(X,identity) != positive_part(X)
| greatest_lower_bound(X,positive_part(X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,identity)),X) ),[0,1],$fot(positive_part(X))]]) ).
cnf(refute_0_185,plain,
( greatest_lower_bound(X,least_upper_bound(X,identity)) != X
| greatest_lower_bound(X,positive_part(X)) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,identity),positive_part(X)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
greatest_lower_bound(X,positive_part(X)) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,identity)),X) )],[refute_0_181,refute_0_185]) ).
cnf(refute_0_187,plain,
greatest_lower_bound(X_53,positive_part(X_53)) = X_53,
inference(subst,[],[refute_0_186:[bind(X,$fot(X_53))]]) ).
cnf(refute_0_188,plain,
greatest_lower_bound(positive_part(X_53),X_53) = greatest_lower_bound(X_53,positive_part(X_53)),
inference(subst,[],[refute_0_163:[bind(X,$fot(X_53)),bind(Y,$fot(positive_part(X_53)))]]) ).
cnf(refute_0_189,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_190,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_17,refute_0_189]) ).
cnf(refute_0_191,plain,
( greatest_lower_bound(X_53,positive_part(X_53)) != X_53
| greatest_lower_bound(positive_part(X_53),X_53) != greatest_lower_bound(X_53,positive_part(X_53))
| greatest_lower_bound(positive_part(X_53),X_53) = X_53 ),
inference(subst,[],[refute_0_190:[bind(X0,$fot(greatest_lower_bound(positive_part(X_53),X_53))),bind(Y0,$fot(greatest_lower_bound(X_53,positive_part(X_53)))),bind(Z0,$fot(X_53))]]) ).
cnf(refute_0_192,plain,
( greatest_lower_bound(X_53,positive_part(X_53)) != X_53
| greatest_lower_bound(positive_part(X_53),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_53),X_53),greatest_lower_bound(X_53,positive_part(X_53))) )],[refute_0_188,refute_0_191]) ).
cnf(refute_0_193,plain,
greatest_lower_bound(positive_part(X_53),X_53) = X_53,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_53,positive_part(X_53)),X_53) )],[refute_0_187,refute_0_192]) ).
cnf(refute_0_194,plain,
( greatest_lower_bound(positive_part(X_53),X_53) != X_53
| least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) != greatest_lower_bound(positive_part(X_53),X_53)
| least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))),greatest_lower_bound(positive_part(X_53),X_53)) ),[1],$fot(X_53)]]) ).
cnf(refute_0_195,plain,
( least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) != greatest_lower_bound(positive_part(X_53),X_53)
| least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) = X_53 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_53),X_53),X_53) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))) = X_53,
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,negative_part(greatest_lower_bound(X_22,X_53))),greatest_lower_bound(positive_part(X_53),X_53)) )],[refute_0_180,refute_0_195]) ).
cnf(refute_0_197,plain,
least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)))) = greatest_lower_bound(X_76,X_22),
inference(subst,[],[refute_0_196:[bind(X_53,$fot(greatest_lower_bound(X_76,X_22)))]]) ).
cnf(refute_0_198,plain,
greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) = X_6,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_199,plain,
least_upper_bound(X_7,X_6) = least_upper_bound(X_6,X_7),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_7)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_200,plain,
( least_upper_bound(X_7,X_6) != least_upper_bound(X_6,X_7)
| least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_7,X_6))),bind(Y0,$fot(least_upper_bound(X_6,X_7)))]]) ).
cnf(refute_0_201,plain,
least_upper_bound(X_6,X_7) = least_upper_bound(X_7,X_6),
inference(resolve,[$cnf( $equal(least_upper_bound(X_7,X_6),least_upper_bound(X_6,X_7)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| least_upper_bound(X_6,X_7) != least_upper_bound(X_7,X_6)
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) ),[0,1],$fot(least_upper_bound(X_7,X_6))]]) ).
cnf(refute_0_203,plain,
( greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)) != X_6
| greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_6,X_7),least_upper_bound(X_7,X_6)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
greatest_lower_bound(X_6,least_upper_bound(X_7,X_6)) = X_6,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_6,least_upper_bound(X_6,X_7)),X_6) )],[refute_0_198,refute_0_203]) ).
cnf(refute_0_205,plain,
greatest_lower_bound(greatest_lower_bound(X_27,Y),least_upper_bound(X_27,greatest_lower_bound(X_27,Y))) = greatest_lower_bound(X_27,Y),
inference(subst,[],[refute_0_204:[bind(X_6,$fot(greatest_lower_bound(X_27,Y))),bind(X_7,$fot(X_27))]]) ).
cnf(refute_0_206,plain,
least_upper_bound(X_27,greatest_lower_bound(X_27,Y)) = X_27,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_207,plain,
( greatest_lower_bound(greatest_lower_bound(X_27,Y),least_upper_bound(X_27,greatest_lower_bound(X_27,Y))) != greatest_lower_bound(X_27,Y)
| least_upper_bound(X_27,greatest_lower_bound(X_27,Y)) != X_27
| greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27) = greatest_lower_bound(X_27,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_27,Y),least_upper_bound(X_27,greatest_lower_bound(X_27,Y))),greatest_lower_bound(X_27,Y)) ),[0,1],$fot(X_27)]]) ).
cnf(refute_0_208,plain,
( greatest_lower_bound(greatest_lower_bound(X_27,Y),least_upper_bound(X_27,greatest_lower_bound(X_27,Y))) != greatest_lower_bound(X_27,Y)
| greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27) = greatest_lower_bound(X_27,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_27,greatest_lower_bound(X_27,Y)),X_27) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27) = greatest_lower_bound(X_27,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_27,Y),least_upper_bound(X_27,greatest_lower_bound(X_27,Y))),greatest_lower_bound(X_27,Y)) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_211,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_210]) ).
cnf(refute_0_212,plain,
greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27) = greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)),
inference(subst,[],[refute_0_211:[bind(X,$fot(X_27)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_213,plain,
( greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27) != greatest_lower_bound(X_27,Y)
| greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27) != greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27))
| greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27),greatest_lower_bound(X_27,Y)) ),[0],$fot(greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)))]]) ).
cnf(refute_0_214,plain,
( greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27) != greatest_lower_bound(X_27,Y)
| greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27),greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
greatest_lower_bound(X_27,greatest_lower_bound(Y,X_27)) = greatest_lower_bound(X_27,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_27,Y),X_27),greatest_lower_bound(X_27,Y)) )],[refute_0_209,refute_0_214]) ).
cnf(refute_0_216,plain,
greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)) = greatest_lower_bound(X_22,X_76),
inference(subst,[],[refute_0_215:[bind(Y,$fot(X_76)),bind(X_27,$fot(X_22))]]) ).
cnf(refute_0_217,plain,
( greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)) != greatest_lower_bound(X_22,X_76)
| least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)))) != greatest_lower_bound(X_76,X_22)
| least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,X_76))) = greatest_lower_bound(X_76,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)))),greatest_lower_bound(X_76,X_22)) ),[0,1,0],$fot(greatest_lower_bound(X_22,X_76))]]) ).
cnf(refute_0_218,plain,
( least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)))) != greatest_lower_bound(X_76,X_22)
| least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,X_76))) = greatest_lower_bound(X_76,X_22) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)),greatest_lower_bound(X_22,X_76)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,X_76))) = greatest_lower_bound(X_76,X_22),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_76,X_22),negative_part(greatest_lower_bound(X_22,greatest_lower_bound(X_76,X_22)))),greatest_lower_bound(X_76,X_22)) )],[refute_0_197,refute_0_218]) ).
cnf(refute_0_220,plain,
least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(greatest_lower_bound(inverse(A),inverse(B)))) = greatest_lower_bound(inverse(B),inverse(A)),
inference(subst,[],[refute_0_219:[bind(X_22,$fot(inverse(A))),bind(X_76,$fot(inverse(B)))]]) ).
cnf(refute_0_221,plain,
( greatest_lower_bound(inverse(A),inverse(B)) != inverse(least_upper_bound(A,B))
| least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(greatest_lower_bound(inverse(A),inverse(B)))) != greatest_lower_bound(inverse(B),inverse(A))
| least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) = greatest_lower_bound(inverse(B),inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(greatest_lower_bound(inverse(A),inverse(B)))),greatest_lower_bound(inverse(B),inverse(A))) ),[0,1,0],$fot(inverse(least_upper_bound(A,B)))]]) ).
cnf(refute_0_222,plain,
( least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(greatest_lower_bound(inverse(A),inverse(B)))) != greatest_lower_bound(inverse(B),inverse(A))
| least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) = greatest_lower_bound(inverse(B),inverse(A)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(A),inverse(B)),inverse(least_upper_bound(A,B))) )],[refute_0_120,refute_0_221]) ).
cnf(refute_0_223,plain,
least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) = greatest_lower_bound(inverse(B),inverse(A)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(greatest_lower_bound(inverse(A),inverse(B)))),greatest_lower_bound(inverse(B),inverse(A))) )],[refute_0_220,refute_0_222]) ).
cnf(refute_0_224,plain,
greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(least_upper_bound(negative_part(X_48),X_49))) = least_upper_bound(negative_part(X_48),X_49),
inference(subst,[],[refute_0_186:[bind(X,$fot(least_upper_bound(negative_part(X_48),X_49)))]]) ).
cnf(refute_0_225,plain,
least_upper_bound(identity,least_upper_bound(X_36,X_37)) = least_upper_bound(least_upper_bound(identity,X_36),X_37),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_226,plain,
least_upper_bound(identity,X_36) = positive_part(X_36),
inference(subst,[],[refute_0_73:[bind(Y,$fot(X_36))]]) ).
cnf(refute_0_227,plain,
( least_upper_bound(identity,X_36) != positive_part(X_36)
| least_upper_bound(identity,least_upper_bound(X_36,X_37)) != least_upper_bound(least_upper_bound(identity,X_36),X_37)
| least_upper_bound(identity,least_upper_bound(X_36,X_37)) = least_upper_bound(positive_part(X_36),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_36,X_37)),least_upper_bound(least_upper_bound(identity,X_36),X_37)) ),[1,0],$fot(positive_part(X_36))]]) ).
cnf(refute_0_228,plain,
( least_upper_bound(identity,least_upper_bound(X_36,X_37)) != least_upper_bound(least_upper_bound(identity,X_36),X_37)
| least_upper_bound(identity,least_upper_bound(X_36,X_37)) = least_upper_bound(positive_part(X_36),X_37) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_36),positive_part(X_36)) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
least_upper_bound(identity,least_upper_bound(X_36,X_37)) = least_upper_bound(positive_part(X_36),X_37),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_36,X_37)),least_upper_bound(least_upper_bound(identity,X_36),X_37)) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
least_upper_bound(identity,least_upper_bound(X_36,X_37)) = positive_part(least_upper_bound(X_36,X_37)),
inference(subst,[],[refute_0_73:[bind(Y,$fot(least_upper_bound(X_36,X_37)))]]) ).
cnf(refute_0_231,plain,
( least_upper_bound(identity,least_upper_bound(X_36,X_37)) != least_upper_bound(positive_part(X_36),X_37)
| least_upper_bound(identity,least_upper_bound(X_36,X_37)) != positive_part(least_upper_bound(X_36,X_37))
| positive_part(least_upper_bound(X_36,X_37)) = least_upper_bound(positive_part(X_36),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_36,X_37)),least_upper_bound(positive_part(X_36),X_37)) ),[0],$fot(positive_part(least_upper_bound(X_36,X_37)))]]) ).
cnf(refute_0_232,plain,
( least_upper_bound(identity,least_upper_bound(X_36,X_37)) != least_upper_bound(positive_part(X_36),X_37)
| positive_part(least_upper_bound(X_36,X_37)) = least_upper_bound(positive_part(X_36),X_37) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_36,X_37)),positive_part(least_upper_bound(X_36,X_37))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
positive_part(least_upper_bound(X_36,X_37)) = least_upper_bound(positive_part(X_36),X_37),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_36,X_37)),least_upper_bound(positive_part(X_36),X_37)) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
positive_part(least_upper_bound(negative_part(X_22),X_39)) = least_upper_bound(positive_part(negative_part(X_22)),X_39),
inference(subst,[],[refute_0_233:[bind(X_36,$fot(negative_part(X_22))),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_235,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_22)) = positive_part(greatest_lower_bound(identity,X_22)),
inference(subst,[],[refute_0_73:[bind(Y,$fot(greatest_lower_bound(identity,X_22)))]]) ).
cnf(refute_0_236,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_22)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_237,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_22)) != identity
| least_upper_bound(identity,greatest_lower_bound(identity,X_22)) != positive_part(greatest_lower_bound(identity,X_22))
| identity = positive_part(greatest_lower_bound(identity,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_22)),positive_part(greatest_lower_bound(identity,X_22))) ),[0],$fot(identity)]]) ).
cnf(refute_0_238,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_22)) != positive_part(greatest_lower_bound(identity,X_22))
| identity = positive_part(greatest_lower_bound(identity,X_22)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_22)),identity) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
identity = positive_part(greatest_lower_bound(identity,X_22)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_22)),positive_part(greatest_lower_bound(identity,X_22))) )],[refute_0_235,refute_0_238]) ).
cnf(refute_0_240,plain,
greatest_lower_bound(identity,X_22) = negative_part(X_22),
inference(subst,[],[refute_0_86:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_241,plain,
positive_part(greatest_lower_bound(identity,X_22)) = positive_part(greatest_lower_bound(identity,X_22)),
introduced(tautology,[refl,[$fot(positive_part(greatest_lower_bound(identity,X_22)))]]) ).
cnf(refute_0_242,plain,
( greatest_lower_bound(identity,X_22) != negative_part(X_22)
| positive_part(greatest_lower_bound(identity,X_22)) != positive_part(greatest_lower_bound(identity,X_22))
| positive_part(greatest_lower_bound(identity,X_22)) = positive_part(negative_part(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_22)),positive_part(greatest_lower_bound(identity,X_22))) ),[1,0],$fot(negative_part(X_22))]]) ).
cnf(refute_0_243,plain,
( greatest_lower_bound(identity,X_22) != negative_part(X_22)
| positive_part(greatest_lower_bound(identity,X_22)) = positive_part(negative_part(X_22)) ),
inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_22)),positive_part(greatest_lower_bound(identity,X_22))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
positive_part(greatest_lower_bound(identity,X_22)) = positive_part(negative_part(X_22)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_22),negative_part(X_22)) )],[refute_0_240,refute_0_243]) ).
cnf(refute_0_245,plain,
( identity != positive_part(greatest_lower_bound(identity,X_22))
| positive_part(greatest_lower_bound(identity,X_22)) != positive_part(negative_part(X_22))
| identity = positive_part(negative_part(X_22)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,positive_part(negative_part(X_22))) ),[0],$fot(positive_part(greatest_lower_bound(identity,X_22)))]]) ).
cnf(refute_0_246,plain,
( identity != positive_part(greatest_lower_bound(identity,X_22))
| identity = positive_part(negative_part(X_22)) ),
inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_22)),positive_part(negative_part(X_22))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
identity = positive_part(negative_part(X_22)),
inference(resolve,[$cnf( $equal(identity,positive_part(greatest_lower_bound(identity,X_22))) )],[refute_0_239,refute_0_246]) ).
cnf(refute_0_248,plain,
( identity != positive_part(negative_part(X_22))
| positive_part(negative_part(X_22)) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(positive_part(negative_part(X_22))))]]) ).
cnf(refute_0_249,plain,
positive_part(negative_part(X_22)) = identity,
inference(resolve,[$cnf( $equal(identity,positive_part(negative_part(X_22))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
( positive_part(least_upper_bound(negative_part(X_22),X_39)) != least_upper_bound(positive_part(negative_part(X_22)),X_39)
| positive_part(negative_part(X_22)) != identity
| positive_part(least_upper_bound(negative_part(X_22),X_39)) = least_upper_bound(identity,X_39) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_22),X_39)),least_upper_bound(positive_part(negative_part(X_22)),X_39)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_251,plain,
( positive_part(least_upper_bound(negative_part(X_22),X_39)) != least_upper_bound(positive_part(negative_part(X_22)),X_39)
| positive_part(least_upper_bound(negative_part(X_22),X_39)) = least_upper_bound(identity,X_39) ),
inference(resolve,[$cnf( $equal(positive_part(negative_part(X_22)),identity) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
positive_part(least_upper_bound(negative_part(X_22),X_39)) = least_upper_bound(identity,X_39),
inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_22),X_39)),least_upper_bound(positive_part(negative_part(X_22)),X_39)) )],[refute_0_234,refute_0_251]) ).
cnf(refute_0_253,plain,
least_upper_bound(identity,X_39) = positive_part(X_39),
inference(subst,[],[refute_0_73:[bind(Y,$fot(X_39))]]) ).
cnf(refute_0_254,plain,
( least_upper_bound(identity,X_39) != positive_part(X_39)
| positive_part(least_upper_bound(negative_part(X_22),X_39)) != least_upper_bound(identity,X_39)
| positive_part(least_upper_bound(negative_part(X_22),X_39)) = positive_part(X_39) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_22),X_39)),least_upper_bound(identity,X_39)) ),[1],$fot(positive_part(X_39))]]) ).
cnf(refute_0_255,plain,
( positive_part(least_upper_bound(negative_part(X_22),X_39)) != least_upper_bound(identity,X_39)
| positive_part(least_upper_bound(negative_part(X_22),X_39)) = positive_part(X_39) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_39),positive_part(X_39)) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
positive_part(least_upper_bound(negative_part(X_22),X_39)) = positive_part(X_39),
inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_22),X_39)),least_upper_bound(identity,X_39)) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
positive_part(least_upper_bound(negative_part(X_48),X_49)) = positive_part(X_49),
inference(subst,[],[refute_0_256:[bind(X_22,$fot(X_48)),bind(X_39,$fot(X_49))]]) ).
cnf(refute_0_258,plain,
( greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(least_upper_bound(negative_part(X_48),X_49))) != least_upper_bound(negative_part(X_48),X_49)
| positive_part(least_upper_bound(negative_part(X_48),X_49)) != positive_part(X_49)
| greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)) = least_upper_bound(negative_part(X_48),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(least_upper_bound(negative_part(X_48),X_49))),least_upper_bound(negative_part(X_48),X_49)) ),[0,1],$fot(positive_part(X_49))]]) ).
cnf(refute_0_259,plain,
( greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(least_upper_bound(negative_part(X_48),X_49))) != least_upper_bound(negative_part(X_48),X_49)
| greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)) = least_upper_bound(negative_part(X_48),X_49) ),
inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_48),X_49)),positive_part(X_49)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)) = least_upper_bound(negative_part(X_48),X_49),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(least_upper_bound(negative_part(X_48),X_49))),least_upper_bound(negative_part(X_48),X_49)) )],[refute_0_224,refute_0_259]) ).
cnf(refute_0_261,plain,
greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)) = greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)),
inference(subst,[],[refute_0_163:[bind(X,$fot(positive_part(X_49))),bind(Y,$fot(least_upper_bound(negative_part(X_48),X_49)))]]) ).
cnf(refute_0_262,plain,
( greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)) != greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49))
| greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)) != least_upper_bound(negative_part(X_48),X_49)
| greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) = least_upper_bound(negative_part(X_48),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)),least_upper_bound(negative_part(X_48),X_49)) ),[0],$fot(greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)))]]) ).
cnf(refute_0_263,plain,
( greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)) != least_upper_bound(negative_part(X_48),X_49)
| greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) = least_upper_bound(negative_part(X_48),X_49) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)),greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) = least_upper_bound(negative_part(X_48),X_49),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_48),X_49),positive_part(X_49)),least_upper_bound(negative_part(X_48),X_49)) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
greatest_lower_bound(negative_part(X_23),positive_part(negative_part(X_23))) = negative_part(X_23),
inference(subst,[],[refute_0_186:[bind(X,$fot(negative_part(X_23)))]]) ).
cnf(refute_0_266,plain,
identity = positive_part(negative_part(X_23)),
inference(subst,[],[refute_0_247:[bind(X_22,$fot(X_23))]]) ).
cnf(refute_0_267,plain,
( identity != positive_part(negative_part(X_23))
| positive_part(negative_part(X_23)) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(positive_part(negative_part(X_23))))]]) ).
cnf(refute_0_268,plain,
positive_part(negative_part(X_23)) = identity,
inference(resolve,[$cnf( $equal(identity,positive_part(negative_part(X_23))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
( greatest_lower_bound(negative_part(X_23),positive_part(negative_part(X_23))) != negative_part(X_23)
| positive_part(negative_part(X_23)) != identity
| greatest_lower_bound(negative_part(X_23),identity) = negative_part(X_23) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(negative_part(X_23),positive_part(negative_part(X_23))),negative_part(X_23)) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_270,plain,
( greatest_lower_bound(negative_part(X_23),positive_part(negative_part(X_23))) != negative_part(X_23)
| greatest_lower_bound(negative_part(X_23),identity) = negative_part(X_23) ),
inference(resolve,[$cnf( $equal(positive_part(negative_part(X_23)),identity) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
greatest_lower_bound(negative_part(X_23),identity) = negative_part(X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(X_23),positive_part(negative_part(X_23))),negative_part(X_23)) )],[refute_0_265,refute_0_270]) ).
cnf(refute_0_272,plain,
greatest_lower_bound(negative_part(X_23),identity) = negative_part(negative_part(X_23)),
inference(subst,[],[refute_0_19:[bind(X,$fot(negative_part(X_23)))]]) ).
cnf(refute_0_273,plain,
( greatest_lower_bound(negative_part(X_23),identity) != negative_part(X_23)
| greatest_lower_bound(negative_part(X_23),identity) != negative_part(negative_part(X_23))
| negative_part(negative_part(X_23)) = negative_part(X_23) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(negative_part(X_23),identity),negative_part(X_23)) ),[0],$fot(negative_part(negative_part(X_23)))]]) ).
cnf(refute_0_274,plain,
( greatest_lower_bound(negative_part(X_23),identity) != negative_part(X_23)
| negative_part(negative_part(X_23)) = negative_part(X_23) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(X_23),identity),negative_part(negative_part(X_23))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
negative_part(negative_part(X_23)) = negative_part(X_23),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(X_23),identity),negative_part(X_23)) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
negative_part(negative_part(X_48)) = negative_part(X_48),
inference(subst,[],[refute_0_275:[bind(X_23,$fot(X_48))]]) ).
cnf(refute_0_277,plain,
least_upper_bound(X_49,negative_part(negative_part(X_48))) = least_upper_bound(X_49,negative_part(negative_part(X_48))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_49,negative_part(negative_part(X_48))))]]) ).
cnf(refute_0_278,plain,
( least_upper_bound(X_49,negative_part(negative_part(X_48))) != least_upper_bound(X_49,negative_part(negative_part(X_48)))
| negative_part(negative_part(X_48)) != negative_part(X_48)
| least_upper_bound(X_49,negative_part(negative_part(X_48))) = least_upper_bound(X_49,negative_part(X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_49,negative_part(negative_part(X_48))),least_upper_bound(X_49,negative_part(negative_part(X_48)))) ),[1,1],$fot(negative_part(X_48))]]) ).
cnf(refute_0_279,plain,
( negative_part(negative_part(X_48)) != negative_part(X_48)
| least_upper_bound(X_49,negative_part(negative_part(X_48))) = least_upper_bound(X_49,negative_part(X_48)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_49,negative_part(negative_part(X_48))),least_upper_bound(X_49,negative_part(negative_part(X_48)))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
least_upper_bound(X_49,negative_part(negative_part(X_48))) = least_upper_bound(X_49,negative_part(X_48)),
inference(resolve,[$cnf( $equal(negative_part(negative_part(X_48)),negative_part(X_48)) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
least_upper_bound(X_53,negative_part(X_54)) = greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,X_54)),
inference(subst,[],[refute_0_168:[bind(X_50,$fot(X_53)),bind(X_51,$fot(X_54))]]) ).
cnf(refute_0_282,plain,
least_upper_bound(X_54,X_53) = least_upper_bound(X_53,X_54),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_54)),bind(Y,$fot(X_53))]]) ).
cnf(refute_0_283,plain,
( least_upper_bound(X_54,X_53) != least_upper_bound(X_53,X_54)
| least_upper_bound(X_53,X_54) = least_upper_bound(X_54,X_53) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_54,X_53))),bind(Y0,$fot(least_upper_bound(X_53,X_54)))]]) ).
cnf(refute_0_284,plain,
least_upper_bound(X_53,X_54) = least_upper_bound(X_54,X_53),
inference(resolve,[$cnf( $equal(least_upper_bound(X_54,X_53),least_upper_bound(X_53,X_54)) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( least_upper_bound(X_53,X_54) != least_upper_bound(X_54,X_53)
| least_upper_bound(X_53,negative_part(X_54)) != greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,X_54))
| least_upper_bound(X_53,negative_part(X_54)) = greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_53,negative_part(X_54)),greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,X_54))) ),[1,1],$fot(least_upper_bound(X_54,X_53))]]) ).
cnf(refute_0_286,plain,
( least_upper_bound(X_53,negative_part(X_54)) != greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,X_54))
| least_upper_bound(X_53,negative_part(X_54)) = greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,X_54),least_upper_bound(X_54,X_53)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
least_upper_bound(X_53,negative_part(X_54)) = greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,negative_part(X_54)),greatest_lower_bound(positive_part(X_53),least_upper_bound(X_53,X_54))) )],[refute_0_281,refute_0_286]) ).
cnf(refute_0_288,plain,
( least_upper_bound(X_53,negative_part(X_54)) != greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53))
| greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53)) = least_upper_bound(X_53,negative_part(X_54)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_53,negative_part(X_54)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53))))]]) ).
cnf(refute_0_289,plain,
greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53)) = least_upper_bound(X_53,negative_part(X_54)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_53,negative_part(X_54)),greatest_lower_bound(positive_part(X_53),least_upper_bound(X_54,X_53))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) = least_upper_bound(X_49,negative_part(negative_part(X_48))),
inference(subst,[],[refute_0_289:[bind(X_53,$fot(X_49)),bind(X_54,$fot(negative_part(X_48)))]]) ).
cnf(refute_0_291,plain,
( greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) != least_upper_bound(X_49,negative_part(negative_part(X_48)))
| least_upper_bound(X_49,negative_part(negative_part(X_48))) != least_upper_bound(X_49,negative_part(X_48))
| greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) = least_upper_bound(X_49,negative_part(X_48)) ),
inference(subst,[],[refute_0_190:[bind(X0,$fot(greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)))),bind(Y0,$fot(least_upper_bound(X_49,negative_part(negative_part(X_48))))),bind(Z0,$fot(least_upper_bound(X_49,negative_part(X_48))))]]) ).
cnf(refute_0_292,plain,
( least_upper_bound(X_49,negative_part(negative_part(X_48))) != least_upper_bound(X_49,negative_part(X_48))
| greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) = least_upper_bound(X_49,negative_part(X_48)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)),least_upper_bound(X_49,negative_part(negative_part(X_48)))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) = least_upper_bound(X_49,negative_part(X_48)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_49,negative_part(negative_part(X_48))),least_upper_bound(X_49,negative_part(X_48))) )],[refute_0_280,refute_0_292]) ).
cnf(refute_0_294,plain,
( greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) != least_upper_bound(X_49,negative_part(X_48))
| greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) != least_upper_bound(negative_part(X_48),X_49)
| least_upper_bound(X_49,negative_part(X_48)) = least_upper_bound(negative_part(X_48),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)),least_upper_bound(negative_part(X_48),X_49)) ),[0],$fot(least_upper_bound(X_49,negative_part(X_48)))]]) ).
cnf(refute_0_295,plain,
( greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)) != least_upper_bound(negative_part(X_48),X_49)
| least_upper_bound(X_49,negative_part(X_48)) = least_upper_bound(negative_part(X_48),X_49) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)),least_upper_bound(X_49,negative_part(X_48))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
least_upper_bound(X_49,negative_part(X_48)) = least_upper_bound(negative_part(X_48),X_49),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_49),least_upper_bound(negative_part(X_48),X_49)),least_upper_bound(negative_part(X_48),X_49)) )],[refute_0_264,refute_0_295]) ).
cnf(refute_0_297,plain,
( least_upper_bound(X_49,negative_part(X_48)) != least_upper_bound(negative_part(X_48),X_49)
| least_upper_bound(negative_part(X_48),X_49) = least_upper_bound(X_49,negative_part(X_48)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(least_upper_bound(X_49,negative_part(X_48)))),bind(Y0,$fot(least_upper_bound(negative_part(X_48),X_49)))]]) ).
cnf(refute_0_298,plain,
least_upper_bound(negative_part(X_48),X_49) = least_upper_bound(X_49,negative_part(X_48)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_49,negative_part(X_48)),least_upper_bound(negative_part(X_48),X_49)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),
inference(subst,[],[refute_0_298:[bind(X_48,$fot(inverse(least_upper_bound(A,B)))),bind(X_49,$fot(inverse(least_upper_bound(B,A))))]]) ).
cnf(refute_0_300,plain,
greatest_lower_bound(inverse(B),inverse(A)) = inverse(least_upper_bound(B,A)),
inference(subst,[],[refute_0_120:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_301,plain,
least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) = least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))),
introduced(tautology,[refl,[$fot(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))))]]) ).
cnf(refute_0_302,plain,
( greatest_lower_bound(inverse(B),inverse(A)) != inverse(least_upper_bound(B,A))
| least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) != least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A)))
| least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) = least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))),least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A)))) ),[1,1],$fot(inverse(least_upper_bound(B,A)))]]) ).
cnf(refute_0_303,plain,
( greatest_lower_bound(inverse(B),inverse(A)) != inverse(least_upper_bound(B,A))
| least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) = least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))),least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A)))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) = least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(B),inverse(A)),inverse(least_upper_bound(B,A))) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
( least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) != least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A)))
| least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))) != least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))
| least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) ),
inference(subst,[],[refute_0_190:[bind(X0,$fot(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))))),bind(Y0,$fot(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))))),bind(Z0,$fot(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))))]]) ).
cnf(refute_0_306,plain,
( least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))) != least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))
| least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))),least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A)))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),inverse(least_upper_bound(B,A))),least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))) )],[refute_0_299,refute_0_306]) ).
cnf(refute_0_308,plain,
least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))),
inference(subst,[],[refute_0_296:[bind(X_48,$fot(inverse(least_upper_bound(A,B)))),bind(X_49,$fot(greatest_lower_bound(inverse(B),inverse(A))))]]) ).
cnf(refute_0_309,plain,
( least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) != least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A)))
| least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) != least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))
| least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) ),
inference(subst,[],[refute_0_190:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))))),bind(Y0,$fot(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))))),bind(Z0,$fot(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))))]]) ).
cnf(refute_0_310,plain,
( least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))) != least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))
| least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))),least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A)))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(least_upper_bound(A,B))),greatest_lower_bound(inverse(B),inverse(A))),least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))) )],[refute_0_307,refute_0_310]) ).
cnf(refute_0_312,plain,
( least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) != greatest_lower_bound(inverse(B),inverse(A))
| least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) != least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = greatest_lower_bound(inverse(B),inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))),greatest_lower_bound(inverse(B),inverse(A))) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))))]]) ).
cnf(refute_0_313,plain,
( least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) != greatest_lower_bound(inverse(B),inverse(A))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = greatest_lower_bound(inverse(B),inverse(A)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))),least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
( greatest_lower_bound(inverse(B),inverse(A)) != inverse(least_upper_bound(B,A))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) != greatest_lower_bound(inverse(B),inverse(A))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(B,A)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),greatest_lower_bound(inverse(B),inverse(A))) ),[1],$fot(inverse(least_upper_bound(B,A)))]]) ).
cnf(refute_0_315,plain,
( least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) != greatest_lower_bound(inverse(B),inverse(A))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(B,A)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(B),inverse(A)),inverse(least_upper_bound(B,A))) )],[refute_0_300,refute_0_314]) ).
cnf(refute_0_316,plain,
( least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))) != greatest_lower_bound(inverse(B),inverse(A))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(B,A)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),greatest_lower_bound(inverse(B),inverse(A))) )],[refute_0_313,refute_0_315]) ).
cnf(refute_0_317,plain,
least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(B,A)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(inverse(B),inverse(A)),negative_part(inverse(least_upper_bound(A,B)))),greatest_lower_bound(inverse(B),inverse(A))) )],[refute_0_223,refute_0_316]) ).
cnf(refute_0_318,plain,
least_upper_bound(inverse(X_66),inverse(least_upper_bound(X_66,identity))) = inverse(X_66),
inference(subst,[],[refute_0_139:[bind(A,$fot(X_66)),bind(B,$fot(identity))]]) ).
cnf(refute_0_319,plain,
positive_part(X_66) = least_upper_bound(X_66,identity),
inference(subst,[],[lat4_1:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_320,plain,
( positive_part(X_66) != least_upper_bound(X_66,identity)
| least_upper_bound(X_66,identity) = positive_part(X_66) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(positive_part(X_66))),bind(Y0,$fot(least_upper_bound(X_66,identity)))]]) ).
cnf(refute_0_321,plain,
least_upper_bound(X_66,identity) = positive_part(X_66),
inference(resolve,[$cnf( $equal(positive_part(X_66),least_upper_bound(X_66,identity)) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
( least_upper_bound(X_66,identity) != positive_part(X_66)
| least_upper_bound(inverse(X_66),inverse(least_upper_bound(X_66,identity))) != inverse(X_66)
| least_upper_bound(inverse(X_66),inverse(positive_part(X_66))) = inverse(X_66) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_66),inverse(least_upper_bound(X_66,identity))),inverse(X_66)) ),[0,1,0],$fot(positive_part(X_66))]]) ).
cnf(refute_0_323,plain,
( least_upper_bound(inverse(X_66),inverse(least_upper_bound(X_66,identity))) != inverse(X_66)
| least_upper_bound(inverse(X_66),inverse(positive_part(X_66))) = inverse(X_66) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_66,identity),positive_part(X_66)) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
least_upper_bound(inverse(X_66),inverse(positive_part(X_66))) = inverse(X_66),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_66),inverse(least_upper_bound(X_66,identity))),inverse(X_66)) )],[refute_0_318,refute_0_323]) ).
cnf(refute_0_325,plain,
least_upper_bound(inverse(least_upper_bound(X_13,X_14)),inverse(positive_part(least_upper_bound(X_13,X_14)))) = inverse(least_upper_bound(X_13,X_14)),
inference(subst,[],[refute_0_324:[bind(X_66,$fot(least_upper_bound(X_13,X_14)))]]) ).
cnf(refute_0_326,plain,
( inverse(least_upper_bound(X_14,X_13)) != inverse(least_upper_bound(X_13,X_14))
| inverse(least_upper_bound(X_13,X_14)) = inverse(least_upper_bound(X_14,X_13)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(X_14,X_13)))),bind(Y0,$fot(inverse(least_upper_bound(X_13,X_14))))]]) ).
cnf(refute_0_327,plain,
inverse(least_upper_bound(X_13,X_14)) = inverse(least_upper_bound(X_14,X_13)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_14,X_13)),inverse(least_upper_bound(X_13,X_14))) )],[refute_0_124,refute_0_326]) ).
cnf(refute_0_328,plain,
( inverse(least_upper_bound(X_13,X_14)) != inverse(least_upper_bound(X_14,X_13))
| least_upper_bound(inverse(least_upper_bound(X_13,X_14)),inverse(positive_part(least_upper_bound(X_13,X_14)))) != inverse(least_upper_bound(X_13,X_14))
| least_upper_bound(inverse(least_upper_bound(X_14,X_13)),inverse(positive_part(least_upper_bound(X_13,X_14)))) = inverse(least_upper_bound(X_13,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_13,X_14)),inverse(positive_part(least_upper_bound(X_13,X_14)))),inverse(least_upper_bound(X_13,X_14))) ),[0,0],$fot(inverse(least_upper_bound(X_14,X_13)))]]) ).
cnf(refute_0_329,plain,
( least_upper_bound(inverse(least_upper_bound(X_13,X_14)),inverse(positive_part(least_upper_bound(X_13,X_14)))) != inverse(least_upper_bound(X_13,X_14))
| least_upper_bound(inverse(least_upper_bound(X_14,X_13)),inverse(positive_part(least_upper_bound(X_13,X_14)))) = inverse(least_upper_bound(X_13,X_14)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_13,X_14)),inverse(least_upper_bound(X_14,X_13))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
least_upper_bound(inverse(least_upper_bound(X_14,X_13)),inverse(positive_part(least_upper_bound(X_13,X_14)))) = inverse(least_upper_bound(X_13,X_14)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_13,X_14)),inverse(positive_part(least_upper_bound(X_13,X_14)))),inverse(least_upper_bound(X_13,X_14))) )],[refute_0_325,refute_0_329]) ).
cnf(refute_0_331,plain,
least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))) = inverse(least_upper_bound(A,B)),
inference(subst,[],[refute_0_330:[bind(X_13,$fot(A)),bind(X_14,$fot(B))]]) ).
cnf(refute_0_332,plain,
negative_part(inverse(least_upper_bound(A,B))) = inverse(positive_part(least_upper_bound(A,B))),
inference(subst,[],[refute_0_93:[bind(B,$fot(least_upper_bound(A,B)))]]) ).
cnf(refute_0_333,plain,
least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))))]]) ).
cnf(refute_0_334,plain,
( least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) != least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))
| negative_part(inverse(least_upper_bound(A,B))) != inverse(positive_part(least_upper_bound(A,B)))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))) ),[1,1],$fot(inverse(positive_part(least_upper_bound(A,B))))]]) ).
cnf(refute_0_335,plain,
( negative_part(inverse(least_upper_bound(A,B))) != inverse(positive_part(least_upper_bound(A,B)))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B))))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))),
inference(resolve,[$cnf( $equal(negative_part(inverse(least_upper_bound(A,B))),inverse(positive_part(least_upper_bound(A,B)))) )],[refute_0_332,refute_0_335]) ).
cnf(refute_0_337,plain,
( least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))) != inverse(least_upper_bound(A,B))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) != least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B))))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(A,B)) ),
inference(subst,[],[refute_0_190:[bind(X0,$fot(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))))),bind(Z0,$fot(inverse(least_upper_bound(A,B))))]]) ).
cnf(refute_0_338,plain,
( least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))) != inverse(least_upper_bound(A,B))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(A,B)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B))))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) = inverse(least_upper_bound(A,B)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),inverse(positive_part(least_upper_bound(A,B)))),inverse(least_upper_bound(A,B))) )],[refute_0_331,refute_0_338]) ).
cnf(refute_0_340,plain,
( least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) != inverse(least_upper_bound(A,B))
| least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) != inverse(least_upper_bound(B,A))
| inverse(least_upper_bound(A,B)) = inverse(least_upper_bound(B,A)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),inverse(least_upper_bound(B,A))) ),[0],$fot(inverse(least_upper_bound(A,B)))]]) ).
cnf(refute_0_341,plain,
( least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))) != inverse(least_upper_bound(B,A))
| inverse(least_upper_bound(A,B)) = inverse(least_upper_bound(B,A)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),inverse(least_upper_bound(A,B))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
inverse(least_upper_bound(A,B)) = inverse(least_upper_bound(B,A)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(B,A)),negative_part(inverse(least_upper_bound(A,B)))),inverse(least_upper_bound(B,A))) )],[refute_0_317,refute_0_341]) ).
cnf(refute_0_343,plain,
( inverse(least_upper_bound(A,B)) != inverse(least_upper_bound(B,A))
| inverse(least_upper_bound(B,A)) = inverse(least_upper_bound(A,B)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(least_upper_bound(A,B)))),bind(Y0,$fot(inverse(least_upper_bound(B,A))))]]) ).
cnf(refute_0_344,plain,
inverse(least_upper_bound(B,A)) = inverse(least_upper_bound(A,B)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(A,B)),inverse(least_upper_bound(B,A))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))) = inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))),
inference(subst,[],[refute_0_344:[bind(A,$fot(inverse(A))),bind(B,$fot(inverse(least_upper_bound(A,B))))]]) ).
cnf(refute_0_346,plain,
( inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))) != inverse(inverse(A))
| inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))) != inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))))
| inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))) = inverse(inverse(A)) ),
inference(subst,[],[refute_0_190:[bind(X0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))))),bind(Y0,$fot(inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))))),bind(Z0,$fot(inverse(inverse(A))))]]) ).
cnf(refute_0_347,plain,
( inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))) != inverse(inverse(A))
| inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))) = inverse(inverse(A)) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B))))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))) = inverse(inverse(A)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(A,B)))),inverse(inverse(A))) )],[refute_0_147,refute_0_347]) ).
cnf(refute_0_349,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)))]]) ).
cnf(refute_0_350,plain,
( multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115))
| inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))) != inverse(inverse(A))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) = multiply(inverse(inverse(A)),multiply(inverse(A),X_115)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115))) ),[1,0],$fot(inverse(inverse(A)))]]) ).
cnf(refute_0_351,plain,
( inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))) != inverse(inverse(A))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) = multiply(inverse(inverse(A)),multiply(inverse(A),X_115)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)),multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) = multiply(inverse(inverse(A)),multiply(inverse(A),X_115)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),inverse(inverse(A))) )],[refute_0_348,refute_0_351]) ).
cnf(refute_0_353,plain,
( multiply(inverse(inverse(A)),multiply(inverse(A),X_115)) != multiply(A,multiply(inverse(A),X_115))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) != multiply(inverse(inverse(A)),multiply(inverse(A),X_115))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) = multiply(A,multiply(inverse(A),X_115)) ),
inference(subst,[],[refute_0_190:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)))),bind(Y0,$fot(multiply(inverse(inverse(A)),multiply(inverse(A),X_115)))),bind(Z0,$fot(multiply(A,multiply(inverse(A),X_115))))]]) ).
cnf(refute_0_354,plain,
( multiply(inverse(inverse(A)),multiply(inverse(A),X_115)) != multiply(A,multiply(inverse(A),X_115))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) = multiply(A,multiply(inverse(A),X_115)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)),multiply(inverse(inverse(A)),multiply(inverse(A),X_115))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) = multiply(A,multiply(inverse(A),X_115)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(A)),multiply(inverse(A),X_115)),multiply(A,multiply(inverse(A),X_115))) )],[refute_0_143,refute_0_354]) ).
cnf(refute_0_356,plain,
( X_115 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115))
| multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)) != multiply(A,multiply(inverse(A),X_115))
| X_115 = multiply(A,multiply(inverse(A),X_115)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_115,multiply(A,multiply(inverse(A),X_115))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)))]]) ).
cnf(refute_0_357,plain,
( X_115 != multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115))
| X_115 = multiply(A,multiply(inverse(A),X_115)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115)),multiply(A,multiply(inverse(A),X_115))) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
X_115 = multiply(A,multiply(inverse(A),X_115)),
inference(resolve,[$cnf( $equal(X_115,multiply(inverse(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(A))),multiply(inverse(A),X_115))) )],[refute_0_142,refute_0_357]) ).
cnf(refute_0_359,plain,
inverse(inverse(A)) = multiply(A,multiply(inverse(A),inverse(inverse(A)))),
inference(subst,[],[refute_0_358:[bind(X_115,$fot(inverse(inverse(A))))]]) ).
cnf(refute_0_360,plain,
identity = multiply(X_119,multiply(inverse(X_119),identity)),
inference(subst,[],[refute_0_358:[bind(A,$fot(X_119)),bind(X_115,$fot(identity))]]) ).
cnf(refute_0_361,plain,
inverse(X_119) = multiply(inverse(X_119),identity),
inference(subst,[],[refute_0_57:[bind(X_111,$fot(inverse(X_119)))]]) ).
cnf(refute_0_362,plain,
( inverse(X_119) != multiply(inverse(X_119),identity)
| multiply(inverse(X_119),identity) = inverse(X_119) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(inverse(X_119))),bind(Y0,$fot(multiply(inverse(X_119),identity)))]]) ).
cnf(refute_0_363,plain,
multiply(inverse(X_119),identity) = inverse(X_119),
inference(resolve,[$cnf( $equal(inverse(X_119),multiply(inverse(X_119),identity)) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
( multiply(inverse(X_119),identity) != inverse(X_119)
| identity != multiply(X_119,multiply(inverse(X_119),identity))
| identity = multiply(X_119,inverse(X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,multiply(X_119,multiply(inverse(X_119),identity))) ),[1,1],$fot(inverse(X_119))]]) ).
cnf(refute_0_365,plain,
( identity != multiply(X_119,multiply(inverse(X_119),identity))
| identity = multiply(X_119,inverse(X_119)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_119),identity),inverse(X_119)) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
identity = multiply(X_119,inverse(X_119)),
inference(resolve,[$cnf( $equal(identity,multiply(X_119,multiply(inverse(X_119),identity))) )],[refute_0_360,refute_0_365]) ).
cnf(refute_0_367,plain,
identity = multiply(inverse(A),inverse(inverse(A))),
inference(subst,[],[refute_0_366:[bind(X_119,$fot(inverse(A)))]]) ).
cnf(refute_0_368,plain,
( identity != multiply(inverse(A),inverse(inverse(A)))
| multiply(inverse(A),inverse(inverse(A))) = identity ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(inverse(A),inverse(inverse(A)))))]]) ).
cnf(refute_0_369,plain,
multiply(inverse(A),inverse(inverse(A))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(inverse(A),inverse(inverse(A)))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
( multiply(inverse(A),inverse(inverse(A))) != identity
| inverse(inverse(A)) != multiply(A,multiply(inverse(A),inverse(inverse(A))))
| inverse(inverse(A)) = multiply(A,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(A)),multiply(A,multiply(inverse(A),inverse(inverse(A))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_371,plain,
( inverse(inverse(A)) != multiply(A,multiply(inverse(A),inverse(inverse(A))))
| inverse(inverse(A)) = multiply(A,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(A),inverse(inverse(A))),identity) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
inverse(inverse(A)) = multiply(A,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(A)),multiply(A,multiply(inverse(A),inverse(inverse(A))))) )],[refute_0_359,refute_0_371]) ).
cnf(refute_0_373,plain,
( X_111 != multiply(X_111,identity)
| multiply(X_111,identity) = X_111 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_111)),bind(Y0,$fot(multiply(X_111,identity)))]]) ).
cnf(refute_0_374,plain,
multiply(X_111,identity) = X_111,
inference(resolve,[$cnf( $equal(X_111,multiply(X_111,identity)) )],[refute_0_57,refute_0_373]) ).
cnf(refute_0_375,plain,
multiply(A,identity) = A,
inference(subst,[],[refute_0_374:[bind(X_111,$fot(A))]]) ).
cnf(refute_0_376,plain,
( multiply(A,identity) != A
| inverse(inverse(A)) != multiply(A,identity)
| inverse(inverse(A)) = A ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(A)),multiply(A,identity)) ),[1],$fot(A)]]) ).
cnf(refute_0_377,plain,
( inverse(inverse(A)) != multiply(A,identity)
| inverse(inverse(A)) = A ),
inference(resolve,[$cnf( $equal(multiply(A,identity),A) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
inverse(inverse(A)) = A,
inference(resolve,[$cnf( $equal(inverse(inverse(A)),multiply(A,identity)) )],[refute_0_372,refute_0_377]) ).
cnf(refute_0_379,plain,
inverse(inverse(positive_part(X_109))) = positive_part(X_109),
inference(subst,[],[refute_0_378:[bind(A,$fot(positive_part(X_109)))]]) ).
cnf(refute_0_380,plain,
multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) = multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)))]]) ).
cnf(refute_0_381,plain,
( multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) != multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109))
| inverse(inverse(positive_part(X_109))) != positive_part(X_109)
| multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) = multiply(positive_part(X_109),negative_part(X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)),multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109))) ),[1,0],$fot(positive_part(X_109))]]) ).
cnf(refute_0_382,plain,
( inverse(inverse(positive_part(X_109))) != positive_part(X_109)
| multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) = multiply(positive_part(X_109),negative_part(X_109)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)),multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) = multiply(positive_part(X_109),negative_part(X_109)),
inference(resolve,[$cnf( $equal(inverse(inverse(positive_part(X_109))),positive_part(X_109)) )],[refute_0_379,refute_0_382]) ).
cnf(refute_0_384,plain,
( X_109 != multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109))
| multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)) != multiply(positive_part(X_109),negative_part(X_109))
| X_109 = multiply(positive_part(X_109),negative_part(X_109)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_109,multiply(positive_part(X_109),negative_part(X_109))) ),[0],$fot(multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)))]]) ).
cnf(refute_0_385,plain,
( X_109 != multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109))
| X_109 = multiply(positive_part(X_109),negative_part(X_109)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109)),multiply(positive_part(X_109),negative_part(X_109))) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
X_109 = multiply(positive_part(X_109),negative_part(X_109)),
inference(resolve,[$cnf( $equal(X_109,multiply(inverse(inverse(positive_part(X_109))),negative_part(X_109))) )],[refute_0_109,refute_0_385]) ).
cnf(refute_0_387,plain,
( X_109 != multiply(positive_part(X_109),negative_part(X_109))
| multiply(positive_part(X_109),negative_part(X_109)) = X_109 ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(X_109)),bind(Y0,$fot(multiply(positive_part(X_109),negative_part(X_109))))]]) ).
cnf(refute_0_388,plain,
multiply(positive_part(X_109),negative_part(X_109)) = X_109,
inference(resolve,[$cnf( $equal(X_109,multiply(positive_part(X_109),negative_part(X_109))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
multiply(positive_part(a),negative_part(a)) = a,
inference(subst,[],[refute_0_388:[bind(X_109,$fot(a))]]) ).
cnf(refute_0_390,plain,
( multiply(positive_part(a),negative_part(a)) != a
| a != a
| a = multiply(positive_part(a),negative_part(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a,multiply(positive_part(a),negative_part(a))) ),[1],$fot(a)]]) ).
cnf(refute_0_391,plain,
( a != a
| a = multiply(positive_part(a),negative_part(a)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(a),negative_part(a)),a) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
a != a,
inference(resolve,[$cnf( $equal(a,multiply(positive_part(a),negative_part(a))) )],[refute_0_391,prove_lat4]) ).
cnf(refute_0_393,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_394,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_393,refute_0_392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 13:58:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.90/1.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.90/1.14
% 0.90/1.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.90/1.17
%------------------------------------------------------------------------------