TSTP Solution File: GRP167-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP167-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 10:37:09 EDT 2022
% Result : Unsatisfiable 4.86s 5.06s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 169
% Syntax : Number of clauses : 770 ( 408 unt; 0 nHn; 362 RR)
% Number of literals : 1286 (1285 equ; 518 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 : 1301 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(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_58),X_58),X_59) = multiply(inverse(X_58),multiply(X_58,X_59)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_58))),bind(Y,$fot(X_58)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_58),X_58) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_58))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(inverse(X_58),X_58),X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| multiply(inverse(X_58),X_58) != identity
| multiply(identity,X_59) = multiply(inverse(X_58),multiply(X_58,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_58),X_58),X_59),multiply(inverse(X_58),multiply(X_58,X_59))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_58),X_58),X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| multiply(identity,X_59) = multiply(inverse(X_58),multiply(X_58,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),X_58),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_59) = multiply(inverse(X_58),multiply(X_58,X_59)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_58),X_58),X_59),multiply(inverse(X_58),multiply(X_58,X_59))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_59) = X_59,
inference(subst,[],[left_identity:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_59) != X_59
| multiply(identity,X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| X_59 = multiply(inverse(X_58),multiply(X_58,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_59),multiply(inverse(X_58),multiply(X_58,X_59))) ),[0],$fot(X_59)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_59) != multiply(inverse(X_58),multiply(X_58,X_59))
| X_59 = multiply(inverse(X_58),multiply(X_58,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_59),X_59) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_59 = multiply(inverse(X_58),multiply(X_58,X_59)),
inference(resolve,[$cnf( $equal(multiply(identity,X_59),multiply(inverse(X_58),multiply(X_58,X_59))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
X_59 = multiply(inverse(negative_part(inverse(X_59))),multiply(negative_part(inverse(X_59)),X_59)),
inference(subst,[],[refute_0_8:[bind(X_58,$fot(negative_part(inverse(X_59))))]]) ).
cnf(refute_0_10,plain,
multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) = greatest_lower_bound(multiply(inverse(X_159),X_159),multiply(X_161,X_159)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_159)),bind(Y,$fot(inverse(X_159))),bind(Z,$fot(X_161))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_159),X_159) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_159))]]) ).
cnf(refute_0_12,plain,
( multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) != greatest_lower_bound(multiply(inverse(X_159),X_159),multiply(X_161,X_159))
| multiply(inverse(X_159),X_159) != identity
| multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) = greatest_lower_bound(identity,multiply(X_161,X_159)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_159),X_161),X_159),greatest_lower_bound(multiply(inverse(X_159),X_159),multiply(X_161,X_159))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_13,plain,
( multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) != greatest_lower_bound(multiply(inverse(X_159),X_159),multiply(X_161,X_159))
| multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) = greatest_lower_bound(identity,multiply(X_161,X_159)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_159),X_159),identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) = greatest_lower_bound(identity,multiply(X_161,X_159)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_159),X_161),X_159),greatest_lower_bound(multiply(inverse(X_159),X_159),multiply(X_161,X_159))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
greatest_lower_bound(X,identity) = greatest_lower_bound(identity,X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_16,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_17,plain,
( negative_part(X) != greatest_lower_bound(X,identity)
| negative_part(X) = greatest_lower_bound(identity,X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,identity),greatest_lower_bound(identity,X)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
negative_part(X) = greatest_lower_bound(identity,X),
inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) )],[lat4_2,refute_0_17]) ).
cnf(refute_0_19,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_20,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_21,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( negative_part(X) != greatest_lower_bound(identity,X)
| greatest_lower_bound(identity,X) = negative_part(X) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(greatest_lower_bound(identity,X)))]]) ).
cnf(refute_0_23,plain,
greatest_lower_bound(identity,X) = negative_part(X),
inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(identity,X)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
greatest_lower_bound(identity,multiply(X_161,X_159)) = negative_part(multiply(X_161,X_159)),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(X_161,X_159)))]]) ).
cnf(refute_0_25,plain,
( multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) != greatest_lower_bound(identity,multiply(X_161,X_159))
| greatest_lower_bound(identity,multiply(X_161,X_159)) != negative_part(multiply(X_161,X_159))
| multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) = negative_part(multiply(X_161,X_159)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(inverse(X_159),X_161),X_159),negative_part(multiply(X_161,X_159))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_161,X_159)))]]) ).
cnf(refute_0_26,plain,
( multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) != greatest_lower_bound(identity,multiply(X_161,X_159))
| multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) = negative_part(multiply(X_161,X_159)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_161,X_159)),negative_part(multiply(X_161,X_159))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(greatest_lower_bound(inverse(X_159),X_161),X_159) = negative_part(multiply(X_161,X_159)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_159),X_161),X_159),greatest_lower_bound(identity,multiply(X_161,X_159))) )],[refute_0_14,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(greatest_lower_bound(inverse(X_162),identity),X_162) = negative_part(multiply(identity,X_162)),
inference(subst,[],[refute_0_27:[bind(X_159,$fot(X_162)),bind(X_161,$fot(identity))]]) ).
cnf(refute_0_29,plain,
negative_part(inverse(X_162)) = greatest_lower_bound(inverse(X_162),identity),
inference(subst,[],[lat4_2:[bind(X,$fot(inverse(X_162)))]]) ).
cnf(refute_0_30,plain,
( negative_part(inverse(X_162)) != greatest_lower_bound(inverse(X_162),identity)
| greatest_lower_bound(inverse(X_162),identity) = negative_part(inverse(X_162)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(inverse(X_162)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_162),identity)))]]) ).
cnf(refute_0_31,plain,
greatest_lower_bound(inverse(X_162),identity) = negative_part(inverse(X_162)),
inference(resolve,[$cnf( $equal(negative_part(inverse(X_162)),greatest_lower_bound(inverse(X_162),identity)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( multiply(greatest_lower_bound(inverse(X_162),identity),X_162) != negative_part(multiply(identity,X_162))
| greatest_lower_bound(inverse(X_162),identity) != negative_part(inverse(X_162))
| multiply(negative_part(inverse(X_162)),X_162) = negative_part(multiply(identity,X_162)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_162),identity),X_162),negative_part(multiply(identity,X_162))) ),[0,0],$fot(negative_part(inverse(X_162)))]]) ).
cnf(refute_0_33,plain,
( multiply(greatest_lower_bound(inverse(X_162),identity),X_162) != negative_part(multiply(identity,X_162))
| multiply(negative_part(inverse(X_162)),X_162) = negative_part(multiply(identity,X_162)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_162),identity),negative_part(inverse(X_162))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(negative_part(inverse(X_162)),X_162) = negative_part(multiply(identity,X_162)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_162),identity),X_162),negative_part(multiply(identity,X_162))) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(identity,X_162) = X_162,
inference(subst,[],[left_identity:[bind(X,$fot(X_162))]]) ).
cnf(refute_0_36,plain,
negative_part(multiply(identity,X_162)) = negative_part(multiply(identity,X_162)),
introduced(tautology,[refl,[$fot(negative_part(multiply(identity,X_162)))]]) ).
cnf(refute_0_37,plain,
( multiply(identity,X_162) != X_162
| negative_part(multiply(identity,X_162)) != negative_part(multiply(identity,X_162))
| negative_part(multiply(identity,X_162)) = negative_part(X_162) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(multiply(identity,X_162)),negative_part(multiply(identity,X_162))) ),[1,0],$fot(X_162)]]) ).
cnf(refute_0_38,plain,
( multiply(identity,X_162) != X_162
| negative_part(multiply(identity,X_162)) = negative_part(X_162) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(identity,X_162)),negative_part(multiply(identity,X_162))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
negative_part(multiply(identity,X_162)) = negative_part(X_162),
inference(resolve,[$cnf( $equal(multiply(identity,X_162),X_162) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( multiply(negative_part(inverse(X_162)),X_162) != negative_part(multiply(identity,X_162))
| negative_part(multiply(identity,X_162)) != negative_part(X_162)
| multiply(negative_part(inverse(X_162)),X_162) = negative_part(X_162) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(inverse(X_162)),X_162),negative_part(X_162)) ),[0],$fot(negative_part(multiply(identity,X_162)))]]) ).
cnf(refute_0_41,plain,
( multiply(negative_part(inverse(X_162)),X_162) != negative_part(multiply(identity,X_162))
| multiply(negative_part(inverse(X_162)),X_162) = negative_part(X_162) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(identity,X_162)),negative_part(X_162)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(negative_part(inverse(X_162)),X_162) = negative_part(X_162),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_162)),X_162),negative_part(multiply(identity,X_162))) )],[refute_0_34,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(negative_part(inverse(X_59)),X_59) = negative_part(X_59),
inference(subst,[],[refute_0_42:[bind(X_162,$fot(X_59))]]) ).
cnf(refute_0_44,plain,
( X_59 != multiply(inverse(negative_part(inverse(X_59))),multiply(negative_part(inverse(X_59)),X_59))
| multiply(negative_part(inverse(X_59)),X_59) != negative_part(X_59)
| X_59 = multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,multiply(inverse(negative_part(inverse(X_59))),multiply(negative_part(inverse(X_59)),X_59))) ),[1,1],$fot(negative_part(X_59))]]) ).
cnf(refute_0_45,plain,
( X_59 != multiply(inverse(negative_part(inverse(X_59))),multiply(negative_part(inverse(X_59)),X_59))
| X_59 = multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_59)),X_59),negative_part(X_59)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
X_59 = multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(negative_part(inverse(X_59))),multiply(negative_part(inverse(X_59)),X_59))) )],[refute_0_9,refute_0_45]) ).
cnf(refute_0_47,plain,
X_59 = multiply(inverse(least_upper_bound(X_147,inverse(X_59))),multiply(least_upper_bound(X_147,inverse(X_59)),X_59)),
inference(subst,[],[refute_0_8:[bind(X_58,$fot(least_upper_bound(X_147,inverse(X_59))))]]) ).
cnf(refute_0_48,plain,
multiply(least_upper_bound(X_141,inverse(X_140)),X_140) = least_upper_bound(multiply(X_141,X_140),multiply(inverse(X_140),X_140)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_140)),bind(Y,$fot(X_141)),bind(Z,$fot(inverse(X_140)))]]) ).
cnf(refute_0_49,plain,
multiply(inverse(X_140),X_140) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_140))]]) ).
cnf(refute_0_50,plain,
( multiply(inverse(X_140),X_140) != identity
| multiply(least_upper_bound(X_141,inverse(X_140)),X_140) != least_upper_bound(multiply(X_141,X_140),multiply(inverse(X_140),X_140))
| multiply(least_upper_bound(X_141,inverse(X_140)),X_140) = least_upper_bound(multiply(X_141,X_140),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_141,inverse(X_140)),X_140),least_upper_bound(multiply(X_141,X_140),multiply(inverse(X_140),X_140))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_51,plain,
( multiply(least_upper_bound(X_141,inverse(X_140)),X_140) != least_upper_bound(multiply(X_141,X_140),multiply(inverse(X_140),X_140))
| multiply(least_upper_bound(X_141,inverse(X_140)),X_140) = least_upper_bound(multiply(X_141,X_140),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_140),X_140),identity) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(least_upper_bound(X_141,inverse(X_140)),X_140) = least_upper_bound(multiply(X_141,X_140),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_141,inverse(X_140)),X_140),least_upper_bound(multiply(X_141,X_140),multiply(inverse(X_140),X_140))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
least_upper_bound(X,identity) = least_upper_bound(identity,X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_54,plain,
( least_upper_bound(X,identity) != least_upper_bound(identity,X)
| positive_part(X) != least_upper_bound(X,identity)
| positive_part(X) = least_upper_bound(identity,X) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(X),least_upper_bound(X,identity)) ),[1],$fot(least_upper_bound(identity,X))]]) ).
cnf(refute_0_55,plain,
( positive_part(X) != least_upper_bound(X,identity)
| positive_part(X) = least_upper_bound(identity,X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,identity),least_upper_bound(identity,X)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
positive_part(X) = least_upper_bound(identity,X),
inference(resolve,[$cnf( $equal(positive_part(X),least_upper_bound(X,identity)) )],[lat4_1,refute_0_55]) ).
cnf(refute_0_57,plain,
( positive_part(X) != least_upper_bound(identity,X)
| least_upper_bound(identity,X) = positive_part(X) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(positive_part(X))),bind(Y0,$fot(least_upper_bound(identity,X)))]]) ).
cnf(refute_0_58,plain,
least_upper_bound(identity,X) = positive_part(X),
inference(resolve,[$cnf( $equal(positive_part(X),least_upper_bound(identity,X)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
least_upper_bound(identity,multiply(X_141,X_140)) = positive_part(multiply(X_141,X_140)),
inference(subst,[],[refute_0_58:[bind(X,$fot(multiply(X_141,X_140)))]]) ).
cnf(refute_0_60,plain,
least_upper_bound(X_17,greatest_lower_bound(X_17,X_18)) = X_17,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_17)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_61,plain,
greatest_lower_bound(X_18,X_17) = greatest_lower_bound(X_17,X_18),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_18)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_62,plain,
( greatest_lower_bound(X_18,X_17) != greatest_lower_bound(X_17,X_18)
| greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,X_17) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X_18,X_17))),bind(Y0,$fot(greatest_lower_bound(X_17,X_18)))]]) ).
cnf(refute_0_63,plain,
greatest_lower_bound(X_17,X_18) = greatest_lower_bound(X_18,X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,X_17),greatest_lower_bound(X_17,X_18)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( greatest_lower_bound(X_17,X_18) != greatest_lower_bound(X_18,X_17)
| least_upper_bound(X_17,greatest_lower_bound(X_17,X_18)) != X_17
| least_upper_bound(X_17,greatest_lower_bound(X_18,X_17)) = X_17 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,greatest_lower_bound(X_17,X_18)),X_17) ),[0,1],$fot(greatest_lower_bound(X_18,X_17))]]) ).
cnf(refute_0_65,plain,
( least_upper_bound(X_17,greatest_lower_bound(X_17,X_18)) != X_17
| least_upper_bound(X_17,greatest_lower_bound(X_18,X_17)) = X_17 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,X_18),greatest_lower_bound(X_18,X_17)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
least_upper_bound(X_17,greatest_lower_bound(X_18,X_17)) = X_17,
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,greatest_lower_bound(X_17,X_18)),X_17) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
least_upper_bound(least_upper_bound(X_41,X_42),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) = least_upper_bound(X_41,X_42),
inference(subst,[],[refute_0_66:[bind(X_17,$fot(least_upper_bound(X_41,X_42))),bind(X_18,$fot(positive_part(X_41)))]]) ).
cnf(refute_0_68,plain,
least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,identity)),
inference(subst,[],[lat4_3:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_69,plain,
positive_part(X_38) = least_upper_bound(X_38,identity),
inference(subst,[],[lat4_1:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_70,plain,
( positive_part(X_38) != least_upper_bound(X_38,identity)
| least_upper_bound(X_38,identity) = positive_part(X_38) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(positive_part(X_38))),bind(Y0,$fot(least_upper_bound(X_38,identity)))]]) ).
cnf(refute_0_71,plain,
least_upper_bound(X_38,identity) = positive_part(X_38),
inference(resolve,[$cnf( $equal(positive_part(X_38),least_upper_bound(X_38,identity)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) != greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,identity))
| least_upper_bound(X_38,identity) != positive_part(X_38)
| least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,identity))) ),[1,1],$fot(positive_part(X_38))]]) ).
cnf(refute_0_73,plain,
( least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) != greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,identity))
| least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,identity),positive_part(X_38)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,identity))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
( negative_part(X) != greatest_lower_bound(X,identity)
| greatest_lower_bound(X,identity) = negative_part(X) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(greatest_lower_bound(X,identity)))]]) ).
cnf(refute_0_76,plain,
greatest_lower_bound(X,identity) = negative_part(X),
inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) )],[lat4_2,refute_0_75]) ).
cnf(refute_0_77,plain,
greatest_lower_bound(X_39,identity) = negative_part(X_39),
inference(subst,[],[refute_0_76:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_78,plain,
least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)))]]) ).
cnf(refute_0_79,plain,
( greatest_lower_bound(X_39,identity) != negative_part(X_39)
| least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) != least_upper_bound(X_38,greatest_lower_bound(X_39,identity))
| least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = least_upper_bound(X_38,negative_part(X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),least_upper_bound(X_38,greatest_lower_bound(X_39,identity))) ),[1,1],$fot(negative_part(X_39))]]) ).
cnf(refute_0_80,plain,
( greatest_lower_bound(X_39,identity) != negative_part(X_39)
| least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = least_upper_bound(X_38,negative_part(X_39)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),least_upper_bound(X_38,greatest_lower_bound(X_39,identity))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) = least_upper_bound(X_38,negative_part(X_39)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,identity),negative_part(X_39)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) != greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))
| least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) != least_upper_bound(X_38,negative_part(X_39))
| least_upper_bound(X_38,negative_part(X_39)) = greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))) ),[0],$fot(least_upper_bound(X_38,negative_part(X_39)))]]) ).
cnf(refute_0_83,plain,
( least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) != greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))
| least_upper_bound(X_38,negative_part(X_39)) = greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),least_upper_bound(X_38,negative_part(X_39))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_85,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_84]) ).
cnf(refute_0_86,plain,
greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)) = greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)),
inference(subst,[],[refute_0_85:[bind(X,$fot(positive_part(X_38))),bind(Y,$fot(least_upper_bound(X_38,X_39)))]]) ).
cnf(refute_0_87,plain,
( greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)) != greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39))
| least_upper_bound(X_38,negative_part(X_39)) != greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))
| least_upper_bound(X_38,negative_part(X_39)) = greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_38,negative_part(X_39)),greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))) ),[1],$fot(greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)))]]) ).
cnf(refute_0_88,plain,
( least_upper_bound(X_38,negative_part(X_39)) != greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))
| least_upper_bound(X_38,negative_part(X_39)) = greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38)),greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( least_upper_bound(X_38,greatest_lower_bound(X_39,identity)) != greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))
| least_upper_bound(X_38,negative_part(X_39)) = greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,negative_part(X_39)),greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
least_upper_bound(X_38,negative_part(X_39)) = greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,identity)),greatest_lower_bound(least_upper_bound(X_38,X_39),positive_part(X_38))) )],[refute_0_74,refute_0_89]) ).
cnf(refute_0_91,plain,
least_upper_bound(X_41,negative_part(X_42)) = greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)),
inference(subst,[],[refute_0_90:[bind(X_38,$fot(X_41)),bind(X_39,$fot(X_42))]]) ).
cnf(refute_0_92,plain,
( least_upper_bound(X_41,negative_part(X_42)) != greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))
| greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)) = least_upper_bound(X_41,negative_part(X_42)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_41,negative_part(X_42)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))))]]) ).
cnf(refute_0_93,plain,
greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)) = least_upper_bound(X_41,negative_part(X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,negative_part(X_42)),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)) != least_upper_bound(X_41,negative_part(X_42))
| least_upper_bound(least_upper_bound(X_41,X_42),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) != least_upper_bound(X_41,X_42)
| least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))) = least_upper_bound(X_41,X_42) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))),least_upper_bound(X_41,X_42)) ),[0,1],$fot(least_upper_bound(X_41,negative_part(X_42)))]]) ).
cnf(refute_0_95,plain,
( least_upper_bound(least_upper_bound(X_41,X_42),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) != least_upper_bound(X_41,X_42)
| least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))) = least_upper_bound(X_41,X_42) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)),least_upper_bound(X_41,negative_part(X_42))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))) = least_upper_bound(X_41,X_42),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))),least_upper_bound(X_41,X_42)) )],[refute_0_67,refute_0_95]) ).
cnf(refute_0_97,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_98,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_97]) ).
cnf(refute_0_99,plain,
least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))) = least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))),
inference(subst,[],[refute_0_98:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(least_upper_bound(X_41,negative_part(X_42))))]]) ).
cnf(refute_0_100,plain,
( least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))) != least_upper_bound(X_41,X_42)
| least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))) != least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))))
| least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) = least_upper_bound(X_41,X_42) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))),least_upper_bound(X_41,X_42)) ),[0],$fot(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))))]]) ).
cnf(refute_0_101,plain,
( least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))) != least_upper_bound(X_41,X_42)
| least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) = least_upper_bound(X_41,X_42) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))),least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) = least_upper_bound(X_41,X_42),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_41,X_42),least_upper_bound(X_41,negative_part(X_42))),least_upper_bound(X_41,X_42)) )],[refute_0_96,refute_0_101]) ).
cnf(refute_0_103,plain,
least_upper_bound(X_17,greatest_lower_bound(X_17,identity)) = X_17,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_17)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_104,plain,
negative_part(X_17) = greatest_lower_bound(X_17,identity),
inference(subst,[],[lat4_2:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_105,plain,
( negative_part(X_17) != greatest_lower_bound(X_17,identity)
| greatest_lower_bound(X_17,identity) = negative_part(X_17) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(X_17))),bind(Y0,$fot(greatest_lower_bound(X_17,identity)))]]) ).
cnf(refute_0_106,plain,
greatest_lower_bound(X_17,identity) = negative_part(X_17),
inference(resolve,[$cnf( $equal(negative_part(X_17),greatest_lower_bound(X_17,identity)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( greatest_lower_bound(X_17,identity) != negative_part(X_17)
| least_upper_bound(X_17,greatest_lower_bound(X_17,identity)) != X_17
| least_upper_bound(X_17,negative_part(X_17)) = X_17 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,greatest_lower_bound(X_17,identity)),X_17) ),[0,1],$fot(negative_part(X_17))]]) ).
cnf(refute_0_108,plain,
( least_upper_bound(X_17,greatest_lower_bound(X_17,identity)) != X_17
| least_upper_bound(X_17,negative_part(X_17)) = X_17 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,identity),negative_part(X_17)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
least_upper_bound(X_17,negative_part(X_17)) = X_17,
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,greatest_lower_bound(X_17,identity)),X_17) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))) = least_upper_bound(X_78,X_79),
inference(subst,[],[refute_0_109:[bind(X_17,$fot(least_upper_bound(X_78,X_79)))]]) ).
cnf(refute_0_111,plain,
least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(negative_part(least_upper_bound(X_78,X_79))))]]) ).
cnf(refute_0_112,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) != least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79)))
| least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))) = least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79)))))]]) ).
cnf(refute_0_113,plain,
least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))) = least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79)))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))) != least_upper_bound(X_78,X_79)
| least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))) != least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))))
| least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(X_78,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))),least_upper_bound(X_78,X_79)) ),[0],$fot(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))))]]) ).
cnf(refute_0_115,plain,
( least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))) != least_upper_bound(X_78,X_79)
| least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(X_78,X_79) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))),least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(X_78,X_79),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(least_upper_bound(X_78,X_79))),least_upper_bound(X_78,X_79)) )],[refute_0_110,refute_0_115]) ).
cnf(refute_0_117,plain,
least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) = greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,least_upper_bound(Y,X_41))),
inference(subst,[],[refute_0_90:[bind(X_38,$fot(X_41)),bind(X_39,$fot(least_upper_bound(Y,X_41)))]]) ).
cnf(refute_0_118,plain,
least_upper_bound(least_upper_bound(X_27,Y),greatest_lower_bound(X_27,least_upper_bound(X_27,Y))) = least_upper_bound(X_27,Y),
inference(subst,[],[refute_0_66:[bind(X_17,$fot(least_upper_bound(X_27,Y))),bind(X_18,$fot(X_27))]]) ).
cnf(refute_0_119,plain,
greatest_lower_bound(X_27,least_upper_bound(X_27,Y)) = X_27,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_120,plain,
( greatest_lower_bound(X_27,least_upper_bound(X_27,Y)) != X_27
| least_upper_bound(least_upper_bound(X_27,Y),greatest_lower_bound(X_27,least_upper_bound(X_27,Y))) != least_upper_bound(X_27,Y)
| least_upper_bound(least_upper_bound(X_27,Y),X_27) = least_upper_bound(X_27,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_27,Y),greatest_lower_bound(X_27,least_upper_bound(X_27,Y))),least_upper_bound(X_27,Y)) ),[0,1],$fot(X_27)]]) ).
cnf(refute_0_121,plain,
( least_upper_bound(least_upper_bound(X_27,Y),greatest_lower_bound(X_27,least_upper_bound(X_27,Y))) != least_upper_bound(X_27,Y)
| least_upper_bound(least_upper_bound(X_27,Y),X_27) = least_upper_bound(X_27,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_27,least_upper_bound(X_27,Y)),X_27) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
least_upper_bound(least_upper_bound(X_27,Y),X_27) = least_upper_bound(X_27,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_27,Y),greatest_lower_bound(X_27,least_upper_bound(X_27,Y))),least_upper_bound(X_27,Y)) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
least_upper_bound(least_upper_bound(X_27,Y),X_27) = least_upper_bound(X_27,least_upper_bound(Y,X_27)),
inference(subst,[],[refute_0_98:[bind(X,$fot(X_27)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_124,plain,
( least_upper_bound(least_upper_bound(X_27,Y),X_27) != least_upper_bound(X_27,Y)
| least_upper_bound(least_upper_bound(X_27,Y),X_27) != least_upper_bound(X_27,least_upper_bound(Y,X_27))
| least_upper_bound(X_27,least_upper_bound(Y,X_27)) = least_upper_bound(X_27,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_27,Y),X_27),least_upper_bound(X_27,Y)) ),[0],$fot(least_upper_bound(X_27,least_upper_bound(Y,X_27)))]]) ).
cnf(refute_0_125,plain,
( least_upper_bound(least_upper_bound(X_27,Y),X_27) != least_upper_bound(X_27,Y)
| least_upper_bound(X_27,least_upper_bound(Y,X_27)) = least_upper_bound(X_27,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_27,Y),X_27),least_upper_bound(X_27,least_upper_bound(Y,X_27))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
least_upper_bound(X_27,least_upper_bound(Y,X_27)) = least_upper_bound(X_27,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_27,Y),X_27),least_upper_bound(X_27,Y)) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
least_upper_bound(X_41,least_upper_bound(Y,X_41)) = least_upper_bound(X_41,Y),
inference(subst,[],[refute_0_126:[bind(X_27,$fot(X_41))]]) ).
cnf(refute_0_128,plain,
( least_upper_bound(X_41,least_upper_bound(Y,X_41)) != least_upper_bound(X_41,Y)
| least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) != greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,least_upper_bound(Y,X_41)))
| least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) = greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,least_upper_bound(Y,X_41)))) ),[1,1],$fot(least_upper_bound(X_41,Y))]]) ).
cnf(refute_0_129,plain,
( least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) != greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,least_upper_bound(Y,X_41)))
| least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) = greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(Y,X_41)),least_upper_bound(X_41,Y)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) = greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,least_upper_bound(Y,X_41)))) )],[refute_0_117,refute_0_129]) ).
cnf(refute_0_131,plain,
( least_upper_bound(X_38,negative_part(X_39)) != greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39))
| greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)) = least_upper_bound(X_38,negative_part(X_39)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_38,negative_part(X_39)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39))))]]) ).
cnf(refute_0_132,plain,
greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39)) = least_upper_bound(X_38,negative_part(X_39)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,negative_part(X_39)),greatest_lower_bound(positive_part(X_38),least_upper_bound(X_38,X_39))) )],[refute_0_90,refute_0_131]) ).
cnf(refute_0_133,plain,
greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y)) = least_upper_bound(X_41,negative_part(Y)),
inference(subst,[],[refute_0_132:[bind(X_38,$fot(X_41)),bind(X_39,$fot(Y))]]) ).
cnf(refute_0_134,plain,
( greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y)) != least_upper_bound(X_41,negative_part(Y))
| least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) != greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y))
| least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) = least_upper_bound(X_41,negative_part(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y))) ),[1],$fot(least_upper_bound(X_41,negative_part(Y)))]]) ).
cnf(refute_0_135,plain,
( least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) != greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y))
| least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) = least_upper_bound(X_41,negative_part(Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y)),least_upper_bound(X_41,negative_part(Y))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))) = least_upper_bound(X_41,negative_part(Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,negative_part(least_upper_bound(Y,X_41))),greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,Y))) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))) = least_upper_bound(X_79,negative_part(X_78)),
inference(subst,[],[refute_0_136:[bind(Y,$fot(X_78)),bind(X_41,$fot(X_79))]]) ).
cnf(refute_0_138,plain,
least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))))]]) ).
cnf(refute_0_139,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) != least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))))
| least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))) != least_upper_bound(X_79,negative_part(X_78))
| least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))))) ),[1,1],$fot(least_upper_bound(X_79,negative_part(X_78)))]]) ).
cnf(refute_0_140,plain,
( least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))) != least_upper_bound(X_79,negative_part(X_78))
| least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) = least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79))),least_upper_bound(X_79,negative_part(X_78))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) != least_upper_bound(X_78,X_79)
| least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) != least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78)))
| least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78))) = least_upper_bound(X_78,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),least_upper_bound(X_78,X_79)) ),[0],$fot(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78))))]]) ).
cnf(refute_0_143,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))) != least_upper_bound(X_78,X_79)
| least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78))) = least_upper_bound(X_78,X_79) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78)))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_78))) = least_upper_bound(X_78,X_79),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(least_upper_bound(X_78,X_79)))),least_upper_bound(X_78,X_79)) )],[refute_0_116,refute_0_143]) ).
cnf(refute_0_145,plain,
least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))) = least_upper_bound(X_42,X_41),
inference(subst,[],[refute_0_144:[bind(X_78,$fot(X_42)),bind(X_79,$fot(X_41))]]) ).
cnf(refute_0_146,plain,
least_upper_bound(X_78,least_upper_bound(X_79,least_upper_bound(Y,X_79))) = least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(least_upper_bound(Y,X_79)))]]) ).
cnf(refute_0_147,plain,
least_upper_bound(X_79,least_upper_bound(Y,X_79)) = least_upper_bound(X_79,Y),
inference(subst,[],[refute_0_126:[bind(X_27,$fot(X_79))]]) ).
cnf(refute_0_148,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,least_upper_bound(Y,X_79))) != least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79))
| least_upper_bound(X_79,least_upper_bound(Y,X_79)) != least_upper_bound(X_79,Y)
| least_upper_bound(X_78,least_upper_bound(X_79,Y)) = least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,least_upper_bound(Y,X_79))),least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79))) ),[0,1],$fot(least_upper_bound(X_79,Y))]]) ).
cnf(refute_0_149,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,least_upper_bound(Y,X_79))) != least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79))
| least_upper_bound(X_78,least_upper_bound(X_79,Y)) = least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,least_upper_bound(Y,X_79)),least_upper_bound(X_79,Y)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
least_upper_bound(X_78,least_upper_bound(X_79,Y)) = least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,least_upper_bound(Y,X_79))),least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
least_upper_bound(least_upper_bound(X_78,X_79),Y) = least_upper_bound(X_78,least_upper_bound(X_79,Y)),
inference(subst,[],[refute_0_98:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_152,plain,
least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)) = least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)))]]) ).
cnf(refute_0_153,plain,
( least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)) != least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y))
| least_upper_bound(least_upper_bound(X_78,X_79),Y) != least_upper_bound(X_78,least_upper_bound(X_79,Y))
| least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)),least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y))) ),[1,1],$fot(least_upper_bound(X_78,least_upper_bound(X_79,Y)))]]) ).
cnf(refute_0_154,plain,
( least_upper_bound(least_upper_bound(X_78,X_79),Y) != least_upper_bound(X_78,least_upper_bound(X_79,Y))
| least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)),least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),Y),least_upper_bound(X_78,least_upper_bound(X_79,Y))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
least_upper_bound(X,least_upper_bound(X_78,X_79)) = least_upper_bound(least_upper_bound(X_78,X_79),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_78,X_79)))]]) ).
cnf(refute_0_157,plain,
least_upper_bound(X_78,least_upper_bound(X_79,X)) = least_upper_bound(least_upper_bound(X_78,X_79),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(X))]]) ).
cnf(refute_0_158,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,X)) != least_upper_bound(least_upper_bound(X_78,X_79),X)
| least_upper_bound(least_upper_bound(X_78,X_79),X) = least_upper_bound(X_78,least_upper_bound(X_79,X)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_78,least_upper_bound(X_79,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_78,X_79),X)))]]) ).
cnf(refute_0_159,plain,
least_upper_bound(least_upper_bound(X_78,X_79),X) = least_upper_bound(X_78,least_upper_bound(X_79,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,X)),least_upper_bound(least_upper_bound(X_78,X_79),X)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( least_upper_bound(X,least_upper_bound(X_78,X_79)) != least_upper_bound(least_upper_bound(X_78,X_79),X)
| least_upper_bound(least_upper_bound(X_78,X_79),X) != least_upper_bound(X_78,least_upper_bound(X_79,X))
| least_upper_bound(X,least_upper_bound(X_78,X_79)) = least_upper_bound(X_78,least_upper_bound(X_79,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_78,X_79)),least_upper_bound(X_78,least_upper_bound(X_79,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_78,X_79),X))]]) ).
cnf(refute_0_161,plain,
( least_upper_bound(X,least_upper_bound(X_78,X_79)) != least_upper_bound(least_upper_bound(X_78,X_79),X)
| least_upper_bound(X,least_upper_bound(X_78,X_79)) = least_upper_bound(X_78,least_upper_bound(X_79,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),X),least_upper_bound(X_78,least_upper_bound(X_79,X))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
least_upper_bound(X,least_upper_bound(X_78,X_79)) = least_upper_bound(X_78,least_upper_bound(X_79,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_78,X_79)),least_upper_bound(least_upper_bound(X_78,X_79),X)) )],[refute_0_156,refute_0_161]) ).
cnf(refute_0_163,plain,
( least_upper_bound(X,least_upper_bound(X_78,X_79)) != least_upper_bound(X_78,least_upper_bound(X_79,X))
| least_upper_bound(X_78,least_upper_bound(X_79,X)) = least_upper_bound(X,least_upper_bound(X_78,X_79)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_78,X_79)))),bind(Y0,$fot(least_upper_bound(X_78,least_upper_bound(X_79,X))))]]) ).
cnf(refute_0_164,plain,
least_upper_bound(X_78,least_upper_bound(X_79,X)) = least_upper_bound(X,least_upper_bound(X_78,X_79)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_78,X_79)),least_upper_bound(X_78,least_upper_bound(X_79,X))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) = least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)),
inference(subst,[],[refute_0_164:[bind(X,$fot(X_79)),bind(X_78,$fot(least_upper_bound(X_78,X_79))),bind(X_79,$fot(Y))]]) ).
cnf(refute_0_166,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_167,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_21,refute_0_166]) ).
cnf(refute_0_168,plain,
( least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)) != least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))
| least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) != least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y))
| least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)))),bind(Y0,$fot(least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)))),bind(Z0,$fot(least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))))]]) ).
cnf(refute_0_169,plain,
( least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)) != least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))
| least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)),least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,least_upper_bound(least_upper_bound(X_78,X_79),Y)),least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))) )],[refute_0_155,refute_0_169]) ).
cnf(refute_0_171,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,Y)) != least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79))
| least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)) != least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))
| least_upper_bound(X_78,least_upper_bound(X_79,Y)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_78,least_upper_bound(X_79,Y)),least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)))]]) ).
cnf(refute_0_172,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,Y)) != least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79))
| least_upper_bound(X_78,least_upper_bound(X_79,Y)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79)),least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
least_upper_bound(X_78,least_upper_bound(X_79,Y)) = least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,Y)),least_upper_bound(least_upper_bound(X_78,X_79),least_upper_bound(Y,X_79))) )],[refute_0_150,refute_0_172]) ).
cnf(refute_0_174,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,Y)) != least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))
| least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) = least_upper_bound(X_78,least_upper_bound(X_79,Y)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_78,least_upper_bound(X_79,Y)))),bind(Y0,$fot(least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))))]]) ).
cnf(refute_0_175,plain,
least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y))) = least_upper_bound(X_78,least_upper_bound(X_79,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,Y)),least_upper_bound(X_79,least_upper_bound(X_78,least_upper_bound(X_79,Y)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) = least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))),
inference(subst,[],[refute_0_175:[bind(Y,$fot(negative_part(X_42))),bind(X_78,$fot(X_42)),bind(X_79,$fot(X_41))]]) ).
cnf(refute_0_177,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) != least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))
| least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))) != least_upper_bound(X_42,X_41)
| least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) = least_upper_bound(X_42,X_41) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))))),bind(Y0,$fot(least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))))),bind(Z0,$fot(least_upper_bound(X_42,X_41)))]]) ).
cnf(refute_0_178,plain,
( least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))) != least_upper_bound(X_42,X_41)
| least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) = least_upper_bound(X_42,X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))),least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) = least_upper_bound(X_42,X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42))),least_upper_bound(X_42,X_41)) )],[refute_0_145,refute_0_178]) ).
cnf(refute_0_180,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) != least_upper_bound(X_41,X_42)
| least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) != least_upper_bound(X_42,X_41)
| least_upper_bound(X_42,X_41) = least_upper_bound(X_41,X_42) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))),least_upper_bound(X_41,X_42)) ),[0],$fot(least_upper_bound(X_42,X_41))]]) ).
cnf(refute_0_181,plain,
( least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))) != least_upper_bound(X_41,X_42)
| least_upper_bound(X_42,X_41) = least_upper_bound(X_41,X_42) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))),least_upper_bound(X_42,X_41)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
least_upper_bound(X_42,X_41) = least_upper_bound(X_41,X_42),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,least_upper_bound(X_42,least_upper_bound(X_41,negative_part(X_42)))),least_upper_bound(X_41,X_42)) )],[refute_0_102,refute_0_181]) ).
cnf(refute_0_183,plain,
( least_upper_bound(X_42,X_41) != least_upper_bound(X_41,X_42)
| least_upper_bound(X_41,X_42) = least_upper_bound(X_42,X_41) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_42,X_41))),bind(Y0,$fot(least_upper_bound(X_41,X_42)))]]) ).
cnf(refute_0_184,plain,
least_upper_bound(X_41,X_42) = least_upper_bound(X_42,X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,X_41),least_upper_bound(X_41,X_42)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
least_upper_bound(multiply(X_141,X_140),identity) = least_upper_bound(identity,multiply(X_141,X_140)),
inference(subst,[],[refute_0_184:[bind(X_41,$fot(multiply(X_141,X_140))),bind(X_42,$fot(identity))]]) ).
cnf(refute_0_186,plain,
( least_upper_bound(multiply(X_141,X_140),identity) != least_upper_bound(identity,multiply(X_141,X_140))
| least_upper_bound(identity,multiply(X_141,X_140)) != positive_part(multiply(X_141,X_140))
| least_upper_bound(multiply(X_141,X_140),identity) = positive_part(multiply(X_141,X_140)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(multiply(X_141,X_140),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_141,X_140)))),bind(Z0,$fot(positive_part(multiply(X_141,X_140))))]]) ).
cnf(refute_0_187,plain,
( least_upper_bound(identity,multiply(X_141,X_140)) != positive_part(multiply(X_141,X_140))
| least_upper_bound(multiply(X_141,X_140),identity) = positive_part(multiply(X_141,X_140)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_141,X_140),identity),least_upper_bound(identity,multiply(X_141,X_140))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
least_upper_bound(multiply(X_141,X_140),identity) = positive_part(multiply(X_141,X_140)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_141,X_140)),positive_part(multiply(X_141,X_140))) )],[refute_0_59,refute_0_187]) ).
cnf(refute_0_189,plain,
( multiply(least_upper_bound(X_141,inverse(X_140)),X_140) != least_upper_bound(multiply(X_141,X_140),identity)
| least_upper_bound(multiply(X_141,X_140),identity) != positive_part(multiply(X_141,X_140))
| multiply(least_upper_bound(X_141,inverse(X_140)),X_140) = positive_part(multiply(X_141,X_140)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_141,inverse(X_140)),X_140),positive_part(multiply(X_141,X_140))) ),[0],$fot(least_upper_bound(multiply(X_141,X_140),identity))]]) ).
cnf(refute_0_190,plain,
( multiply(least_upper_bound(X_141,inverse(X_140)),X_140) != least_upper_bound(multiply(X_141,X_140),identity)
| multiply(least_upper_bound(X_141,inverse(X_140)),X_140) = positive_part(multiply(X_141,X_140)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_141,X_140),identity),positive_part(multiply(X_141,X_140))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
multiply(least_upper_bound(X_141,inverse(X_140)),X_140) = positive_part(multiply(X_141,X_140)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_141,inverse(X_140)),X_140),least_upper_bound(multiply(X_141,X_140),identity)) )],[refute_0_52,refute_0_190]) ).
cnf(refute_0_192,plain,
multiply(least_upper_bound(X_147,inverse(X_59)),X_59) = positive_part(multiply(X_147,X_59)),
inference(subst,[],[refute_0_191:[bind(X_140,$fot(X_59)),bind(X_141,$fot(X_147))]]) ).
cnf(refute_0_193,plain,
( X_59 != multiply(inverse(least_upper_bound(X_147,inverse(X_59))),multiply(least_upper_bound(X_147,inverse(X_59)),X_59))
| multiply(least_upper_bound(X_147,inverse(X_59)),X_59) != positive_part(multiply(X_147,X_59))
| X_59 = multiply(inverse(least_upper_bound(X_147,inverse(X_59))),positive_part(multiply(X_147,X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(X_147,inverse(X_59))),multiply(least_upper_bound(X_147,inverse(X_59)),X_59))) ),[1,1],$fot(positive_part(multiply(X_147,X_59)))]]) ).
cnf(refute_0_194,plain,
( X_59 != multiply(inverse(least_upper_bound(X_147,inverse(X_59))),multiply(least_upper_bound(X_147,inverse(X_59)),X_59))
| X_59 = multiply(inverse(least_upper_bound(X_147,inverse(X_59))),positive_part(multiply(X_147,X_59))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_147,inverse(X_59)),X_59),positive_part(multiply(X_147,X_59))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
X_59 = multiply(inverse(least_upper_bound(X_147,inverse(X_59))),positive_part(multiply(X_147,X_59))),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(least_upper_bound(X_147,inverse(X_59))),multiply(least_upper_bound(X_147,inverse(X_59)),X_59))) )],[refute_0_47,refute_0_194]) ).
cnf(refute_0_196,plain,
positive_part(X_332) = multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(multiply(negative_part(inverse(X_332)),positive_part(X_332)))),
inference(subst,[],[refute_0_195:[bind(X_147,$fot(negative_part(inverse(X_332)))),bind(X_59,$fot(positive_part(X_332)))]]) ).
cnf(refute_0_197,plain,
multiply(X_96,least_upper_bound(X_97,identity)) = least_upper_bound(multiply(X_96,X_97),multiply(X_96,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_96)),bind(Y,$fot(X_97)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_198,plain,
X_61 = multiply(inverse(inverse(X_61)),multiply(inverse(X_61),X_61)),
inference(subst,[],[refute_0_8:[bind(X_58,$fot(inverse(X_61))),bind(X_59,$fot(X_61))]]) ).
cnf(refute_0_199,plain,
multiply(inverse(X_61),X_61) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_200,plain,
( X_61 != multiply(inverse(inverse(X_61)),multiply(inverse(X_61),X_61))
| multiply(inverse(X_61),X_61) != identity
| X_61 = multiply(inverse(inverse(X_61)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_61,multiply(inverse(inverse(X_61)),multiply(inverse(X_61),X_61))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_201,plain,
( X_61 != multiply(inverse(inverse(X_61)),multiply(inverse(X_61),X_61))
| X_61 = multiply(inverse(inverse(X_61)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),X_61),identity) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
X_61 = multiply(inverse(inverse(X_61)),identity),
inference(resolve,[$cnf( $equal(X_61,multiply(inverse(inverse(X_61)),multiply(inverse(X_61),X_61))) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
multiply(X_60,X_61) = multiply(inverse(inverse(X_60)),multiply(inverse(X_60),multiply(X_60,X_61))),
inference(subst,[],[refute_0_8:[bind(X_58,$fot(inverse(X_60))),bind(X_59,$fot(multiply(X_60,X_61)))]]) ).
cnf(refute_0_204,plain,
X_61 = multiply(inverse(X_60),multiply(X_60,X_61)),
inference(subst,[],[refute_0_8:[bind(X_58,$fot(X_60)),bind(X_59,$fot(X_61))]]) ).
cnf(refute_0_205,plain,
( X_61 != multiply(inverse(X_60),multiply(X_60,X_61))
| multiply(inverse(X_60),multiply(X_60,X_61)) = X_61 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_61)),bind(Y0,$fot(multiply(inverse(X_60),multiply(X_60,X_61))))]]) ).
cnf(refute_0_206,plain,
multiply(inverse(X_60),multiply(X_60,X_61)) = X_61,
inference(resolve,[$cnf( $equal(X_61,multiply(inverse(X_60),multiply(X_60,X_61))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( multiply(X_60,X_61) != multiply(inverse(inverse(X_60)),multiply(inverse(X_60),multiply(X_60,X_61)))
| multiply(inverse(X_60),multiply(X_60,X_61)) != X_61
| multiply(X_60,X_61) = multiply(inverse(inverse(X_60)),X_61) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_60,X_61),multiply(inverse(inverse(X_60)),multiply(inverse(X_60),multiply(X_60,X_61)))) ),[1,1],$fot(X_61)]]) ).
cnf(refute_0_208,plain,
( multiply(X_60,X_61) != multiply(inverse(inverse(X_60)),multiply(inverse(X_60),multiply(X_60,X_61)))
| multiply(X_60,X_61) = multiply(inverse(inverse(X_60)),X_61) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),multiply(X_60,X_61)),X_61) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
multiply(X_60,X_61) = multiply(inverse(inverse(X_60)),X_61),
inference(resolve,[$cnf( $equal(multiply(X_60,X_61),multiply(inverse(inverse(X_60)),multiply(inverse(X_60),multiply(X_60,X_61)))) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
( multiply(X_60,X_61) != multiply(inverse(inverse(X_60)),X_61)
| multiply(inverse(inverse(X_60)),X_61) = multiply(X_60,X_61) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_60,X_61))),bind(Y0,$fot(multiply(inverse(inverse(X_60)),X_61)))]]) ).
cnf(refute_0_211,plain,
multiply(inverse(inverse(X_60)),X_61) = multiply(X_60,X_61),
inference(resolve,[$cnf( $equal(multiply(X_60,X_61),multiply(inverse(inverse(X_60)),X_61)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(inverse(inverse(X_61)),identity) = multiply(X_61,identity),
inference(subst,[],[refute_0_211:[bind(X_60,$fot(X_61)),bind(X_61,$fot(identity))]]) ).
cnf(refute_0_213,plain,
( X_61 != multiply(inverse(inverse(X_61)),identity)
| multiply(inverse(inverse(X_61)),identity) != multiply(X_61,identity)
| X_61 = multiply(X_61,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_61,multiply(X_61,identity)) ),[0],$fot(multiply(inverse(inverse(X_61)),identity))]]) ).
cnf(refute_0_214,plain,
( X_61 != multiply(inverse(inverse(X_61)),identity)
| X_61 = multiply(X_61,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_61)),identity),multiply(X_61,identity)) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
X_61 = multiply(X_61,identity),
inference(resolve,[$cnf( $equal(X_61,multiply(inverse(inverse(X_61)),identity)) )],[refute_0_202,refute_0_214]) ).
cnf(refute_0_216,plain,
X_96 = multiply(X_96,identity),
inference(subst,[],[refute_0_215:[bind(X_61,$fot(X_96))]]) ).
cnf(refute_0_217,plain,
( X_96 != multiply(X_96,identity)
| multiply(X_96,identity) = X_96 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_96)),bind(Y0,$fot(multiply(X_96,identity)))]]) ).
cnf(refute_0_218,plain,
multiply(X_96,identity) = X_96,
inference(resolve,[$cnf( $equal(X_96,multiply(X_96,identity)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
( multiply(X_96,identity) != X_96
| multiply(X_96,least_upper_bound(X_97,identity)) != least_upper_bound(multiply(X_96,X_97),multiply(X_96,identity))
| multiply(X_96,least_upper_bound(X_97,identity)) = least_upper_bound(multiply(X_96,X_97),X_96) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,identity)),least_upper_bound(multiply(X_96,X_97),multiply(X_96,identity))) ),[1,1],$fot(X_96)]]) ).
cnf(refute_0_220,plain,
( multiply(X_96,least_upper_bound(X_97,identity)) != least_upper_bound(multiply(X_96,X_97),multiply(X_96,identity))
| multiply(X_96,least_upper_bound(X_97,identity)) = least_upper_bound(multiply(X_96,X_97),X_96) ),
inference(resolve,[$cnf( $equal(multiply(X_96,identity),X_96) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
multiply(X_96,least_upper_bound(X_97,identity)) = least_upper_bound(multiply(X_96,X_97),X_96),
inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,identity)),least_upper_bound(multiply(X_96,X_97),multiply(X_96,identity))) )],[refute_0_197,refute_0_220]) ).
cnf(refute_0_222,plain,
( positive_part(X) != least_upper_bound(X,identity)
| least_upper_bound(X,identity) = positive_part(X) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(positive_part(X))),bind(Y0,$fot(least_upper_bound(X,identity)))]]) ).
cnf(refute_0_223,plain,
least_upper_bound(X,identity) = positive_part(X),
inference(resolve,[$cnf( $equal(positive_part(X),least_upper_bound(X,identity)) )],[lat4_1,refute_0_222]) ).
cnf(refute_0_224,plain,
least_upper_bound(X_97,identity) = positive_part(X_97),
inference(subst,[],[refute_0_223:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_225,plain,
multiply(X_96,least_upper_bound(X_97,identity)) = multiply(X_96,least_upper_bound(X_97,identity)),
introduced(tautology,[refl,[$fot(multiply(X_96,least_upper_bound(X_97,identity)))]]) ).
cnf(refute_0_226,plain,
( multiply(X_96,least_upper_bound(X_97,identity)) != multiply(X_96,least_upper_bound(X_97,identity))
| least_upper_bound(X_97,identity) != positive_part(X_97)
| multiply(X_96,least_upper_bound(X_97,identity)) = multiply(X_96,positive_part(X_97)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,identity)),multiply(X_96,least_upper_bound(X_97,identity))) ),[1,1],$fot(positive_part(X_97))]]) ).
cnf(refute_0_227,plain,
( least_upper_bound(X_97,identity) != positive_part(X_97)
| multiply(X_96,least_upper_bound(X_97,identity)) = multiply(X_96,positive_part(X_97)) ),
inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,identity)),multiply(X_96,least_upper_bound(X_97,identity))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(X_96,least_upper_bound(X_97,identity)) = multiply(X_96,positive_part(X_97)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_97,identity),positive_part(X_97)) )],[refute_0_224,refute_0_227]) ).
cnf(refute_0_229,plain,
( multiply(X_96,least_upper_bound(X_97,identity)) != multiply(X_96,positive_part(X_97))
| multiply(X_96,least_upper_bound(X_97,identity)) != least_upper_bound(multiply(X_96,X_97),X_96)
| multiply(X_96,positive_part(X_97)) = least_upper_bound(multiply(X_96,X_97),X_96) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,identity)),least_upper_bound(multiply(X_96,X_97),X_96)) ),[0],$fot(multiply(X_96,positive_part(X_97)))]]) ).
cnf(refute_0_230,plain,
( multiply(X_96,least_upper_bound(X_97,identity)) != least_upper_bound(multiply(X_96,X_97),X_96)
| multiply(X_96,positive_part(X_97)) = least_upper_bound(multiply(X_96,X_97),X_96) ),
inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,identity)),multiply(X_96,positive_part(X_97))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
least_upper_bound(multiply(X_96,X_97),X_96) = least_upper_bound(X_96,multiply(X_96,X_97)),
inference(subst,[],[refute_0_184:[bind(X_41,$fot(multiply(X_96,X_97))),bind(X_42,$fot(X_96))]]) ).
cnf(refute_0_232,plain,
( multiply(X_96,positive_part(X_97)) != least_upper_bound(multiply(X_96,X_97),X_96)
| least_upper_bound(multiply(X_96,X_97),X_96) != least_upper_bound(X_96,multiply(X_96,X_97))
| multiply(X_96,positive_part(X_97)) = least_upper_bound(X_96,multiply(X_96,X_97)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_96,positive_part(X_97)),least_upper_bound(X_96,multiply(X_96,X_97))) ),[0],$fot(least_upper_bound(multiply(X_96,X_97),X_96))]]) ).
cnf(refute_0_233,plain,
( multiply(X_96,positive_part(X_97)) != least_upper_bound(multiply(X_96,X_97),X_96)
| multiply(X_96,positive_part(X_97)) = least_upper_bound(X_96,multiply(X_96,X_97)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_96,X_97),X_96),least_upper_bound(X_96,multiply(X_96,X_97))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
( multiply(X_96,least_upper_bound(X_97,identity)) != least_upper_bound(multiply(X_96,X_97),X_96)
| multiply(X_96,positive_part(X_97)) = least_upper_bound(X_96,multiply(X_96,X_97)) ),
inference(resolve,[$cnf( $equal(multiply(X_96,positive_part(X_97)),least_upper_bound(multiply(X_96,X_97),X_96)) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
multiply(X_96,positive_part(X_97)) = least_upper_bound(X_96,multiply(X_96,X_97)),
inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,identity)),least_upper_bound(multiply(X_96,X_97),X_96)) )],[refute_0_221,refute_0_234]) ).
cnf(refute_0_236,plain,
multiply(negative_part(inverse(X_175)),positive_part(X_175)) = least_upper_bound(negative_part(inverse(X_175)),multiply(negative_part(inverse(X_175)),X_175)),
inference(subst,[],[refute_0_235:[bind(X_96,$fot(negative_part(inverse(X_175)))),bind(X_97,$fot(X_175))]]) ).
cnf(refute_0_237,plain,
multiply(negative_part(inverse(X_175)),X_175) = negative_part(X_175),
inference(subst,[],[refute_0_42:[bind(X_162,$fot(X_175))]]) ).
cnf(refute_0_238,plain,
( multiply(negative_part(inverse(X_175)),X_175) != negative_part(X_175)
| multiply(negative_part(inverse(X_175)),positive_part(X_175)) != least_upper_bound(negative_part(inverse(X_175)),multiply(negative_part(inverse(X_175)),X_175))
| multiply(negative_part(inverse(X_175)),positive_part(X_175)) = least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_175)),positive_part(X_175)),least_upper_bound(negative_part(inverse(X_175)),multiply(negative_part(inverse(X_175)),X_175))) ),[1,1],$fot(negative_part(X_175))]]) ).
cnf(refute_0_239,plain,
( multiply(negative_part(inverse(X_175)),positive_part(X_175)) != least_upper_bound(negative_part(inverse(X_175)),multiply(negative_part(inverse(X_175)),X_175))
| multiply(negative_part(inverse(X_175)),positive_part(X_175)) = least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_175)),X_175),negative_part(X_175)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
multiply(negative_part(inverse(X_175)),positive_part(X_175)) = least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175)),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_175)),positive_part(X_175)),least_upper_bound(negative_part(inverse(X_175)),multiply(negative_part(inverse(X_175)),X_175))) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
least_upper_bound(negative_part(X_18),negative_part(X_42)) = greatest_lower_bound(positive_part(negative_part(X_18)),least_upper_bound(negative_part(X_18),X_42)),
inference(subst,[],[refute_0_90:[bind(X_38,$fot(negative_part(X_18))),bind(X_39,$fot(X_42))]]) ).
cnf(refute_0_242,plain,
positive_part(greatest_lower_bound(identity,X_18)) = least_upper_bound(identity,greatest_lower_bound(identity,X_18)),
inference(subst,[],[refute_0_56:[bind(X,$fot(greatest_lower_bound(identity,X_18)))]]) ).
cnf(refute_0_243,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_18)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_244,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_18)) != identity
| positive_part(greatest_lower_bound(identity,X_18)) != least_upper_bound(identity,greatest_lower_bound(identity,X_18))
| positive_part(greatest_lower_bound(identity,X_18)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_18)),least_upper_bound(identity,greatest_lower_bound(identity,X_18))) ),[1],$fot(identity)]]) ).
cnf(refute_0_245,plain,
( positive_part(greatest_lower_bound(identity,X_18)) != least_upper_bound(identity,greatest_lower_bound(identity,X_18))
| positive_part(greatest_lower_bound(identity,X_18)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_18)),identity) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
positive_part(greatest_lower_bound(identity,X_18)) = identity,
inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_18)),least_upper_bound(identity,greatest_lower_bound(identity,X_18))) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
greatest_lower_bound(identity,X_18) = negative_part(X_18),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_248,plain,
positive_part(greatest_lower_bound(identity,X_18)) = positive_part(greatest_lower_bound(identity,X_18)),
introduced(tautology,[refl,[$fot(positive_part(greatest_lower_bound(identity,X_18)))]]) ).
cnf(refute_0_249,plain,
( greatest_lower_bound(identity,X_18) != negative_part(X_18)
| positive_part(greatest_lower_bound(identity,X_18)) != positive_part(greatest_lower_bound(identity,X_18))
| positive_part(greatest_lower_bound(identity,X_18)) = positive_part(negative_part(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_18)),positive_part(greatest_lower_bound(identity,X_18))) ),[1,0],$fot(negative_part(X_18))]]) ).
cnf(refute_0_250,plain,
( greatest_lower_bound(identity,X_18) != negative_part(X_18)
| positive_part(greatest_lower_bound(identity,X_18)) = positive_part(negative_part(X_18)) ),
inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_18)),positive_part(greatest_lower_bound(identity,X_18))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
positive_part(greatest_lower_bound(identity,X_18)) = positive_part(negative_part(X_18)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_18),negative_part(X_18)) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
( positive_part(greatest_lower_bound(identity,X_18)) != identity
| positive_part(greatest_lower_bound(identity,X_18)) != positive_part(negative_part(X_18))
| positive_part(negative_part(X_18)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_18)),identity) ),[0],$fot(positive_part(negative_part(X_18)))]]) ).
cnf(refute_0_253,plain,
( positive_part(greatest_lower_bound(identity,X_18)) != identity
| positive_part(negative_part(X_18)) = identity ),
inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_18)),positive_part(negative_part(X_18))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
positive_part(negative_part(X_18)) = identity,
inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_18)),identity) )],[refute_0_246,refute_0_253]) ).
cnf(refute_0_255,plain,
( least_upper_bound(negative_part(X_18),negative_part(X_42)) != greatest_lower_bound(positive_part(negative_part(X_18)),least_upper_bound(negative_part(X_18),X_42))
| positive_part(negative_part(X_18)) != identity
| least_upper_bound(negative_part(X_18),negative_part(X_42)) = greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(X_18),negative_part(X_42)),greatest_lower_bound(positive_part(negative_part(X_18)),least_upper_bound(negative_part(X_18),X_42))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_256,plain,
( least_upper_bound(negative_part(X_18),negative_part(X_42)) != greatest_lower_bound(positive_part(negative_part(X_18)),least_upper_bound(negative_part(X_18),X_42))
| least_upper_bound(negative_part(X_18),negative_part(X_42)) = greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42)) ),
inference(resolve,[$cnf( $equal(positive_part(negative_part(X_18)),identity) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
least_upper_bound(negative_part(X_18),negative_part(X_42)) = greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_18),negative_part(X_42)),greatest_lower_bound(positive_part(negative_part(X_18)),least_upper_bound(negative_part(X_18),X_42))) )],[refute_0_241,refute_0_256]) ).
cnf(refute_0_258,plain,
greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42)) = negative_part(least_upper_bound(negative_part(X_18),X_42)),
inference(subst,[],[refute_0_23:[bind(X,$fot(least_upper_bound(negative_part(X_18),X_42)))]]) ).
cnf(refute_0_259,plain,
( greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42)) != negative_part(least_upper_bound(negative_part(X_18),X_42))
| least_upper_bound(negative_part(X_18),negative_part(X_42)) != greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42))
| least_upper_bound(negative_part(X_18),negative_part(X_42)) = negative_part(least_upper_bound(negative_part(X_18),X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(X_18),negative_part(X_42)),greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42))) ),[1],$fot(negative_part(least_upper_bound(negative_part(X_18),X_42)))]]) ).
cnf(refute_0_260,plain,
( least_upper_bound(negative_part(X_18),negative_part(X_42)) != greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42))
| least_upper_bound(negative_part(X_18),negative_part(X_42)) = negative_part(least_upper_bound(negative_part(X_18),X_42)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42)),negative_part(least_upper_bound(negative_part(X_18),X_42))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
least_upper_bound(negative_part(X_18),negative_part(X_42)) = negative_part(least_upper_bound(negative_part(X_18),X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_18),negative_part(X_42)),greatest_lower_bound(identity,least_upper_bound(negative_part(X_18),X_42))) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
least_upper_bound(negative_part(X_47),negative_part(X_48)) = negative_part(least_upper_bound(negative_part(X_47),X_48)),
inference(subst,[],[refute_0_261:[bind(X_18,$fot(X_47)),bind(X_42,$fot(X_48))]]) ).
cnf(refute_0_263,plain,
least_upper_bound(X_48,negative_part(X_47)) = least_upper_bound(negative_part(X_47),X_48),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_48)),bind(Y,$fot(negative_part(X_47)))]]) ).
cnf(refute_0_264,plain,
( least_upper_bound(X_48,negative_part(X_47)) != least_upper_bound(negative_part(X_47),X_48)
| least_upper_bound(negative_part(X_47),X_48) = least_upper_bound(X_48,negative_part(X_47)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_48,negative_part(X_47)))),bind(Y0,$fot(least_upper_bound(negative_part(X_47),X_48)))]]) ).
cnf(refute_0_265,plain,
least_upper_bound(negative_part(X_47),X_48) = least_upper_bound(X_48,negative_part(X_47)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_48,negative_part(X_47)),least_upper_bound(negative_part(X_47),X_48)) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
( least_upper_bound(negative_part(X_47),X_48) != least_upper_bound(X_48,negative_part(X_47))
| least_upper_bound(negative_part(X_47),negative_part(X_48)) != negative_part(least_upper_bound(negative_part(X_47),X_48))
| least_upper_bound(negative_part(X_47),negative_part(X_48)) = negative_part(least_upper_bound(X_48,negative_part(X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(X_47),negative_part(X_48)),negative_part(least_upper_bound(negative_part(X_47),X_48))) ),[1,0],$fot(least_upper_bound(X_48,negative_part(X_47)))]]) ).
cnf(refute_0_267,plain,
( least_upper_bound(negative_part(X_47),negative_part(X_48)) != negative_part(least_upper_bound(negative_part(X_47),X_48))
| least_upper_bound(negative_part(X_47),negative_part(X_48)) = negative_part(least_upper_bound(X_48,negative_part(X_47))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_47),X_48),least_upper_bound(X_48,negative_part(X_47))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
least_upper_bound(negative_part(X_47),negative_part(X_48)) = negative_part(least_upper_bound(X_48,negative_part(X_47))),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_47),negative_part(X_48)),negative_part(least_upper_bound(negative_part(X_47),X_48))) )],[refute_0_262,refute_0_267]) ).
cnf(refute_0_269,plain,
( least_upper_bound(negative_part(X_47),negative_part(X_48)) != negative_part(least_upper_bound(X_48,negative_part(X_47)))
| least_upper_bound(negative_part(X_47),negative_part(X_48)) != negative_part(least_upper_bound(negative_part(X_47),X_48))
| negative_part(least_upper_bound(negative_part(X_47),X_48)) = negative_part(least_upper_bound(X_48,negative_part(X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(X_47),negative_part(X_48)),negative_part(least_upper_bound(X_48,negative_part(X_47)))) ),[0],$fot(negative_part(least_upper_bound(negative_part(X_47),X_48)))]]) ).
cnf(refute_0_270,plain,
( least_upper_bound(negative_part(X_47),negative_part(X_48)) != negative_part(least_upper_bound(X_48,negative_part(X_47)))
| negative_part(least_upper_bound(negative_part(X_47),X_48)) = negative_part(least_upper_bound(X_48,negative_part(X_47))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_47),negative_part(X_48)),negative_part(least_upper_bound(negative_part(X_47),X_48))) )],[refute_0_262,refute_0_269]) ).
cnf(refute_0_271,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(greatest_lower_bound(identity,X_34),X_35),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_272,plain,
negative_part(X_34) = greatest_lower_bound(identity,X_34),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_34))]]) ).
cnf(refute_0_273,plain,
( negative_part(X_34) != greatest_lower_bound(identity,X_34)
| greatest_lower_bound(identity,X_34) = negative_part(X_34) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(X_34))),bind(Y0,$fot(greatest_lower_bound(identity,X_34)))]]) ).
cnf(refute_0_274,plain,
greatest_lower_bound(identity,X_34) = negative_part(X_34),
inference(resolve,[$cnf( $equal(negative_part(X_34),greatest_lower_bound(identity,X_34)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
( greatest_lower_bound(identity,X_34) != negative_part(X_34)
| greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) != greatest_lower_bound(greatest_lower_bound(identity,X_34),X_35)
| greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(negative_part(X_34),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)),greatest_lower_bound(greatest_lower_bound(identity,X_34),X_35)) ),[1,0],$fot(negative_part(X_34))]]) ).
cnf(refute_0_276,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) != greatest_lower_bound(greatest_lower_bound(identity,X_34),X_35)
| greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(negative_part(X_34),X_35) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_34),negative_part(X_34)) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(negative_part(X_34),X_35),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)),greatest_lower_bound(greatest_lower_bound(identity,X_34),X_35)) )],[refute_0_271,refute_0_276]) ).
cnf(refute_0_278,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) = negative_part(greatest_lower_bound(X_34,X_35)),
inference(subst,[],[refute_0_23:[bind(X,$fot(greatest_lower_bound(X_34,X_35)))]]) ).
cnf(refute_0_279,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) != greatest_lower_bound(negative_part(X_34),X_35)
| greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) != negative_part(greatest_lower_bound(X_34,X_35))
| negative_part(greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(negative_part(X_34),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)),greatest_lower_bound(negative_part(X_34),X_35)) ),[0],$fot(negative_part(greatest_lower_bound(X_34,X_35)))]]) ).
cnf(refute_0_280,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)) != greatest_lower_bound(negative_part(X_34),X_35)
| negative_part(greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(negative_part(X_34),X_35) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)),negative_part(greatest_lower_bound(X_34,X_35))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
negative_part(greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(negative_part(X_34),X_35),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_34,X_35)),greatest_lower_bound(negative_part(X_34),X_35)) )],[refute_0_277,refute_0_280]) ).
cnf(refute_0_282,plain,
negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) = greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)),
inference(subst,[],[refute_0_281:[bind(X_34,$fot(positive_part(X_41))),bind(X_35,$fot(least_upper_bound(X_41,X_42)))]]) ).
cnf(refute_0_283,plain,
( greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)) != least_upper_bound(X_41,negative_part(X_42))
| negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) != greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))
| negative_part(least_upper_bound(X_41,negative_part(X_42))) = greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))),greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))) ),[0,0],$fot(least_upper_bound(X_41,negative_part(X_42)))]]) ).
cnf(refute_0_284,plain,
( negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) != greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))
| negative_part(least_upper_bound(X_41,negative_part(X_42))) = greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)),least_upper_bound(X_41,negative_part(X_42))) )],[refute_0_93,refute_0_283]) ).
cnf(refute_0_285,plain,
negative_part(least_upper_bound(X_41,negative_part(X_42))) = greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)),
inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))),greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))) )],[refute_0_282,refute_0_284]) ).
cnf(refute_0_286,plain,
negative_part(greatest_lower_bound(positive_part(X_10),X_37)) = greatest_lower_bound(negative_part(positive_part(X_10)),X_37),
inference(subst,[],[refute_0_281:[bind(X_34,$fot(positive_part(X_10))),bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_287,plain,
greatest_lower_bound(identity,positive_part(X_10)) = greatest_lower_bound(positive_part(X_10),identity),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(positive_part(X_10)))]]) ).
cnf(refute_0_288,plain,
greatest_lower_bound(identity,least_upper_bound(identity,X_10)) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_289,plain,
positive_part(X_10) = least_upper_bound(identity,X_10),
inference(subst,[],[refute_0_56:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_290,plain,
( positive_part(X_10) != least_upper_bound(identity,X_10)
| least_upper_bound(identity,X_10) = positive_part(X_10) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(positive_part(X_10))),bind(Y0,$fot(least_upper_bound(identity,X_10)))]]) ).
cnf(refute_0_291,plain,
least_upper_bound(identity,X_10) = positive_part(X_10),
inference(resolve,[$cnf( $equal(positive_part(X_10),least_upper_bound(identity,X_10)) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_10)) != identity
| least_upper_bound(identity,X_10) != positive_part(X_10)
| greatest_lower_bound(identity,positive_part(X_10)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_10)),identity) ),[0,1],$fot(positive_part(X_10))]]) ).
cnf(refute_0_293,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,X_10)) != identity
| greatest_lower_bound(identity,positive_part(X_10)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_10),positive_part(X_10)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
greatest_lower_bound(identity,positive_part(X_10)) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_10)),identity) )],[refute_0_288,refute_0_293]) ).
cnf(refute_0_295,plain,
( greatest_lower_bound(identity,positive_part(X_10)) != greatest_lower_bound(positive_part(X_10),identity)
| greatest_lower_bound(identity,positive_part(X_10)) != identity
| identity = greatest_lower_bound(positive_part(X_10),identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,positive_part(X_10)),greatest_lower_bound(positive_part(X_10),identity)) ),[0],$fot(identity)]]) ).
cnf(refute_0_296,plain,
( greatest_lower_bound(identity,positive_part(X_10)) != greatest_lower_bound(positive_part(X_10),identity)
| identity = greatest_lower_bound(positive_part(X_10),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,positive_part(X_10)),identity) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
identity = greatest_lower_bound(positive_part(X_10),identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,positive_part(X_10)),greatest_lower_bound(positive_part(X_10),identity)) )],[refute_0_287,refute_0_296]) ).
cnf(refute_0_298,plain,
greatest_lower_bound(positive_part(X_10),identity) = negative_part(positive_part(X_10)),
inference(subst,[],[refute_0_76:[bind(X,$fot(positive_part(X_10)))]]) ).
cnf(refute_0_299,plain,
( greatest_lower_bound(positive_part(X_10),identity) != negative_part(positive_part(X_10))
| identity != greatest_lower_bound(positive_part(X_10),identity)
| identity = negative_part(positive_part(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(positive_part(X_10),identity)) ),[1],$fot(negative_part(positive_part(X_10)))]]) ).
cnf(refute_0_300,plain,
( identity != greatest_lower_bound(positive_part(X_10),identity)
| identity = negative_part(positive_part(X_10)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_10),identity),negative_part(positive_part(X_10))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
identity = negative_part(positive_part(X_10)),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(positive_part(X_10),identity)) )],[refute_0_297,refute_0_300]) ).
cnf(refute_0_302,plain,
( identity != negative_part(positive_part(X_10))
| negative_part(positive_part(X_10)) = identity ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(identity)),bind(Y0,$fot(negative_part(positive_part(X_10))))]]) ).
cnf(refute_0_303,plain,
negative_part(positive_part(X_10)) = identity,
inference(resolve,[$cnf( $equal(identity,negative_part(positive_part(X_10))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
( negative_part(greatest_lower_bound(positive_part(X_10),X_37)) != greatest_lower_bound(negative_part(positive_part(X_10)),X_37)
| negative_part(positive_part(X_10)) != identity
| negative_part(greatest_lower_bound(positive_part(X_10),X_37)) = greatest_lower_bound(identity,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_10),X_37)),greatest_lower_bound(negative_part(positive_part(X_10)),X_37)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_305,plain,
( negative_part(greatest_lower_bound(positive_part(X_10),X_37)) != greatest_lower_bound(negative_part(positive_part(X_10)),X_37)
| negative_part(greatest_lower_bound(positive_part(X_10),X_37)) = greatest_lower_bound(identity,X_37) ),
inference(resolve,[$cnf( $equal(negative_part(positive_part(X_10)),identity) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
negative_part(greatest_lower_bound(positive_part(X_10),X_37)) = greatest_lower_bound(identity,X_37),
inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_10),X_37)),greatest_lower_bound(negative_part(positive_part(X_10)),X_37)) )],[refute_0_286,refute_0_305]) ).
cnf(refute_0_307,plain,
greatest_lower_bound(identity,X_37) = negative_part(X_37),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_308,plain,
( greatest_lower_bound(identity,X_37) != negative_part(X_37)
| negative_part(greatest_lower_bound(positive_part(X_10),X_37)) != greatest_lower_bound(identity,X_37)
| negative_part(greatest_lower_bound(positive_part(X_10),X_37)) = negative_part(X_37) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_10),X_37)),greatest_lower_bound(identity,X_37)) ),[1],$fot(negative_part(X_37))]]) ).
cnf(refute_0_309,plain,
( negative_part(greatest_lower_bound(positive_part(X_10),X_37)) != greatest_lower_bound(identity,X_37)
| negative_part(greatest_lower_bound(positive_part(X_10),X_37)) = negative_part(X_37) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_37),negative_part(X_37)) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
negative_part(greatest_lower_bound(positive_part(X_10),X_37)) = negative_part(X_37),
inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_10),X_37)),greatest_lower_bound(identity,X_37)) )],[refute_0_306,refute_0_309]) ).
cnf(refute_0_311,plain,
negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) = negative_part(least_upper_bound(X_41,X_42)),
inference(subst,[],[refute_0_310:[bind(X_10,$fot(X_41)),bind(X_37,$fot(least_upper_bound(X_41,X_42)))]]) ).
cnf(refute_0_312,plain,
( negative_part(greatest_lower_bound(X_34,X_35)) != greatest_lower_bound(negative_part(X_34),X_35)
| greatest_lower_bound(negative_part(X_34),X_35) = negative_part(greatest_lower_bound(X_34,X_35)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(greatest_lower_bound(X_34,X_35)))),bind(Y0,$fot(greatest_lower_bound(negative_part(X_34),X_35)))]]) ).
cnf(refute_0_313,plain,
greatest_lower_bound(negative_part(X_34),X_35) = negative_part(greatest_lower_bound(X_34,X_35)),
inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_34,X_35)),greatest_lower_bound(negative_part(X_34),X_35)) )],[refute_0_281,refute_0_312]) ).
cnf(refute_0_314,plain,
greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) = negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))),
inference(subst,[],[refute_0_313:[bind(X_34,$fot(positive_part(X_41))),bind(X_35,$fot(least_upper_bound(X_41,X_42)))]]) ).
cnf(refute_0_315,plain,
( greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) != negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)))
| negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) != negative_part(least_upper_bound(X_41,X_42))
| greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) = negative_part(least_upper_bound(X_41,X_42)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)))),bind(Y0,$fot(negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))))),bind(Z0,$fot(negative_part(least_upper_bound(X_41,X_42))))]]) ).
cnf(refute_0_316,plain,
( negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))) != negative_part(least_upper_bound(X_41,X_42))
| greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) = negative_part(least_upper_bound(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)),negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42)))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) = negative_part(least_upper_bound(X_41,X_42)),
inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_41),least_upper_bound(X_41,X_42))),negative_part(least_upper_bound(X_41,X_42))) )],[refute_0_311,refute_0_316]) ).
cnf(refute_0_318,plain,
( greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)) != negative_part(least_upper_bound(X_41,X_42))
| negative_part(least_upper_bound(X_41,negative_part(X_42))) != greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))
| negative_part(least_upper_bound(X_41,negative_part(X_42))) = negative_part(least_upper_bound(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(X_41,negative_part(X_42))),greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))) ),[1],$fot(negative_part(least_upper_bound(X_41,X_42)))]]) ).
cnf(refute_0_319,plain,
( negative_part(least_upper_bound(X_41,negative_part(X_42))) != greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))
| negative_part(least_upper_bound(X_41,negative_part(X_42))) = negative_part(least_upper_bound(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42)),negative_part(least_upper_bound(X_41,X_42))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
negative_part(least_upper_bound(X_41,negative_part(X_42))) = negative_part(least_upper_bound(X_41,X_42)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_41,negative_part(X_42))),greatest_lower_bound(negative_part(positive_part(X_41)),least_upper_bound(X_41,X_42))) )],[refute_0_285,refute_0_319]) ).
cnf(refute_0_321,plain,
negative_part(least_upper_bound(X_48,negative_part(X_47))) = negative_part(least_upper_bound(X_48,X_47)),
inference(subst,[],[refute_0_320:[bind(X_41,$fot(X_48)),bind(X_42,$fot(X_47))]]) ).
cnf(refute_0_322,plain,
( negative_part(least_upper_bound(X_48,negative_part(X_47))) != negative_part(least_upper_bound(X_48,X_47))
| negative_part(least_upper_bound(negative_part(X_47),X_48)) != negative_part(least_upper_bound(X_48,negative_part(X_47)))
| negative_part(least_upper_bound(negative_part(X_47),X_48)) = negative_part(least_upper_bound(X_48,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_47),X_48)),negative_part(least_upper_bound(X_48,negative_part(X_47)))) ),[1],$fot(negative_part(least_upper_bound(X_48,X_47)))]]) ).
cnf(refute_0_323,plain,
( negative_part(least_upper_bound(negative_part(X_47),X_48)) != negative_part(least_upper_bound(X_48,negative_part(X_47)))
| negative_part(least_upper_bound(negative_part(X_47),X_48)) = negative_part(least_upper_bound(X_48,X_47)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_48,negative_part(X_47))),negative_part(least_upper_bound(X_48,X_47))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
( least_upper_bound(negative_part(X_47),negative_part(X_48)) != negative_part(least_upper_bound(X_48,negative_part(X_47)))
| negative_part(least_upper_bound(negative_part(X_47),X_48)) = negative_part(least_upper_bound(X_48,X_47)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_47),X_48)),negative_part(least_upper_bound(X_48,negative_part(X_47)))) )],[refute_0_270,refute_0_323]) ).
cnf(refute_0_325,plain,
negative_part(least_upper_bound(negative_part(X_47),X_48)) = negative_part(least_upper_bound(X_48,X_47)),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_47),negative_part(X_48)),negative_part(least_upper_bound(X_48,negative_part(X_47)))) )],[refute_0_268,refute_0_324]) ).
cnf(refute_0_326,plain,
negative_part(least_upper_bound(negative_part(X_18),X_42)) = negative_part(least_upper_bound(X_42,X_18)),
inference(subst,[],[refute_0_325:[bind(X_47,$fot(X_18)),bind(X_48,$fot(X_42))]]) ).
cnf(refute_0_327,plain,
( least_upper_bound(negative_part(X_18),negative_part(X_42)) != negative_part(least_upper_bound(negative_part(X_18),X_42))
| negative_part(least_upper_bound(negative_part(X_18),X_42)) != negative_part(least_upper_bound(X_42,X_18))
| least_upper_bound(negative_part(X_18),negative_part(X_42)) = negative_part(least_upper_bound(X_42,X_18)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(negative_part(X_18),negative_part(X_42)),negative_part(least_upper_bound(X_42,X_18))) ),[0],$fot(negative_part(least_upper_bound(negative_part(X_18),X_42)))]]) ).
cnf(refute_0_328,plain,
( least_upper_bound(negative_part(X_18),negative_part(X_42)) != negative_part(least_upper_bound(negative_part(X_18),X_42))
| least_upper_bound(negative_part(X_18),negative_part(X_42)) = negative_part(least_upper_bound(X_42,X_18)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_18),X_42)),negative_part(least_upper_bound(X_42,X_18))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
least_upper_bound(negative_part(X_18),negative_part(X_42)) = negative_part(least_upper_bound(X_42,X_18)),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_18),negative_part(X_42)),negative_part(least_upper_bound(negative_part(X_18),X_42))) )],[refute_0_261,refute_0_328]) ).
cnf(refute_0_330,plain,
least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175)) = negative_part(least_upper_bound(X_175,inverse(X_175))),
inference(subst,[],[refute_0_329:[bind(X_18,$fot(inverse(X_175))),bind(X_42,$fot(X_175))]]) ).
cnf(refute_0_331,plain,
( multiply(negative_part(inverse(X_175)),positive_part(X_175)) != least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175))
| least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175)) != negative_part(least_upper_bound(X_175,inverse(X_175)))
| multiply(negative_part(inverse(X_175)),positive_part(X_175)) = negative_part(least_upper_bound(X_175,inverse(X_175))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(inverse(X_175)),positive_part(X_175)),negative_part(least_upper_bound(X_175,inverse(X_175)))) ),[0],$fot(least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175)))]]) ).
cnf(refute_0_332,plain,
( multiply(negative_part(inverse(X_175)),positive_part(X_175)) != least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175))
| multiply(negative_part(inverse(X_175)),positive_part(X_175)) = negative_part(least_upper_bound(X_175,inverse(X_175))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175)),negative_part(least_upper_bound(X_175,inverse(X_175)))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
multiply(negative_part(inverse(X_175)),positive_part(X_175)) = negative_part(least_upper_bound(X_175,inverse(X_175))),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_175)),positive_part(X_175)),least_upper_bound(negative_part(inverse(X_175)),negative_part(X_175))) )],[refute_0_240,refute_0_332]) ).
cnf(refute_0_334,plain,
multiply(negative_part(inverse(X_332)),positive_part(X_332)) = negative_part(least_upper_bound(X_332,inverse(X_332))),
inference(subst,[],[refute_0_333:[bind(X_175,$fot(X_332))]]) ).
cnf(refute_0_335,plain,
( multiply(negative_part(inverse(X_332)),positive_part(X_332)) != negative_part(least_upper_bound(X_332,inverse(X_332)))
| positive_part(X_332) != multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(multiply(negative_part(inverse(X_332)),positive_part(X_332))))
| positive_part(X_332) = multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(X_332),multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(multiply(negative_part(inverse(X_332)),positive_part(X_332))))) ),[1,1,0],$fot(negative_part(least_upper_bound(X_332,inverse(X_332))))]]) ).
cnf(refute_0_336,plain,
( positive_part(X_332) != multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(multiply(negative_part(inverse(X_332)),positive_part(X_332))))
| positive_part(X_332) = multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_332)),positive_part(X_332)),negative_part(least_upper_bound(X_332,inverse(X_332)))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
positive_part(X_332) = multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),
inference(resolve,[$cnf( $equal(positive_part(X_332),multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(multiply(negative_part(inverse(X_332)),positive_part(X_332))))) )],[refute_0_196,refute_0_336]) ).
cnf(refute_0_338,plain,
( X_61 != multiply(X_61,identity)
| multiply(X_61,identity) = X_61 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_61)),bind(Y0,$fot(multiply(X_61,identity)))]]) ).
cnf(refute_0_339,plain,
multiply(X_61,identity) = X_61,
inference(resolve,[$cnf( $equal(X_61,multiply(X_61,identity)) )],[refute_0_215,refute_0_338]) ).
cnf(refute_0_340,plain,
multiply(inverse(negative_part(inverse(X_332))),identity) = inverse(negative_part(inverse(X_332))),
inference(subst,[],[refute_0_339:[bind(X_61,$fot(inverse(negative_part(inverse(X_332)))))]]) ).
cnf(refute_0_341,plain,
positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))) = identity,
inference(subst,[],[refute_0_254:[bind(X_18,$fot(least_upper_bound(X_332,inverse(X_332))))]]) ).
cnf(refute_0_342,plain,
multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),
introduced(tautology,[refl,[$fot(multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))))]]) ).
cnf(refute_0_343,plain,
( multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) != multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))
| positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))) != identity
| multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_344,plain,
( positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))) != identity
| multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),identity),
inference(resolve,[$cnf( $equal(positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))),identity) )],[refute_0_341,refute_0_344]) ).
cnf(refute_0_346,plain,
multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = least_upper_bound(inverse(positive_part(X_320)),multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320)))),
inference(subst,[],[refute_0_235:[bind(X_96,$fot(inverse(positive_part(X_320)))),bind(X_97,$fot(positive_part(inverse(X_320))))]]) ).
cnf(refute_0_347,plain,
X_61 = multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_61)),
inference(subst,[],[refute_0_8:[bind(X_58,$fot(multiply(X,Y))),bind(X_59,$fot(X_61))]]) ).
cnf(refute_0_348,plain,
multiply(multiply(X,Y),X_61) = multiply(X,multiply(Y,X_61)),
inference(subst,[],[associativity:[bind(Z,$fot(X_61))]]) ).
cnf(refute_0_349,plain,
( X_61 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_61))
| multiply(multiply(X,Y),X_61) != multiply(X,multiply(Y,X_61))
| X_61 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(X_61,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_61))) ),[1,1],$fot(multiply(X,multiply(Y,X_61)))]]) ).
cnf(refute_0_350,plain,
( X_61 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_61))
| X_61 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_61))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_61),multiply(X,multiply(Y,X_61))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
X_61 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_61))),
inference(resolve,[$cnf( $equal(X_61,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_61))) )],[refute_0_347,refute_0_350]) ).
cnf(refute_0_352,plain,
inverse(X_70) = multiply(inverse(multiply(X_69,X_70)),multiply(X_69,multiply(X_70,inverse(X_70)))),
inference(subst,[],[refute_0_351:[bind(X,$fot(X_69)),bind(Y,$fot(X_70)),bind(X_61,$fot(inverse(X_70)))]]) ).
cnf(refute_0_353,plain,
multiply(inverse(inverse(X_63)),inverse(X_63)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_63)))]]) ).
cnf(refute_0_354,plain,
multiply(X_63,inverse(X_63)) = multiply(inverse(inverse(X_63)),inverse(X_63)),
inference(subst,[],[refute_0_209:[bind(X_60,$fot(X_63)),bind(X_61,$fot(inverse(X_63)))]]) ).
cnf(refute_0_355,plain,
( multiply(X_63,inverse(X_63)) != multiply(inverse(inverse(X_63)),inverse(X_63))
| multiply(inverse(inverse(X_63)),inverse(X_63)) = multiply(X_63,inverse(X_63)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_63,inverse(X_63)))),bind(Y0,$fot(multiply(inverse(inverse(X_63)),inverse(X_63))))]]) ).
cnf(refute_0_356,plain,
multiply(inverse(inverse(X_63)),inverse(X_63)) = multiply(X_63,inverse(X_63)),
inference(resolve,[$cnf( $equal(multiply(X_63,inverse(X_63)),multiply(inverse(inverse(X_63)),inverse(X_63))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
( multiply(inverse(inverse(X_63)),inverse(X_63)) != multiply(X_63,inverse(X_63))
| multiply(inverse(inverse(X_63)),inverse(X_63)) != identity
| multiply(X_63,inverse(X_63)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_63)),inverse(X_63)),identity) ),[0],$fot(multiply(X_63,inverse(X_63)))]]) ).
cnf(refute_0_358,plain,
( multiply(inverse(inverse(X_63)),inverse(X_63)) != identity
| multiply(X_63,inverse(X_63)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_63)),inverse(X_63)),multiply(X_63,inverse(X_63))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
multiply(X_63,inverse(X_63)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_63)),inverse(X_63)),identity) )],[refute_0_353,refute_0_358]) ).
cnf(refute_0_360,plain,
multiply(X_70,inverse(X_70)) = identity,
inference(subst,[],[refute_0_359:[bind(X_63,$fot(X_70))]]) ).
cnf(refute_0_361,plain,
( multiply(X_70,inverse(X_70)) != identity
| inverse(X_70) != multiply(inverse(multiply(X_69,X_70)),multiply(X_69,multiply(X_70,inverse(X_70))))
| inverse(X_70) = multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(X_69,X_70)),multiply(X_69,multiply(X_70,inverse(X_70))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_362,plain,
( inverse(X_70) != multiply(inverse(multiply(X_69,X_70)),multiply(X_69,multiply(X_70,inverse(X_70))))
| inverse(X_70) = multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_70,inverse(X_70)),identity) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
inverse(X_70) = multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)),
inference(resolve,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(X_69,X_70)),multiply(X_69,multiply(X_70,inverse(X_70))))) )],[refute_0_352,refute_0_362]) ).
cnf(refute_0_364,plain,
multiply(X_69,identity) = X_69,
inference(subst,[],[refute_0_339:[bind(X_61,$fot(X_69))]]) ).
cnf(refute_0_365,plain,
multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) = multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)))]]) ).
cnf(refute_0_366,plain,
( multiply(X_69,identity) != X_69
| multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) != multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity))
| multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) = multiply(inverse(multiply(X_69,X_70)),X_69) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)),multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity))) ),[1,1],$fot(X_69)]]) ).
cnf(refute_0_367,plain,
( multiply(X_69,identity) != X_69
| multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) = multiply(inverse(multiply(X_69,X_70)),X_69) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)),multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) = multiply(inverse(multiply(X_69,X_70)),X_69),
inference(resolve,[$cnf( $equal(multiply(X_69,identity),X_69) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
( multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)) != multiply(inverse(multiply(X_69,X_70)),X_69)
| inverse(X_70) != multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity))
| inverse(X_70) = multiply(inverse(multiply(X_69,X_70)),X_69) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity))) ),[1],$fot(multiply(inverse(multiply(X_69,X_70)),X_69))]]) ).
cnf(refute_0_370,plain,
( inverse(X_70) != multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity))
| inverse(X_70) = multiply(inverse(multiply(X_69,X_70)),X_69) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity)),multiply(inverse(multiply(X_69,X_70)),X_69)) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
inverse(X_70) = multiply(inverse(multiply(X_69,X_70)),X_69),
inference(resolve,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(X_69,X_70)),multiply(X_69,identity))) )],[refute_0_363,refute_0_370]) ).
cnf(refute_0_372,plain,
inverse(X_70) = multiply(inverse(multiply(positive_part(inverse(X_70)),X_70)),positive_part(inverse(X_70))),
inference(subst,[],[refute_0_371:[bind(X_69,$fot(positive_part(inverse(X_70))))]]) ).
cnf(refute_0_373,plain,
multiply(least_upper_bound(X_141,identity),X_140) = least_upper_bound(multiply(X_141,X_140),multiply(identity,X_140)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_140)),bind(Y,$fot(X_141)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_374,plain,
multiply(identity,X_140) = X_140,
inference(subst,[],[left_identity:[bind(X,$fot(X_140))]]) ).
cnf(refute_0_375,plain,
( multiply(identity,X_140) != X_140
| multiply(least_upper_bound(X_141,identity),X_140) != least_upper_bound(multiply(X_141,X_140),multiply(identity,X_140))
| multiply(least_upper_bound(X_141,identity),X_140) = least_upper_bound(multiply(X_141,X_140),X_140) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_141,identity),X_140),least_upper_bound(multiply(X_141,X_140),multiply(identity,X_140))) ),[1,1],$fot(X_140)]]) ).
cnf(refute_0_376,plain,
( multiply(least_upper_bound(X_141,identity),X_140) != least_upper_bound(multiply(X_141,X_140),multiply(identity,X_140))
| multiply(least_upper_bound(X_141,identity),X_140) = least_upper_bound(multiply(X_141,X_140),X_140) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_140),X_140) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
multiply(least_upper_bound(X_141,identity),X_140) = least_upper_bound(multiply(X_141,X_140),X_140),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_141,identity),X_140),least_upper_bound(multiply(X_141,X_140),multiply(identity,X_140))) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
least_upper_bound(X_141,identity) = positive_part(X_141),
inference(subst,[],[refute_0_223:[bind(X,$fot(X_141))]]) ).
cnf(refute_0_379,plain,
multiply(least_upper_bound(X_141,identity),X_140) = multiply(least_upper_bound(X_141,identity),X_140),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_141,identity),X_140))]]) ).
cnf(refute_0_380,plain,
( multiply(least_upper_bound(X_141,identity),X_140) != multiply(least_upper_bound(X_141,identity),X_140)
| least_upper_bound(X_141,identity) != positive_part(X_141)
| multiply(least_upper_bound(X_141,identity),X_140) = multiply(positive_part(X_141),X_140) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_141,identity),X_140),multiply(least_upper_bound(X_141,identity),X_140)) ),[1,0],$fot(positive_part(X_141))]]) ).
cnf(refute_0_381,plain,
( least_upper_bound(X_141,identity) != positive_part(X_141)
| multiply(least_upper_bound(X_141,identity),X_140) = multiply(positive_part(X_141),X_140) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_141,identity),X_140),multiply(least_upper_bound(X_141,identity),X_140)) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
multiply(least_upper_bound(X_141,identity),X_140) = multiply(positive_part(X_141),X_140),
inference(resolve,[$cnf( $equal(least_upper_bound(X_141,identity),positive_part(X_141)) )],[refute_0_378,refute_0_381]) ).
cnf(refute_0_383,plain,
( multiply(least_upper_bound(X_141,identity),X_140) != multiply(positive_part(X_141),X_140)
| multiply(least_upper_bound(X_141,identity),X_140) != least_upper_bound(multiply(X_141,X_140),X_140)
| multiply(positive_part(X_141),X_140) = least_upper_bound(multiply(X_141,X_140),X_140) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_141,identity),X_140),least_upper_bound(multiply(X_141,X_140),X_140)) ),[0],$fot(multiply(positive_part(X_141),X_140))]]) ).
cnf(refute_0_384,plain,
( multiply(least_upper_bound(X_141,identity),X_140) != least_upper_bound(multiply(X_141,X_140),X_140)
| multiply(positive_part(X_141),X_140) = least_upper_bound(multiply(X_141,X_140),X_140) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_141,identity),X_140),multiply(positive_part(X_141),X_140)) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
least_upper_bound(multiply(X_141,X_140),X_140) = least_upper_bound(X_140,multiply(X_141,X_140)),
inference(subst,[],[refute_0_184:[bind(X_41,$fot(multiply(X_141,X_140))),bind(X_42,$fot(X_140))]]) ).
cnf(refute_0_386,plain,
( multiply(positive_part(X_141),X_140) != least_upper_bound(multiply(X_141,X_140),X_140)
| least_upper_bound(multiply(X_141,X_140),X_140) != least_upper_bound(X_140,multiply(X_141,X_140))
| multiply(positive_part(X_141),X_140) = least_upper_bound(X_140,multiply(X_141,X_140)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(X_141),X_140),least_upper_bound(X_140,multiply(X_141,X_140))) ),[0],$fot(least_upper_bound(multiply(X_141,X_140),X_140))]]) ).
cnf(refute_0_387,plain,
( multiply(positive_part(X_141),X_140) != least_upper_bound(multiply(X_141,X_140),X_140)
| multiply(positive_part(X_141),X_140) = least_upper_bound(X_140,multiply(X_141,X_140)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_141,X_140),X_140),least_upper_bound(X_140,multiply(X_141,X_140))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
( multiply(least_upper_bound(X_141,identity),X_140) != least_upper_bound(multiply(X_141,X_140),X_140)
| multiply(positive_part(X_141),X_140) = least_upper_bound(X_140,multiply(X_141,X_140)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_141),X_140),least_upper_bound(multiply(X_141,X_140),X_140)) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
multiply(positive_part(X_141),X_140) = least_upper_bound(X_140,multiply(X_141,X_140)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_141,identity),X_140),least_upper_bound(multiply(X_141,X_140),X_140)) )],[refute_0_377,refute_0_388]) ).
cnf(refute_0_390,plain,
multiply(positive_part(inverse(X_143)),X_143) = least_upper_bound(X_143,multiply(inverse(X_143),X_143)),
inference(subst,[],[refute_0_389:[bind(X_140,$fot(X_143)),bind(X_141,$fot(inverse(X_143)))]]) ).
cnf(refute_0_391,plain,
multiply(inverse(X_143),X_143) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_143))]]) ).
cnf(refute_0_392,plain,
( multiply(inverse(X_143),X_143) != identity
| multiply(positive_part(inverse(X_143)),X_143) != least_upper_bound(X_143,multiply(inverse(X_143),X_143))
| multiply(positive_part(inverse(X_143)),X_143) = least_upper_bound(X_143,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X_143)),X_143),least_upper_bound(X_143,multiply(inverse(X_143),X_143))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_393,plain,
( multiply(positive_part(inverse(X_143)),X_143) != least_upper_bound(X_143,multiply(inverse(X_143),X_143))
| multiply(positive_part(inverse(X_143)),X_143) = least_upper_bound(X_143,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_143),X_143),identity) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
multiply(positive_part(inverse(X_143)),X_143) = least_upper_bound(X_143,identity),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_143)),X_143),least_upper_bound(X_143,multiply(inverse(X_143),X_143))) )],[refute_0_390,refute_0_393]) ).
cnf(refute_0_395,plain,
least_upper_bound(X_143,identity) = positive_part(X_143),
inference(subst,[],[refute_0_223:[bind(X,$fot(X_143))]]) ).
cnf(refute_0_396,plain,
( multiply(positive_part(inverse(X_143)),X_143) != least_upper_bound(X_143,identity)
| least_upper_bound(X_143,identity) != positive_part(X_143)
| multiply(positive_part(inverse(X_143)),X_143) = positive_part(X_143) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(inverse(X_143)),X_143),positive_part(X_143)) ),[0],$fot(least_upper_bound(X_143,identity))]]) ).
cnf(refute_0_397,plain,
( multiply(positive_part(inverse(X_143)),X_143) != least_upper_bound(X_143,identity)
| multiply(positive_part(inverse(X_143)),X_143) = positive_part(X_143) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_143,identity),positive_part(X_143)) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
multiply(positive_part(inverse(X_143)),X_143) = positive_part(X_143),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_143)),X_143),least_upper_bound(X_143,identity)) )],[refute_0_394,refute_0_397]) ).
cnf(refute_0_399,plain,
multiply(positive_part(inverse(X_70)),X_70) = positive_part(X_70),
inference(subst,[],[refute_0_398:[bind(X_143,$fot(X_70))]]) ).
cnf(refute_0_400,plain,
( multiply(positive_part(inverse(X_70)),X_70) != positive_part(X_70)
| inverse(X_70) != multiply(inverse(multiply(positive_part(inverse(X_70)),X_70)),positive_part(inverse(X_70)))
| inverse(X_70) = multiply(inverse(positive_part(X_70)),positive_part(inverse(X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(positive_part(inverse(X_70)),X_70)),positive_part(inverse(X_70)))) ),[1,0,0],$fot(positive_part(X_70))]]) ).
cnf(refute_0_401,plain,
( inverse(X_70) != multiply(inverse(multiply(positive_part(inverse(X_70)),X_70)),positive_part(inverse(X_70)))
| inverse(X_70) = multiply(inverse(positive_part(X_70)),positive_part(inverse(X_70))) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_70)),X_70),positive_part(X_70)) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
inverse(X_70) = multiply(inverse(positive_part(X_70)),positive_part(inverse(X_70))),
inference(resolve,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(positive_part(inverse(X_70)),X_70)),positive_part(inverse(X_70)))) )],[refute_0_372,refute_0_401]) ).
cnf(refute_0_403,plain,
inverse(X_320) = multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))),
inference(subst,[],[refute_0_402:[bind(X_70,$fot(X_320))]]) ).
cnf(refute_0_404,plain,
( inverse(X_320) != multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320)))
| multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))) = inverse(X_320) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(X_320))),bind(Y0,$fot(multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320)))))]]) ).
cnf(refute_0_405,plain,
multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))) = inverse(X_320),
inference(resolve,[$cnf( $equal(inverse(X_320),multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320)))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
( multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))) != inverse(X_320)
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != least_upper_bound(inverse(positive_part(X_320)),multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))))
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),least_upper_bound(inverse(positive_part(X_320)),multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))))) ),[1,1],$fot(inverse(X_320))]]) ).
cnf(refute_0_407,plain,
( multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != least_upper_bound(inverse(positive_part(X_320)),multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))))
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))),inverse(X_320)) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),least_upper_bound(inverse(positive_part(X_320)),multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))))) )],[refute_0_346,refute_0_407]) ).
cnf(refute_0_409,plain,
least_upper_bound(positive_part(X_10),negative_part(positive_part(X_10))) = positive_part(X_10),
inference(subst,[],[refute_0_109:[bind(X_17,$fot(positive_part(X_10)))]]) ).
cnf(refute_0_410,plain,
( least_upper_bound(positive_part(X_10),negative_part(positive_part(X_10))) != positive_part(X_10)
| negative_part(positive_part(X_10)) != identity
| least_upper_bound(positive_part(X_10),identity) = positive_part(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(positive_part(X_10),negative_part(positive_part(X_10))),positive_part(X_10)) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_411,plain,
( least_upper_bound(positive_part(X_10),negative_part(positive_part(X_10))) != positive_part(X_10)
| least_upper_bound(positive_part(X_10),identity) = positive_part(X_10) ),
inference(resolve,[$cnf( $equal(negative_part(positive_part(X_10)),identity) )],[refute_0_303,refute_0_410]) ).
cnf(refute_0_412,plain,
least_upper_bound(positive_part(X_10),identity) = positive_part(X_10),
inference(resolve,[$cnf( $equal(least_upper_bound(positive_part(X_10),negative_part(positive_part(X_10))),positive_part(X_10)) )],[refute_0_409,refute_0_411]) ).
cnf(refute_0_413,plain,
least_upper_bound(positive_part(X_10),identity) = positive_part(positive_part(X_10)),
inference(subst,[],[refute_0_223:[bind(X,$fot(positive_part(X_10)))]]) ).
cnf(refute_0_414,plain,
( least_upper_bound(positive_part(X_10),identity) != positive_part(X_10)
| least_upper_bound(positive_part(X_10),identity) != positive_part(positive_part(X_10))
| positive_part(positive_part(X_10)) = positive_part(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(positive_part(X_10),identity),positive_part(X_10)) ),[0],$fot(positive_part(positive_part(X_10)))]]) ).
cnf(refute_0_415,plain,
( least_upper_bound(positive_part(X_10),identity) != positive_part(X_10)
| positive_part(positive_part(X_10)) = positive_part(X_10) ),
inference(resolve,[$cnf( $equal(least_upper_bound(positive_part(X_10),identity),positive_part(positive_part(X_10))) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
positive_part(positive_part(X_10)) = positive_part(X_10),
inference(resolve,[$cnf( $equal(least_upper_bound(positive_part(X_10),identity),positive_part(X_10)) )],[refute_0_412,refute_0_415]) ).
cnf(refute_0_417,plain,
positive_part(positive_part(inverse(X_320))) = positive_part(inverse(X_320)),
inference(subst,[],[refute_0_416:[bind(X_10,$fot(inverse(X_320)))]]) ).
cnf(refute_0_418,plain,
multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),
introduced(tautology,[refl,[$fot(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))))]]) ).
cnf(refute_0_419,plain,
( multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320))))
| positive_part(positive_part(inverse(X_320))) != positive_part(inverse(X_320))
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320))))) ),[1,1],$fot(positive_part(inverse(X_320)))]]) ).
cnf(refute_0_420,plain,
( positive_part(positive_part(inverse(X_320))) != positive_part(inverse(X_320))
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320))))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))),
inference(resolve,[$cnf( $equal(positive_part(positive_part(inverse(X_320))),positive_part(inverse(X_320))) )],[refute_0_417,refute_0_420]) ).
cnf(refute_0_422,plain,
( multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))) != inverse(X_320)
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320)))
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = inverse(X_320) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))))),bind(Y0,$fot(multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))))),bind(Z0,$fot(inverse(X_320)))]]) ).
cnf(refute_0_423,plain,
( multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))) != inverse(X_320)
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = inverse(X_320) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320)))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) = inverse(X_320),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(inverse(X_320))),inverse(X_320)) )],[refute_0_405,refute_0_423]) ).
cnf(refute_0_425,plain,
( multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != inverse(X_320)
| multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))
| inverse(X_320) = least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))) ),[0],$fot(inverse(X_320))]]) ).
cnf(refute_0_426,plain,
( multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))
| inverse(X_320) = least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),inverse(X_320)) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)) = least_upper_bound(inverse(X_320),inverse(positive_part(X_320))),
inference(subst,[],[refute_0_184:[bind(X_41,$fot(inverse(positive_part(X_320)))),bind(X_42,$fot(inverse(X_320)))]]) ).
cnf(refute_0_428,plain,
( inverse(X_320) != least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))
| least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)) != least_upper_bound(inverse(X_320),inverse(positive_part(X_320)))
| inverse(X_320) = least_upper_bound(inverse(X_320),inverse(positive_part(X_320))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(X_320),least_upper_bound(inverse(X_320),inverse(positive_part(X_320)))) ),[0],$fot(least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)))]]) ).
cnf(refute_0_429,plain,
( inverse(X_320) != least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))
| inverse(X_320) = least_upper_bound(inverse(X_320),inverse(positive_part(X_320))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_320)),inverse(X_320)),least_upper_bound(inverse(X_320),inverse(positive_part(X_320)))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
( multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))) != least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))
| inverse(X_320) = least_upper_bound(inverse(X_320),inverse(positive_part(X_320))) ),
inference(resolve,[$cnf( $equal(inverse(X_320),least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))) )],[refute_0_426,refute_0_429]) ).
cnf(refute_0_431,plain,
inverse(X_320) = least_upper_bound(inverse(X_320),inverse(positive_part(X_320))),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_320)),positive_part(positive_part(inverse(X_320)))),least_upper_bound(inverse(positive_part(X_320)),inverse(X_320))) )],[refute_0_408,refute_0_430]) ).
cnf(refute_0_432,plain,
( inverse(X_320) != least_upper_bound(inverse(X_320),inverse(positive_part(X_320)))
| least_upper_bound(inverse(X_320),inverse(positive_part(X_320))) = inverse(X_320) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(X_320))),bind(Y0,$fot(least_upper_bound(inverse(X_320),inverse(positive_part(X_320)))))]]) ).
cnf(refute_0_433,plain,
least_upper_bound(inverse(X_320),inverse(positive_part(X_320))) = inverse(X_320),
inference(resolve,[$cnf( $equal(inverse(X_320),least_upper_bound(inverse(X_320),inverse(positive_part(X_320)))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
least_upper_bound(inverse(X_332),inverse(positive_part(X_332))) = inverse(X_332),
inference(subst,[],[refute_0_433:[bind(X_320,$fot(X_332))]]) ).
cnf(refute_0_435,plain,
negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) = negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))),
introduced(tautology,[refl,[$fot(negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))))]]) ).
cnf(refute_0_436,plain,
( least_upper_bound(inverse(X_332),inverse(positive_part(X_332))) != inverse(X_332)
| negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) != negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))
| negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) = negative_part(inverse(X_332)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))),negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))) ),[1,0],$fot(inverse(X_332))]]) ).
cnf(refute_0_437,plain,
( least_upper_bound(inverse(X_332),inverse(positive_part(X_332))) != inverse(X_332)
| negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) = negative_part(inverse(X_332)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))),negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) = negative_part(inverse(X_332)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))),inverse(X_332)) )],[refute_0_434,refute_0_437]) ).
cnf(refute_0_439,plain,
negative_part(least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258))) = negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)),
inference(subst,[],[refute_0_325:[bind(X_48,$fot(least_upper_bound(negative_part(X_47),X_258)))]]) ).
cnf(refute_0_440,plain,
least_upper_bound(X_32,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,X_31),
inference(subst,[],[refute_0_126:[bind(Y,$fot(X_31)),bind(X_27,$fot(X_32))]]) ).
cnf(refute_0_441,plain,
least_upper_bound(X_32,X_31) = least_upper_bound(X_31,X_32),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_32)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_442,plain,
( least_upper_bound(X_32,X_31) != least_upper_bound(X_31,X_32)
| least_upper_bound(X_31,X_32) = least_upper_bound(X_32,X_31) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_32,X_31))),bind(Y0,$fot(least_upper_bound(X_31,X_32)))]]) ).
cnf(refute_0_443,plain,
least_upper_bound(X_31,X_32) = least_upper_bound(X_32,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,X_31),least_upper_bound(X_31,X_32)) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
( least_upper_bound(X_31,X_32) != least_upper_bound(X_32,X_31)
| least_upper_bound(X_32,least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,X_31)
| least_upper_bound(X_32,least_upper_bound(X_32,X_31)) = least_upper_bound(X_32,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_31,X_32)),least_upper_bound(X_32,X_31)) ),[0,1],$fot(least_upper_bound(X_32,X_31))]]) ).
cnf(refute_0_445,plain,
( least_upper_bound(X_32,least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,X_31)
| least_upper_bound(X_32,least_upper_bound(X_32,X_31)) = least_upper_bound(X_32,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_31,X_32),least_upper_bound(X_32,X_31)) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
least_upper_bound(X_32,least_upper_bound(X_32,X_31)) = least_upper_bound(X_32,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_31,X_32)),least_upper_bound(X_32,X_31)) )],[refute_0_440,refute_0_445]) ).
cnf(refute_0_447,plain,
least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258)) = least_upper_bound(negative_part(X_47),X_258),
inference(subst,[],[refute_0_446:[bind(X_31,$fot(X_258)),bind(X_32,$fot(negative_part(X_47)))]]) ).
cnf(refute_0_448,plain,
( least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258)) != least_upper_bound(negative_part(X_47),X_258)
| negative_part(least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258))) != negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))
| negative_part(least_upper_bound(negative_part(X_47),X_258)) = negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258))),negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))) ),[0,0],$fot(least_upper_bound(negative_part(X_47),X_258))]]) ).
cnf(refute_0_449,plain,
( negative_part(least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258))) != negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))
| negative_part(least_upper_bound(negative_part(X_47),X_258)) = negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258)),least_upper_bound(negative_part(X_47),X_258)) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
negative_part(least_upper_bound(negative_part(X_47),X_258)) = negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_47),least_upper_bound(negative_part(X_47),X_258))),negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))) )],[refute_0_439,refute_0_449]) ).
cnf(refute_0_451,plain,
negative_part(least_upper_bound(negative_part(X_47),X_258)) = negative_part(least_upper_bound(X_258,X_47)),
inference(subst,[],[refute_0_325:[bind(X_48,$fot(X_258))]]) ).
cnf(refute_0_452,plain,
( negative_part(least_upper_bound(negative_part(X_47),X_258)) != negative_part(least_upper_bound(X_258,X_47))
| negative_part(least_upper_bound(negative_part(X_47),X_258)) != negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))
| negative_part(least_upper_bound(X_258,X_47)) = negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_47),X_258)),negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))) ),[0],$fot(negative_part(least_upper_bound(X_258,X_47)))]]) ).
cnf(refute_0_453,plain,
( negative_part(least_upper_bound(negative_part(X_47),X_258)) != negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))
| negative_part(least_upper_bound(X_258,X_47)) = negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_47),X_258)),negative_part(least_upper_bound(X_258,X_47))) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
least_upper_bound(X_47,least_upper_bound(X_258,X_47)) = least_upper_bound(X_47,X_258),
inference(subst,[],[refute_0_126:[bind(Y,$fot(X_258)),bind(X_27,$fot(X_47))]]) ).
cnf(refute_0_455,plain,
negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) = negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))),
introduced(tautology,[refl,[$fot(negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))))]]) ).
cnf(refute_0_456,plain,
( least_upper_bound(X_47,least_upper_bound(X_258,X_47)) != least_upper_bound(X_47,X_258)
| negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) != negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))
| negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) = negative_part(least_upper_bound(X_47,X_258)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))),negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))) ),[1,0],$fot(least_upper_bound(X_47,X_258))]]) ).
cnf(refute_0_457,plain,
( least_upper_bound(X_47,least_upper_bound(X_258,X_47)) != least_upper_bound(X_47,X_258)
| negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) = negative_part(least_upper_bound(X_47,X_258)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))),negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) = negative_part(least_upper_bound(X_47,X_258)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_47,least_upper_bound(X_258,X_47)),least_upper_bound(X_47,X_258)) )],[refute_0_454,refute_0_457]) ).
cnf(refute_0_459,plain,
negative_part(least_upper_bound(negative_part(least_upper_bound(negative_part(X_199),X_200)),X_48)) = negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))),
inference(subst,[],[refute_0_325:[bind(X_47,$fot(least_upper_bound(negative_part(X_199),X_200)))]]) ).
cnf(refute_0_460,plain,
negative_part(least_upper_bound(negative_part(X_199),X_200)) = negative_part(least_upper_bound(X_200,X_199)),
inference(subst,[],[refute_0_325:[bind(X_47,$fot(X_199)),bind(X_48,$fot(X_200))]]) ).
cnf(refute_0_461,plain,
( negative_part(least_upper_bound(negative_part(X_199),X_200)) != negative_part(least_upper_bound(X_200,X_199))
| negative_part(least_upper_bound(negative_part(least_upper_bound(negative_part(X_199),X_200)),X_48)) != negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))
| negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)) = negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(negative_part(least_upper_bound(negative_part(X_199),X_200)),X_48)),negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))) ),[0,0,0],$fot(negative_part(least_upper_bound(X_200,X_199)))]]) ).
cnf(refute_0_462,plain,
( negative_part(least_upper_bound(negative_part(least_upper_bound(negative_part(X_199),X_200)),X_48)) != negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))
| negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)) = negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_199),X_200)),negative_part(least_upper_bound(X_200,X_199))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)) = negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(least_upper_bound(negative_part(X_199),X_200)),X_48)),negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))) )],[refute_0_459,refute_0_462]) ).
cnf(refute_0_464,plain,
negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)) = negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))),
inference(subst,[],[refute_0_325:[bind(X_47,$fot(least_upper_bound(X_200,X_199)))]]) ).
cnf(refute_0_465,plain,
( negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)) != negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199)))
| negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)) != negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))
| negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))) = negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)),negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))) ),[0],$fot(negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))))]]) ).
cnf(refute_0_466,plain,
( negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)) != negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))
| negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))) = negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)),negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199)))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))) = negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(least_upper_bound(X_200,X_199)),X_48)),negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))) )],[refute_0_463,refute_0_466]) ).
cnf(refute_0_468,plain,
( negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))) != negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))
| negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))) = negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))))),bind(Y0,$fot(negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))))]]) ).
cnf(refute_0_469,plain,
negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200))) = negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_48,least_upper_bound(X_200,X_199))),negative_part(least_upper_bound(X_48,least_upper_bound(negative_part(X_199),X_200)))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258))) = negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))),
inference(subst,[],[refute_0_469:[bind(X_199,$fot(X_47)),bind(X_200,$fot(X_258)),bind(X_48,$fot(X_47))]]) ).
cnf(refute_0_471,plain,
negative_part(least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))) = negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)),
inference(subst,[],[refute_0_325:[bind(X_47,$fot(X_199)),bind(X_48,$fot(least_upper_bound(negative_part(negative_part(X_199)),X_78)))]]) ).
cnf(refute_0_472,plain,
least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_79))) = least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(negative_part(X_79)))]]) ).
cnf(refute_0_473,plain,
least_upper_bound(X_79,negative_part(X_79)) = X_79,
inference(subst,[],[refute_0_109:[bind(X_17,$fot(X_79))]]) ).
cnf(refute_0_474,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_79))) != least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79))
| least_upper_bound(X_79,negative_part(X_79)) != X_79
| least_upper_bound(X_78,X_79) = least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_79))),least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79))) ),[0,1],$fot(X_79)]]) ).
cnf(refute_0_475,plain,
( least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_79))) != least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79))
| least_upper_bound(X_78,X_79) = least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_79,negative_part(X_79)),X_79) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
least_upper_bound(X_78,X_79) = least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,least_upper_bound(X_79,negative_part(X_79))),least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79))) )],[refute_0_472,refute_0_475]) ).
cnf(refute_0_477,plain,
least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79)) = least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78)),
inference(subst,[],[refute_0_164:[bind(X,$fot(X_79)),bind(X_78,$fot(negative_part(X_79))),bind(X_79,$fot(X_78))]]) ).
cnf(refute_0_478,plain,
greatest_lower_bound(X_9,least_upper_bound(X_9,X_10)) = X_9,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_9)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_479,plain,
least_upper_bound(X_10,X_9) = least_upper_bound(X_9,X_10),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_10)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_480,plain,
( least_upper_bound(X_10,X_9) != least_upper_bound(X_9,X_10)
| least_upper_bound(X_9,X_10) = least_upper_bound(X_10,X_9) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_10,X_9))),bind(Y0,$fot(least_upper_bound(X_9,X_10)))]]) ).
cnf(refute_0_481,plain,
least_upper_bound(X_9,X_10) = least_upper_bound(X_10,X_9),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_9),least_upper_bound(X_9,X_10)) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
( greatest_lower_bound(X_9,least_upper_bound(X_9,X_10)) != X_9
| least_upper_bound(X_9,X_10) != least_upper_bound(X_10,X_9)
| greatest_lower_bound(X_9,least_upper_bound(X_10,X_9)) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_9,least_upper_bound(X_9,X_10)),X_9) ),[0,1],$fot(least_upper_bound(X_10,X_9))]]) ).
cnf(refute_0_483,plain,
( greatest_lower_bound(X_9,least_upper_bound(X_9,X_10)) != X_9
| greatest_lower_bound(X_9,least_upper_bound(X_10,X_9)) = X_9 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_10),least_upper_bound(X_10,X_9)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
greatest_lower_bound(X_9,least_upper_bound(X_10,X_9)) = X_9,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,least_upper_bound(X_9,X_10)),X_9) )],[refute_0_478,refute_0_483]) ).
cnf(refute_0_485,plain,
greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,least_upper_bound(X_31,X_10))) = least_upper_bound(X_31,X_10),
inference(subst,[],[refute_0_484:[bind(X_9,$fot(least_upper_bound(X_31,X_10)))]]) ).
cnf(refute_0_486,plain,
least_upper_bound(X_10,least_upper_bound(X_31,X_10)) = least_upper_bound(X_10,X_31),
inference(subst,[],[refute_0_126:[bind(Y,$fot(X_31)),bind(X_27,$fot(X_10))]]) ).
cnf(refute_0_487,plain,
( greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,least_upper_bound(X_31,X_10))) != least_upper_bound(X_31,X_10)
| least_upper_bound(X_10,least_upper_bound(X_31,X_10)) != least_upper_bound(X_10,X_31)
| greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) = least_upper_bound(X_31,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,least_upper_bound(X_31,X_10))),least_upper_bound(X_31,X_10)) ),[0,1],$fot(least_upper_bound(X_10,X_31))]]) ).
cnf(refute_0_488,plain,
( greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,least_upper_bound(X_31,X_10))) != least_upper_bound(X_31,X_10)
| greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) = least_upper_bound(X_31,X_10) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,least_upper_bound(X_31,X_10)),least_upper_bound(X_10,X_31)) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) = least_upper_bound(X_31,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,least_upper_bound(X_31,X_10))),least_upper_bound(X_31,X_10)) )],[refute_0_485,refute_0_488]) ).
cnf(refute_0_490,plain,
greatest_lower_bound(X_31,X_31) = X_31,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_491,plain,
least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)) = least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)))]]) ).
cnf(refute_0_492,plain,
( greatest_lower_bound(X_31,X_31) != X_31
| least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)) != least_upper_bound(X_10,greatest_lower_bound(X_31,X_31))
| least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)) = least_upper_bound(X_10,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)),least_upper_bound(X_10,greatest_lower_bound(X_31,X_31))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_493,plain,
( greatest_lower_bound(X_31,X_31) != X_31
| least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)) = least_upper_bound(X_10,X_31) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)),least_upper_bound(X_10,greatest_lower_bound(X_31,X_31))) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)) = least_upper_bound(X_10,X_31),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,X_31),X_31) )],[refute_0_490,refute_0_493]) ).
cnf(refute_0_495,plain,
least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) = greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,X_40)),
inference(subst,[],[lat4_3:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X_40))]]) ).
cnf(refute_0_496,plain,
least_upper_bound(X_39,X_38) = least_upper_bound(X_38,X_39),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_497,plain,
( least_upper_bound(X_39,X_38) != least_upper_bound(X_38,X_39)
| least_upper_bound(X_38,X_39) = least_upper_bound(X_39,X_38) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_39,X_38))),bind(Y0,$fot(least_upper_bound(X_38,X_39)))]]) ).
cnf(refute_0_498,plain,
least_upper_bound(X_38,X_39) = least_upper_bound(X_39,X_38),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_39)) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
( least_upper_bound(X_38,X_39) != least_upper_bound(X_39,X_38)
| least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) != greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,X_40))
| least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) = greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)),greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,X_40))) ),[1,0],$fot(least_upper_bound(X_39,X_38))]]) ).
cnf(refute_0_500,plain,
( least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) != greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,X_40))
| least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) = greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,X_39),least_upper_bound(X_39,X_38)) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) = greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)),greatest_lower_bound(least_upper_bound(X_38,X_39),least_upper_bound(X_38,X_40))) )],[refute_0_495,refute_0_500]) ).
cnf(refute_0_502,plain,
( least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) != greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40))
| greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40)) = least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40))))]]) ).
cnf(refute_0_503,plain,
greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40)) = least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_38,greatest_lower_bound(X_39,X_40)),greatest_lower_bound(least_upper_bound(X_39,X_38),least_upper_bound(X_38,X_40))) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) = least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)),
inference(subst,[],[refute_0_503:[bind(X_38,$fot(X_10)),bind(X_39,$fot(X_31)),bind(X_40,$fot(X_31))]]) ).
cnf(refute_0_505,plain,
( greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) != least_upper_bound(X_10,greatest_lower_bound(X_31,X_31))
| least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)) != least_upper_bound(X_10,X_31)
| greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) = least_upper_bound(X_10,X_31) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)))),bind(Y0,$fot(least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)))),bind(Z0,$fot(least_upper_bound(X_10,X_31)))]]) ).
cnf(refute_0_506,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)) != least_upper_bound(X_10,X_31)
| greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) = least_upper_bound(X_10,X_31) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)),least_upper_bound(X_10,greatest_lower_bound(X_31,X_31))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) = least_upper_bound(X_10,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_31,X_31)),least_upper_bound(X_10,X_31)) )],[refute_0_494,refute_0_506]) ).
cnf(refute_0_508,plain,
( greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) != least_upper_bound(X_10,X_31)
| greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) != least_upper_bound(X_31,X_10)
| least_upper_bound(X_10,X_31) = least_upper_bound(X_31,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)),least_upper_bound(X_31,X_10)) ),[0],$fot(least_upper_bound(X_10,X_31))]]) ).
cnf(refute_0_509,plain,
( greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)) != least_upper_bound(X_31,X_10)
| least_upper_bound(X_10,X_31) = least_upper_bound(X_31,X_10) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)),least_upper_bound(X_10,X_31)) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
least_upper_bound(X_10,X_31) = least_upper_bound(X_31,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_31,X_10),least_upper_bound(X_10,X_31)),least_upper_bound(X_31,X_10)) )],[refute_0_489,refute_0_509]) ).
cnf(refute_0_511,plain,
( least_upper_bound(X_10,X_31) != least_upper_bound(X_31,X_10)
| least_upper_bound(X_31,X_10) = least_upper_bound(X_10,X_31) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_10,X_31))),bind(Y0,$fot(least_upper_bound(X_31,X_10)))]]) ).
cnf(refute_0_512,plain,
least_upper_bound(X_31,X_10) = least_upper_bound(X_10,X_31),
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_31),least_upper_bound(X_31,X_10)) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) = least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79)),
inference(subst,[],[refute_0_512:[bind(X_10,$fot(negative_part(X_79))),bind(X_31,$fot(least_upper_bound(X_78,X_79)))]]) ).
cnf(refute_0_514,plain,
( least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) != least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79))
| least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79)) != least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78))
| least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) = least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)))),bind(Y0,$fot(least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79)))),bind(Z0,$fot(least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78))))]]) ).
cnf(refute_0_515,plain,
( least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79)) != least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78))
| least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) = least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)),least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) = least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78)),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_79),least_upper_bound(X_78,X_79)),least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78))) )],[refute_0_477,refute_0_515]) ).
cnf(refute_0_517,plain,
( least_upper_bound(X_78,X_79) != least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79))
| least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)) != least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78))
| least_upper_bound(X_78,X_79) = least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_78,X_79),least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78))) ),[0],$fot(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)))]]) ).
cnf(refute_0_518,plain,
( least_upper_bound(X_78,X_79) != least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79))
| least_upper_bound(X_78,X_79) = least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79)),least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
least_upper_bound(X_78,X_79) = least_upper_bound(X_79,least_upper_bound(negative_part(X_79),X_78)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,X_79),least_upper_bound(least_upper_bound(X_78,X_79),negative_part(X_79))) )],[refute_0_476,refute_0_518]) ).
cnf(refute_0_520,plain,
least_upper_bound(X_78,negative_part(X_199)) = least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78)),
inference(subst,[],[refute_0_519:[bind(X_79,$fot(negative_part(X_199)))]]) ).
cnf(refute_0_521,plain,
( least_upper_bound(X_78,negative_part(X_199)) != least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))
| least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78)) = least_upper_bound(X_78,negative_part(X_199)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(least_upper_bound(X_78,negative_part(X_199)))),bind(Y0,$fot(least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))))]]) ).
cnf(refute_0_522,plain,
least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78)) = least_upper_bound(X_78,negative_part(X_199)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_78,negative_part(X_199)),least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
( least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78)) != least_upper_bound(X_78,negative_part(X_199))
| negative_part(least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))) != negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))
| negative_part(least_upper_bound(X_78,negative_part(X_199))) = negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))),negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))) ),[0,0],$fot(least_upper_bound(X_78,negative_part(X_199)))]]) ).
cnf(refute_0_524,plain,
( negative_part(least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))) != negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))
| negative_part(least_upper_bound(X_78,negative_part(X_199))) = negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78)),least_upper_bound(X_78,negative_part(X_199))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
negative_part(least_upper_bound(X_78,negative_part(X_199))) = negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_199),least_upper_bound(negative_part(negative_part(X_199)),X_78))),negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))) )],[refute_0_471,refute_0_524]) ).
cnf(refute_0_526,plain,
negative_part(least_upper_bound(X_78,negative_part(X_199))) = negative_part(least_upper_bound(X_78,X_199)),
inference(subst,[],[refute_0_320:[bind(X_41,$fot(X_78)),bind(X_42,$fot(X_199))]]) ).
cnf(refute_0_527,plain,
( negative_part(least_upper_bound(X_78,negative_part(X_199))) != negative_part(least_upper_bound(X_78,X_199))
| negative_part(least_upper_bound(X_78,negative_part(X_199))) != negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))
| negative_part(least_upper_bound(X_78,X_199)) = negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(X_78,negative_part(X_199))),negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))) ),[0],$fot(negative_part(least_upper_bound(X_78,X_199)))]]) ).
cnf(refute_0_528,plain,
( negative_part(least_upper_bound(X_78,negative_part(X_199))) != negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))
| negative_part(least_upper_bound(X_78,X_199)) = negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_78,negative_part(X_199))),negative_part(least_upper_bound(X_78,X_199))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))) = least_upper_bound(X_199,X_78),
inference(subst,[],[refute_0_144:[bind(X_78,$fot(X_199)),bind(X_79,$fot(X_78))]]) ).
cnf(refute_0_530,plain,
negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) = negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))),
introduced(tautology,[refl,[$fot(negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))))]]) ).
cnf(refute_0_531,plain,
( least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))) != least_upper_bound(X_199,X_78)
| negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) != negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))
| negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) = negative_part(least_upper_bound(X_199,X_78)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))),negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))) ),[1,0],$fot(least_upper_bound(X_199,X_78))]]) ).
cnf(refute_0_532,plain,
( least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))) != least_upper_bound(X_199,X_78)
| negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) = negative_part(least_upper_bound(X_199,X_78)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))),negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) = negative_part(least_upper_bound(X_199,X_78)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))),least_upper_bound(X_199,X_78)) )],[refute_0_529,refute_0_532]) ).
cnf(refute_0_534,plain,
negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78))) = negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))),
inference(subst,[],[refute_0_469:[bind(X_199,$fot(negative_part(X_199))),bind(X_200,$fot(X_78)),bind(X_48,$fot(X_199))]]) ).
cnf(refute_0_535,plain,
least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) = negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))),
inference(subst,[],[refute_0_329:[bind(X_18,$fot(negative_part(X_194))),bind(X_42,$fot(negative_part(X_193)))]]) ).
cnf(refute_0_536,plain,
least_upper_bound(negative_part(X_193),negative_part(X_194)) = negative_part(least_upper_bound(X_194,X_193)),
inference(subst,[],[refute_0_329:[bind(X_18,$fot(X_193)),bind(X_42,$fot(X_194))]]) ).
cnf(refute_0_537,plain,
( least_upper_bound(negative_part(X_193),negative_part(X_194)) != negative_part(least_upper_bound(X_194,X_193))
| least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) != negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194)))
| least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) = negative_part(negative_part(least_upper_bound(X_194,X_193))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))),negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194)))) ),[1,0],$fot(negative_part(least_upper_bound(X_194,X_193)))]]) ).
cnf(refute_0_538,plain,
( least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) != negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194)))
| least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) = negative_part(negative_part(least_upper_bound(X_194,X_193))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_193),negative_part(X_194)),negative_part(least_upper_bound(X_194,X_193))) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) = negative_part(negative_part(least_upper_bound(X_194,X_193))),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))),negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194)))) )],[refute_0_535,refute_0_538]) ).
cnf(refute_0_540,plain,
negative_part(least_upper_bound(negative_part(X_194),X_193)) = negative_part(least_upper_bound(X_193,X_194)),
inference(subst,[],[refute_0_325:[bind(X_47,$fot(X_194)),bind(X_48,$fot(X_193))]]) ).
cnf(refute_0_541,plain,
negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))) = negative_part(least_upper_bound(negative_part(X_194),X_193)),
inference(subst,[],[refute_0_325:[bind(X_47,$fot(X_193)),bind(X_48,$fot(negative_part(X_194)))]]) ).
cnf(refute_0_542,plain,
( negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))) != negative_part(least_upper_bound(negative_part(X_194),X_193))
| negative_part(least_upper_bound(negative_part(X_194),X_193)) != negative_part(least_upper_bound(X_193,X_194))
| negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))) = negative_part(least_upper_bound(X_193,X_194)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))))),bind(Y0,$fot(negative_part(least_upper_bound(negative_part(X_194),X_193)))),bind(Z0,$fot(negative_part(least_upper_bound(X_193,X_194))))]]) ).
cnf(refute_0_543,plain,
( negative_part(least_upper_bound(negative_part(X_194),X_193)) != negative_part(least_upper_bound(X_193,X_194))
| negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))) = negative_part(least_upper_bound(X_193,X_194)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))),negative_part(least_upper_bound(negative_part(X_194),X_193))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))) = negative_part(least_upper_bound(X_193,X_194)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_194),X_193)),negative_part(least_upper_bound(X_193,X_194))) )],[refute_0_540,refute_0_543]) ).
cnf(refute_0_545,plain,
( least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) != negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194)))
| negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))) != negative_part(least_upper_bound(X_193,X_194))
| least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) = negative_part(least_upper_bound(X_193,X_194)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))))),bind(Y0,$fot(negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))))),bind(Z0,$fot(negative_part(least_upper_bound(X_193,X_194))))]]) ).
cnf(refute_0_546,plain,
( negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))) != negative_part(least_upper_bound(X_193,X_194))
| least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) = negative_part(least_upper_bound(X_193,X_194)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))),negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194)))) )],[refute_0_535,refute_0_545]) ).
cnf(refute_0_547,plain,
least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) = negative_part(least_upper_bound(X_193,X_194)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_193),negative_part(X_194))),negative_part(least_upper_bound(X_193,X_194))) )],[refute_0_544,refute_0_546]) ).
cnf(refute_0_548,plain,
( least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) != negative_part(least_upper_bound(X_193,X_194))
| least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) != negative_part(negative_part(least_upper_bound(X_194,X_193)))
| negative_part(least_upper_bound(X_193,X_194)) = negative_part(negative_part(least_upper_bound(X_194,X_193))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))),negative_part(negative_part(least_upper_bound(X_194,X_193)))) ),[0],$fot(negative_part(least_upper_bound(X_193,X_194)))]]) ).
cnf(refute_0_549,plain,
( least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) != negative_part(negative_part(least_upper_bound(X_194,X_193)))
| negative_part(least_upper_bound(X_193,X_194)) = negative_part(negative_part(least_upper_bound(X_194,X_193))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))),negative_part(least_upper_bound(X_193,X_194))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
greatest_lower_bound(X_9,least_upper_bound(X_9,identity)) = X_9,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_9)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_551,plain,
positive_part(X_9) = least_upper_bound(X_9,identity),
inference(subst,[],[lat4_1:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_552,plain,
( positive_part(X_9) != least_upper_bound(X_9,identity)
| least_upper_bound(X_9,identity) = positive_part(X_9) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(positive_part(X_9))),bind(Y0,$fot(least_upper_bound(X_9,identity)))]]) ).
cnf(refute_0_553,plain,
least_upper_bound(X_9,identity) = positive_part(X_9),
inference(resolve,[$cnf( $equal(positive_part(X_9),least_upper_bound(X_9,identity)) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
( greatest_lower_bound(X_9,least_upper_bound(X_9,identity)) != X_9
| least_upper_bound(X_9,identity) != positive_part(X_9)
| greatest_lower_bound(X_9,positive_part(X_9)) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_9,least_upper_bound(X_9,identity)),X_9) ),[0,1],$fot(positive_part(X_9))]]) ).
cnf(refute_0_555,plain,
( greatest_lower_bound(X_9,least_upper_bound(X_9,identity)) != X_9
| greatest_lower_bound(X_9,positive_part(X_9)) = X_9 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,identity),positive_part(X_9)) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
greatest_lower_bound(X_9,positive_part(X_9)) = X_9,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,least_upper_bound(X_9,identity)),X_9) )],[refute_0_550,refute_0_555]) ).
cnf(refute_0_557,plain,
greatest_lower_bound(negative_part(X_19),positive_part(negative_part(X_19))) = negative_part(X_19),
inference(subst,[],[refute_0_556:[bind(X_9,$fot(negative_part(X_19)))]]) ).
cnf(refute_0_558,plain,
positive_part(negative_part(X_19)) = identity,
inference(subst,[],[refute_0_254:[bind(X_18,$fot(X_19))]]) ).
cnf(refute_0_559,plain,
( greatest_lower_bound(negative_part(X_19),positive_part(negative_part(X_19))) != negative_part(X_19)
| positive_part(negative_part(X_19)) != identity
| greatest_lower_bound(negative_part(X_19),identity) = negative_part(X_19) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(negative_part(X_19),positive_part(negative_part(X_19))),negative_part(X_19)) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_560,plain,
( greatest_lower_bound(negative_part(X_19),positive_part(negative_part(X_19))) != negative_part(X_19)
| greatest_lower_bound(negative_part(X_19),identity) = negative_part(X_19) ),
inference(resolve,[$cnf( $equal(positive_part(negative_part(X_19)),identity) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
greatest_lower_bound(negative_part(X_19),identity) = negative_part(X_19),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(X_19),positive_part(negative_part(X_19))),negative_part(X_19)) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
greatest_lower_bound(negative_part(X_19),identity) = negative_part(negative_part(X_19)),
inference(subst,[],[refute_0_76:[bind(X,$fot(negative_part(X_19)))]]) ).
cnf(refute_0_563,plain,
( greatest_lower_bound(negative_part(X_19),identity) != negative_part(X_19)
| greatest_lower_bound(negative_part(X_19),identity) != negative_part(negative_part(X_19))
| negative_part(negative_part(X_19)) = negative_part(X_19) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(negative_part(X_19),identity),negative_part(X_19)) ),[0],$fot(negative_part(negative_part(X_19)))]]) ).
cnf(refute_0_564,plain,
( greatest_lower_bound(negative_part(X_19),identity) != negative_part(X_19)
| negative_part(negative_part(X_19)) = negative_part(X_19) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(X_19),identity),negative_part(negative_part(X_19))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
negative_part(negative_part(X_19)) = negative_part(X_19),
inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(X_19),identity),negative_part(X_19)) )],[refute_0_561,refute_0_564]) ).
cnf(refute_0_566,plain,
negative_part(negative_part(least_upper_bound(X_194,X_193))) = negative_part(least_upper_bound(X_194,X_193)),
inference(subst,[],[refute_0_565:[bind(X_19,$fot(least_upper_bound(X_194,X_193)))]]) ).
cnf(refute_0_567,plain,
( negative_part(least_upper_bound(X_193,X_194)) != negative_part(negative_part(least_upper_bound(X_194,X_193)))
| negative_part(negative_part(least_upper_bound(X_194,X_193))) != negative_part(least_upper_bound(X_194,X_193))
| negative_part(least_upper_bound(X_193,X_194)) = negative_part(least_upper_bound(X_194,X_193)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(negative_part(least_upper_bound(X_193,X_194)),negative_part(least_upper_bound(X_194,X_193))) ),[0],$fot(negative_part(negative_part(least_upper_bound(X_194,X_193))))]]) ).
cnf(refute_0_568,plain,
( negative_part(least_upper_bound(X_193,X_194)) != negative_part(negative_part(least_upper_bound(X_194,X_193)))
| negative_part(least_upper_bound(X_193,X_194)) = negative_part(least_upper_bound(X_194,X_193)) ),
inference(resolve,[$cnf( $equal(negative_part(negative_part(least_upper_bound(X_194,X_193))),negative_part(least_upper_bound(X_194,X_193))) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
( least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))) != negative_part(negative_part(least_upper_bound(X_194,X_193)))
| negative_part(least_upper_bound(X_193,X_194)) = negative_part(least_upper_bound(X_194,X_193)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_193,X_194)),negative_part(negative_part(least_upper_bound(X_194,X_193)))) )],[refute_0_549,refute_0_568]) ).
cnf(refute_0_570,plain,
negative_part(least_upper_bound(X_193,X_194)) = negative_part(least_upper_bound(X_194,X_193)),
inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(negative_part(X_194)),negative_part(negative_part(X_193))),negative_part(negative_part(least_upper_bound(X_194,X_193)))) )],[refute_0_539,refute_0_569]) ).
cnf(refute_0_571,plain,
( negative_part(least_upper_bound(X_193,X_194)) != negative_part(least_upper_bound(X_194,X_193))
| negative_part(least_upper_bound(X_194,X_193)) = negative_part(least_upper_bound(X_193,X_194)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(least_upper_bound(X_193,X_194)))),bind(Y0,$fot(negative_part(least_upper_bound(X_194,X_193))))]]) ).
cnf(refute_0_572,plain,
negative_part(least_upper_bound(X_194,X_193)) = negative_part(least_upper_bound(X_193,X_194)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_193,X_194)),negative_part(least_upper_bound(X_194,X_193))) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) = negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78))),
inference(subst,[],[refute_0_572:[bind(X_193,$fot(X_199)),bind(X_194,$fot(least_upper_bound(negative_part(negative_part(X_199)),X_78)))]]) ).
cnf(refute_0_574,plain,
( negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78))) != negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))
| negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) != negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78)))
| negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) = negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)))),bind(Y0,$fot(negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78))))),bind(Z0,$fot(negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))))]]) ).
cnf(refute_0_575,plain,
( negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78))) != negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))
| negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) = negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)),negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78)))) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) = negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_199,least_upper_bound(negative_part(negative_part(X_199)),X_78))),negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))) )],[refute_0_534,refute_0_575]) ).
cnf(refute_0_577,plain,
( negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) != negative_part(least_upper_bound(X_199,X_78))
| negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) != negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))
| negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) = negative_part(least_upper_bound(X_199,X_78)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)))),bind(Y0,$fot(negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))))),bind(Z0,$fot(negative_part(least_upper_bound(X_199,X_78))))]]) ).
cnf(refute_0_578,plain,
( negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))) != negative_part(least_upper_bound(X_199,X_78))
| negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) = negative_part(least_upper_bound(X_199,X_78)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)),negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199))))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) = negative_part(least_upper_bound(X_199,X_78)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_199,least_upper_bound(X_78,negative_part(X_199)))),negative_part(least_upper_bound(X_199,X_78))) )],[refute_0_533,refute_0_578]) ).
cnf(refute_0_580,plain,
( negative_part(least_upper_bound(X_78,X_199)) != negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))
| negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)) != negative_part(least_upper_bound(X_199,X_78))
| negative_part(least_upper_bound(X_78,X_199)) = negative_part(least_upper_bound(X_199,X_78)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(negative_part(least_upper_bound(X_78,X_199)),negative_part(least_upper_bound(X_199,X_78))) ),[0],$fot(negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)))]]) ).
cnf(refute_0_581,plain,
( negative_part(least_upper_bound(X_78,X_199)) != negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))
| negative_part(least_upper_bound(X_78,X_199)) = negative_part(least_upper_bound(X_199,X_78)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199)),negative_part(least_upper_bound(X_199,X_78))) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
( negative_part(least_upper_bound(X_78,negative_part(X_199))) != negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))
| negative_part(least_upper_bound(X_78,X_199)) = negative_part(least_upper_bound(X_199,X_78)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_78,X_199)),negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))) )],[refute_0_528,refute_0_581]) ).
cnf(refute_0_583,plain,
negative_part(least_upper_bound(X_78,X_199)) = negative_part(least_upper_bound(X_199,X_78)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_78,negative_part(X_199))),negative_part(least_upper_bound(least_upper_bound(negative_part(negative_part(X_199)),X_78),X_199))) )],[refute_0_525,refute_0_582]) ).
cnf(refute_0_584,plain,
( negative_part(least_upper_bound(X_78,X_199)) != negative_part(least_upper_bound(X_199,X_78))
| negative_part(least_upper_bound(X_199,X_78)) = negative_part(least_upper_bound(X_78,X_199)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(least_upper_bound(X_78,X_199)))),bind(Y0,$fot(negative_part(least_upper_bound(X_199,X_78))))]]) ).
cnf(refute_0_585,plain,
negative_part(least_upper_bound(X_199,X_78)) = negative_part(least_upper_bound(X_78,X_199)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_78,X_199)),negative_part(least_upper_bound(X_199,X_78))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) = negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258))),
inference(subst,[],[refute_0_585:[bind(X_199,$fot(least_upper_bound(negative_part(X_47),X_258))),bind(X_78,$fot(X_47))]]) ).
cnf(refute_0_587,plain,
( negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258))) != negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))
| negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) != negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258)))
| negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) = negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)))),bind(Y0,$fot(negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258))))),bind(Z0,$fot(negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))))]]) ).
cnf(refute_0_588,plain,
( negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258))) != negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))
| negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) = negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)),negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258)))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) = negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_47,least_upper_bound(negative_part(X_47),X_258))),negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))) )],[refute_0_470,refute_0_588]) ).
cnf(refute_0_590,plain,
( negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) != negative_part(least_upper_bound(X_47,X_258))
| negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) != negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))
| negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) = negative_part(least_upper_bound(X_47,X_258)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)))),bind(Y0,$fot(negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))))),bind(Z0,$fot(negative_part(least_upper_bound(X_47,X_258))))]]) ).
cnf(refute_0_591,plain,
( negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))) != negative_part(least_upper_bound(X_47,X_258))
| negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) = negative_part(least_upper_bound(X_47,X_258)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)),negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47)))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) = negative_part(least_upper_bound(X_47,X_258)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_47,least_upper_bound(X_258,X_47))),negative_part(least_upper_bound(X_47,X_258))) )],[refute_0_458,refute_0_591]) ).
cnf(refute_0_593,plain,
( negative_part(least_upper_bound(X_258,X_47)) != negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))
| negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)) != negative_part(least_upper_bound(X_47,X_258))
| negative_part(least_upper_bound(X_258,X_47)) = negative_part(least_upper_bound(X_47,X_258)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(negative_part(least_upper_bound(X_258,X_47)),negative_part(least_upper_bound(X_47,X_258))) ),[0],$fot(negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)))]]) ).
cnf(refute_0_594,plain,
( negative_part(least_upper_bound(X_258,X_47)) != negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))
| negative_part(least_upper_bound(X_258,X_47)) = negative_part(least_upper_bound(X_47,X_258)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47)),negative_part(least_upper_bound(X_47,X_258))) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
( negative_part(least_upper_bound(negative_part(X_47),X_258)) != negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))
| negative_part(least_upper_bound(X_258,X_47)) = negative_part(least_upper_bound(X_47,X_258)) ),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_258,X_47)),negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))) )],[refute_0_453,refute_0_594]) ).
cnf(refute_0_596,plain,
negative_part(least_upper_bound(X_258,X_47)) = negative_part(least_upper_bound(X_47,X_258)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(negative_part(X_47),X_258)),negative_part(least_upper_bound(least_upper_bound(negative_part(X_47),X_258),X_47))) )],[refute_0_450,refute_0_595]) ).
cnf(refute_0_597,plain,
( negative_part(least_upper_bound(X_258,X_47)) != negative_part(least_upper_bound(X_47,X_258))
| negative_part(least_upper_bound(X_47,X_258)) = negative_part(least_upper_bound(X_258,X_47)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(negative_part(least_upper_bound(X_258,X_47)))),bind(Y0,$fot(negative_part(least_upper_bound(X_47,X_258))))]]) ).
cnf(refute_0_598,plain,
negative_part(least_upper_bound(X_47,X_258)) = negative_part(least_upper_bound(X_258,X_47)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_258,X_47)),negative_part(least_upper_bound(X_47,X_258))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332))) = negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))),
inference(subst,[],[refute_0_598:[bind(X_258,$fot(inverse(X_332))),bind(X_47,$fot(inverse(positive_part(X_332))))]]) ).
cnf(refute_0_600,plain,
least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) = greatest_lower_bound(positive_part(inverse(positive_part(X_102))),least_upper_bound(inverse(positive_part(X_102)),X_39)),
inference(subst,[],[refute_0_90:[bind(X_38,$fot(inverse(positive_part(X_102))))]]) ).
cnf(refute_0_601,plain,
multiply(inverse(X_97),least_upper_bound(X_97,X_98)) = least_upper_bound(multiply(inverse(X_97),X_97),multiply(inverse(X_97),X_98)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_97))),bind(Y,$fot(X_97)),bind(Z,$fot(X_98))]]) ).
cnf(refute_0_602,plain,
multiply(inverse(X_97),X_97) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_97))]]) ).
cnf(refute_0_603,plain,
( multiply(inverse(X_97),X_97) != identity
| multiply(inverse(X_97),least_upper_bound(X_97,X_98)) != least_upper_bound(multiply(inverse(X_97),X_97),multiply(inverse(X_97),X_98))
| multiply(inverse(X_97),least_upper_bound(X_97,X_98)) = least_upper_bound(identity,multiply(inverse(X_97),X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_97),least_upper_bound(X_97,X_98)),least_upper_bound(multiply(inverse(X_97),X_97),multiply(inverse(X_97),X_98))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_604,plain,
( multiply(inverse(X_97),least_upper_bound(X_97,X_98)) != least_upper_bound(multiply(inverse(X_97),X_97),multiply(inverse(X_97),X_98))
| multiply(inverse(X_97),least_upper_bound(X_97,X_98)) = least_upper_bound(identity,multiply(inverse(X_97),X_98)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),X_97),identity) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(inverse(X_97),least_upper_bound(X_97,X_98)) = least_upper_bound(identity,multiply(inverse(X_97),X_98)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),least_upper_bound(X_97,X_98)),least_upper_bound(multiply(inverse(X_97),X_97),multiply(inverse(X_97),X_98))) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
least_upper_bound(identity,multiply(inverse(X_97),X_98)) = positive_part(multiply(inverse(X_97),X_98)),
inference(subst,[],[refute_0_58:[bind(X,$fot(multiply(inverse(X_97),X_98)))]]) ).
cnf(refute_0_607,plain,
( multiply(inverse(X_97),least_upper_bound(X_97,X_98)) != least_upper_bound(identity,multiply(inverse(X_97),X_98))
| least_upper_bound(identity,multiply(inverse(X_97),X_98)) != positive_part(multiply(inverse(X_97),X_98))
| multiply(inverse(X_97),least_upper_bound(X_97,X_98)) = positive_part(multiply(inverse(X_97),X_98)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_97),least_upper_bound(X_97,X_98)),positive_part(multiply(inverse(X_97),X_98))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_97),X_98)))]]) ).
cnf(refute_0_608,plain,
( multiply(inverse(X_97),least_upper_bound(X_97,X_98)) != least_upper_bound(identity,multiply(inverse(X_97),X_98))
| multiply(inverse(X_97),least_upper_bound(X_97,X_98)) = positive_part(multiply(inverse(X_97),X_98)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_97),X_98)),positive_part(multiply(inverse(X_97),X_98))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
multiply(inverse(X_97),least_upper_bound(X_97,X_98)) = positive_part(multiply(inverse(X_97),X_98)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_97),least_upper_bound(X_97,X_98)),least_upper_bound(identity,multiply(inverse(X_97),X_98))) )],[refute_0_605,refute_0_608]) ).
cnf(refute_0_610,plain,
multiply(inverse(X_99),least_upper_bound(X_99,negative_part(X_99))) = positive_part(multiply(inverse(X_99),negative_part(X_99))),
inference(subst,[],[refute_0_609:[bind(X_97,$fot(X_99)),bind(X_98,$fot(negative_part(X_99)))]]) ).
cnf(refute_0_611,plain,
least_upper_bound(X_99,negative_part(X_99)) = X_99,
inference(subst,[],[refute_0_109:[bind(X_17,$fot(X_99))]]) ).
cnf(refute_0_612,plain,
( multiply(inverse(X_99),least_upper_bound(X_99,negative_part(X_99))) != positive_part(multiply(inverse(X_99),negative_part(X_99)))
| least_upper_bound(X_99,negative_part(X_99)) != X_99
| multiply(inverse(X_99),X_99) = positive_part(multiply(inverse(X_99),negative_part(X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_99),least_upper_bound(X_99,negative_part(X_99))),positive_part(multiply(inverse(X_99),negative_part(X_99)))) ),[0,1],$fot(X_99)]]) ).
cnf(refute_0_613,plain,
( multiply(inverse(X_99),least_upper_bound(X_99,negative_part(X_99))) != positive_part(multiply(inverse(X_99),negative_part(X_99)))
| multiply(inverse(X_99),X_99) = positive_part(multiply(inverse(X_99),negative_part(X_99))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_99,negative_part(X_99)),X_99) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
multiply(inverse(X_99),X_99) = positive_part(multiply(inverse(X_99),negative_part(X_99))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),least_upper_bound(X_99,negative_part(X_99))),positive_part(multiply(inverse(X_99),negative_part(X_99)))) )],[refute_0_610,refute_0_613]) ).
cnf(refute_0_615,plain,
multiply(inverse(X_99),X_99) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_99))]]) ).
cnf(refute_0_616,plain,
( multiply(inverse(X_99),X_99) != identity
| multiply(inverse(X_99),X_99) != positive_part(multiply(inverse(X_99),negative_part(X_99)))
| identity = positive_part(multiply(inverse(X_99),negative_part(X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_99),X_99),positive_part(multiply(inverse(X_99),negative_part(X_99)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_617,plain,
( multiply(inverse(X_99),X_99) != positive_part(multiply(inverse(X_99),negative_part(X_99)))
| identity = positive_part(multiply(inverse(X_99),negative_part(X_99))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),X_99),identity) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
identity = positive_part(multiply(inverse(X_99),negative_part(X_99))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_99),X_99),positive_part(multiply(inverse(X_99),negative_part(X_99)))) )],[refute_0_614,refute_0_617]) ).
cnf(refute_0_619,plain,
identity = positive_part(multiply(inverse(positive_part(X_10)),negative_part(positive_part(X_10)))),
inference(subst,[],[refute_0_618:[bind(X_99,$fot(positive_part(X_10)))]]) ).
cnf(refute_0_620,plain,
( identity != positive_part(multiply(inverse(positive_part(X_10)),negative_part(positive_part(X_10))))
| negative_part(positive_part(X_10)) != identity
| identity = positive_part(multiply(inverse(positive_part(X_10)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,positive_part(multiply(inverse(positive_part(X_10)),negative_part(positive_part(X_10))))) ),[1,0,1],$fot(identity)]]) ).
cnf(refute_0_621,plain,
( identity != positive_part(multiply(inverse(positive_part(X_10)),negative_part(positive_part(X_10))))
| identity = positive_part(multiply(inverse(positive_part(X_10)),identity)) ),
inference(resolve,[$cnf( $equal(negative_part(positive_part(X_10)),identity) )],[refute_0_303,refute_0_620]) ).
cnf(refute_0_622,plain,
identity = positive_part(multiply(inverse(positive_part(X_10)),identity)),
inference(resolve,[$cnf( $equal(identity,positive_part(multiply(inverse(positive_part(X_10)),negative_part(positive_part(X_10))))) )],[refute_0_619,refute_0_621]) ).
cnf(refute_0_623,plain,
multiply(inverse(positive_part(X_10)),identity) = inverse(positive_part(X_10)),
inference(subst,[],[refute_0_339:[bind(X_61,$fot(inverse(positive_part(X_10))))]]) ).
cnf(refute_0_624,plain,
positive_part(multiply(inverse(positive_part(X_10)),identity)) = positive_part(multiply(inverse(positive_part(X_10)),identity)),
introduced(tautology,[refl,[$fot(positive_part(multiply(inverse(positive_part(X_10)),identity)))]]) ).
cnf(refute_0_625,plain,
( multiply(inverse(positive_part(X_10)),identity) != inverse(positive_part(X_10))
| positive_part(multiply(inverse(positive_part(X_10)),identity)) != positive_part(multiply(inverse(positive_part(X_10)),identity))
| positive_part(multiply(inverse(positive_part(X_10)),identity)) = positive_part(inverse(positive_part(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_10)),identity)),positive_part(multiply(inverse(positive_part(X_10)),identity))) ),[1,0],$fot(inverse(positive_part(X_10)))]]) ).
cnf(refute_0_626,plain,
( multiply(inverse(positive_part(X_10)),identity) != inverse(positive_part(X_10))
| positive_part(multiply(inverse(positive_part(X_10)),identity)) = positive_part(inverse(positive_part(X_10))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_10)),identity)),positive_part(multiply(inverse(positive_part(X_10)),identity))) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
positive_part(multiply(inverse(positive_part(X_10)),identity)) = positive_part(inverse(positive_part(X_10))),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_10)),identity),inverse(positive_part(X_10))) )],[refute_0_623,refute_0_626]) ).
cnf(refute_0_628,plain,
( identity != positive_part(multiply(inverse(positive_part(X_10)),identity))
| positive_part(multiply(inverse(positive_part(X_10)),identity)) != positive_part(inverse(positive_part(X_10)))
| identity = positive_part(inverse(positive_part(X_10))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,positive_part(inverse(positive_part(X_10)))) ),[0],$fot(positive_part(multiply(inverse(positive_part(X_10)),identity)))]]) ).
cnf(refute_0_629,plain,
( identity != positive_part(multiply(inverse(positive_part(X_10)),identity))
| identity = positive_part(inverse(positive_part(X_10))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_10)),identity)),positive_part(inverse(positive_part(X_10)))) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
identity = positive_part(inverse(positive_part(X_10))),
inference(resolve,[$cnf( $equal(identity,positive_part(multiply(inverse(positive_part(X_10)),identity))) )],[refute_0_622,refute_0_629]) ).
cnf(refute_0_631,plain,
identity = positive_part(inverse(positive_part(X_102))),
inference(subst,[],[refute_0_630:[bind(X_10,$fot(X_102))]]) ).
cnf(refute_0_632,plain,
( identity != positive_part(inverse(positive_part(X_102)))
| positive_part(inverse(positive_part(X_102))) = identity ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(identity)),bind(Y0,$fot(positive_part(inverse(positive_part(X_102)))))]]) ).
cnf(refute_0_633,plain,
positive_part(inverse(positive_part(X_102))) = identity,
inference(resolve,[$cnf( $equal(identity,positive_part(inverse(positive_part(X_102)))) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
( least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) != greatest_lower_bound(positive_part(inverse(positive_part(X_102))),least_upper_bound(inverse(positive_part(X_102)),X_39))
| positive_part(inverse(positive_part(X_102))) != identity
| least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) = greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)),greatest_lower_bound(positive_part(inverse(positive_part(X_102))),least_upper_bound(inverse(positive_part(X_102)),X_39))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_635,plain,
( least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) != greatest_lower_bound(positive_part(inverse(positive_part(X_102))),least_upper_bound(inverse(positive_part(X_102)),X_39))
| least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) = greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39)) ),
inference(resolve,[$cnf( $equal(positive_part(inverse(positive_part(X_102))),identity) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) = greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)),greatest_lower_bound(positive_part(inverse(positive_part(X_102))),least_upper_bound(inverse(positive_part(X_102)),X_39))) )],[refute_0_600,refute_0_635]) ).
cnf(refute_0_637,plain,
greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39)) = negative_part(least_upper_bound(inverse(positive_part(X_102)),X_39)),
inference(subst,[],[refute_0_23:[bind(X,$fot(least_upper_bound(inverse(positive_part(X_102)),X_39)))]]) ).
cnf(refute_0_638,plain,
( greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39)) != negative_part(least_upper_bound(inverse(positive_part(X_102)),X_39))
| least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) != greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39))
| least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) = negative_part(least_upper_bound(inverse(positive_part(X_102)),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)),greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39))) ),[1],$fot(negative_part(least_upper_bound(inverse(positive_part(X_102)),X_39)))]]) ).
cnf(refute_0_639,plain,
( least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) != greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39))
| least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) = negative_part(least_upper_bound(inverse(positive_part(X_102)),X_39)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39)),negative_part(least_upper_bound(inverse(positive_part(X_102)),X_39))) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)) = negative_part(least_upper_bound(inverse(positive_part(X_102)),X_39)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_102)),negative_part(X_39)),greatest_lower_bound(identity,least_upper_bound(inverse(positive_part(X_102)),X_39))) )],[refute_0_636,refute_0_639]) ).
cnf(refute_0_641,plain,
least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) = negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332))),
inference(subst,[],[refute_0_640:[bind(X_102,$fot(X_332)),bind(X_39,$fot(inverse(X_332)))]]) ).
cnf(refute_0_642,plain,
( least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) != negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332)))
| negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332))) != negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))
| least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) = negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))))),bind(Y0,$fot(negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332))))),bind(Z0,$fot(negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))))]]) ).
cnf(refute_0_643,plain,
( negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332))) != negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))
| least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) = negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))),negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332)))) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) = negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(inverse(positive_part(X_332)),inverse(X_332))),negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))) )],[refute_0_599,refute_0_643]) ).
cnf(refute_0_645,plain,
( least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) != negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))
| negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) != negative_part(inverse(X_332))
| least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) = negative_part(inverse(X_332)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))))),bind(Y0,$fot(negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))))),bind(Z0,$fot(negative_part(inverse(X_332))))]]) ).
cnf(refute_0_646,plain,
( negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))) != negative_part(inverse(X_332))
| least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) = negative_part(inverse(X_332)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))),negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332))))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) = negative_part(inverse(X_332)),
inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(inverse(X_332),inverse(positive_part(X_332)))),negative_part(inverse(X_332))) )],[refute_0_438,refute_0_646]) ).
cnf(refute_0_648,plain,
inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))) = inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))))]]) ).
cnf(refute_0_649,plain,
( inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))) != inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))))
| least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) != negative_part(inverse(X_332))
| inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))) = inverse(negative_part(inverse(X_332))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))),inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))))) ),[1,0],$fot(negative_part(inverse(X_332)))]]) ).
cnf(refute_0_650,plain,
( least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))) != negative_part(inverse(X_332))
| inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))) = inverse(negative_part(inverse(X_332))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))),inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))) = inverse(negative_part(inverse(X_332))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))),negative_part(inverse(X_332))) )],[refute_0_647,refute_0_650]) ).
cnf(refute_0_652,plain,
inverse(multiply(X_58,X_59)) = multiply(inverse(multiply(inverse(X_58),multiply(X_58,X_59))),inverse(X_58)),
inference(subst,[],[refute_0_371:[bind(X_69,$fot(inverse(X_58))),bind(X_70,$fot(multiply(X_58,X_59)))]]) ).
cnf(refute_0_653,plain,
( X_59 != multiply(inverse(X_58),multiply(X_58,X_59))
| multiply(inverse(X_58),multiply(X_58,X_59)) = X_59 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_59)),bind(Y0,$fot(multiply(inverse(X_58),multiply(X_58,X_59))))]]) ).
cnf(refute_0_654,plain,
multiply(inverse(X_58),multiply(X_58,X_59)) = X_59,
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(X_58),multiply(X_58,X_59))) )],[refute_0_8,refute_0_653]) ).
cnf(refute_0_655,plain,
( multiply(inverse(X_58),multiply(X_58,X_59)) != X_59
| inverse(multiply(X_58,X_59)) != multiply(inverse(multiply(inverse(X_58),multiply(X_58,X_59))),inverse(X_58))
| inverse(multiply(X_58,X_59)) = multiply(inverse(X_59),inverse(X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_58,X_59)),multiply(inverse(multiply(inverse(X_58),multiply(X_58,X_59))),inverse(X_58))) ),[1,0,0],$fot(X_59)]]) ).
cnf(refute_0_656,plain,
( inverse(multiply(X_58,X_59)) != multiply(inverse(multiply(inverse(X_58),multiply(X_58,X_59))),inverse(X_58))
| inverse(multiply(X_58,X_59)) = multiply(inverse(X_59),inverse(X_58)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),multiply(X_58,X_59)),X_59) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
inverse(multiply(X_58,X_59)) = multiply(inverse(X_59),inverse(X_58)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_58,X_59)),multiply(inverse(multiply(inverse(X_58),multiply(X_58,X_59))),inverse(X_58))) )],[refute_0_652,refute_0_656]) ).
cnf(refute_0_658,plain,
inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) = multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))),
inference(subst,[],[refute_0_657:[bind(X_58,$fot(inverse(X_328))),bind(X_59,$fot(positive_part(multiply(X_328,X_329))))]]) ).
cnf(refute_0_659,plain,
multiply(inverse(X_58),positive_part(multiply(X_58,X_59))) = least_upper_bound(inverse(X_58),multiply(inverse(X_58),multiply(X_58,X_59))),
inference(subst,[],[refute_0_235:[bind(X_96,$fot(inverse(X_58))),bind(X_97,$fot(multiply(X_58,X_59)))]]) ).
cnf(refute_0_660,plain,
( multiply(inverse(X_58),multiply(X_58,X_59)) != X_59
| multiply(inverse(X_58),positive_part(multiply(X_58,X_59))) != least_upper_bound(inverse(X_58),multiply(inverse(X_58),multiply(X_58,X_59)))
| multiply(inverse(X_58),positive_part(multiply(X_58,X_59))) = least_upper_bound(inverse(X_58),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_58),positive_part(multiply(X_58,X_59))),least_upper_bound(inverse(X_58),multiply(inverse(X_58),multiply(X_58,X_59)))) ),[1,1],$fot(X_59)]]) ).
cnf(refute_0_661,plain,
( multiply(inverse(X_58),positive_part(multiply(X_58,X_59))) != least_upper_bound(inverse(X_58),multiply(inverse(X_58),multiply(X_58,X_59)))
| multiply(inverse(X_58),positive_part(multiply(X_58,X_59))) = least_upper_bound(inverse(X_58),X_59) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),multiply(X_58,X_59)),X_59) )],[refute_0_654,refute_0_660]) ).
cnf(refute_0_662,plain,
multiply(inverse(X_58),positive_part(multiply(X_58,X_59))) = least_upper_bound(inverse(X_58),X_59),
inference(resolve,[$cnf( $equal(multiply(inverse(X_58),positive_part(multiply(X_58,X_59))),least_upper_bound(inverse(X_58),multiply(inverse(X_58),multiply(X_58,X_59)))) )],[refute_0_659,refute_0_661]) ).
cnf(refute_0_663,plain,
multiply(inverse(X_328),positive_part(multiply(X_328,X_329))) = least_upper_bound(inverse(X_328),X_329),
inference(subst,[],[refute_0_662:[bind(X_58,$fot(X_328)),bind(X_59,$fot(X_329))]]) ).
cnf(refute_0_664,plain,
( multiply(inverse(X_328),positive_part(multiply(X_328,X_329))) != least_upper_bound(inverse(X_328),X_329)
| inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) != multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))
| inverse(least_upper_bound(inverse(X_328),X_329)) = multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))),multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))) ),[0,0],$fot(least_upper_bound(inverse(X_328),X_329))]]) ).
cnf(refute_0_665,plain,
( inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) != multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))
| inverse(least_upper_bound(inverse(X_328),X_329)) = multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_328),positive_part(multiply(X_328,X_329))),least_upper_bound(inverse(X_328),X_329)) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
inverse(least_upper_bound(inverse(X_328),X_329)) = multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))),multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))) )],[refute_0_658,refute_0_665]) ).
cnf(refute_0_667,plain,
inverse(least_upper_bound(X_210,inverse(X_69))) = multiply(inverse(multiply(X_69,least_upper_bound(X_210,inverse(X_69)))),X_69),
inference(subst,[],[refute_0_371:[bind(X_70,$fot(least_upper_bound(X_210,inverse(X_69))))]]) ).
cnf(refute_0_668,plain,
multiply(X_96,least_upper_bound(X_97,inverse(X_96))) = least_upper_bound(multiply(X_96,X_97),multiply(X_96,inverse(X_96))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_96)),bind(Y,$fot(X_97)),bind(Z,$fot(inverse(X_96)))]]) ).
cnf(refute_0_669,plain,
multiply(X_96,inverse(X_96)) = identity,
inference(subst,[],[refute_0_359:[bind(X_63,$fot(X_96))]]) ).
cnf(refute_0_670,plain,
( multiply(X_96,inverse(X_96)) != identity
| multiply(X_96,least_upper_bound(X_97,inverse(X_96))) != least_upper_bound(multiply(X_96,X_97),multiply(X_96,inverse(X_96)))
| multiply(X_96,least_upper_bound(X_97,inverse(X_96))) = least_upper_bound(multiply(X_96,X_97),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,inverse(X_96))),least_upper_bound(multiply(X_96,X_97),multiply(X_96,inverse(X_96)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_671,plain,
( multiply(X_96,least_upper_bound(X_97,inverse(X_96))) != least_upper_bound(multiply(X_96,X_97),multiply(X_96,inverse(X_96)))
| multiply(X_96,least_upper_bound(X_97,inverse(X_96))) = least_upper_bound(multiply(X_96,X_97),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_96,inverse(X_96)),identity) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
multiply(X_96,least_upper_bound(X_97,inverse(X_96))) = least_upper_bound(multiply(X_96,X_97),identity),
inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,inverse(X_96))),least_upper_bound(multiply(X_96,X_97),multiply(X_96,inverse(X_96)))) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
least_upper_bound(identity,multiply(X_96,X_97)) = positive_part(multiply(X_96,X_97)),
inference(subst,[],[refute_0_58:[bind(X,$fot(multiply(X_96,X_97)))]]) ).
cnf(refute_0_674,plain,
least_upper_bound(multiply(X_96,X_97),identity) = least_upper_bound(identity,multiply(X_96,X_97)),
inference(subst,[],[refute_0_184:[bind(X_41,$fot(multiply(X_96,X_97))),bind(X_42,$fot(identity))]]) ).
cnf(refute_0_675,plain,
( least_upper_bound(multiply(X_96,X_97),identity) != least_upper_bound(identity,multiply(X_96,X_97))
| least_upper_bound(identity,multiply(X_96,X_97)) != positive_part(multiply(X_96,X_97))
| least_upper_bound(multiply(X_96,X_97),identity) = positive_part(multiply(X_96,X_97)) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(least_upper_bound(multiply(X_96,X_97),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_96,X_97)))),bind(Z0,$fot(positive_part(multiply(X_96,X_97))))]]) ).
cnf(refute_0_676,plain,
( least_upper_bound(identity,multiply(X_96,X_97)) != positive_part(multiply(X_96,X_97))
| least_upper_bound(multiply(X_96,X_97),identity) = positive_part(multiply(X_96,X_97)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_96,X_97),identity),least_upper_bound(identity,multiply(X_96,X_97))) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
least_upper_bound(multiply(X_96,X_97),identity) = positive_part(multiply(X_96,X_97)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_96,X_97)),positive_part(multiply(X_96,X_97))) )],[refute_0_673,refute_0_676]) ).
cnf(refute_0_678,plain,
( multiply(X_96,least_upper_bound(X_97,inverse(X_96))) != least_upper_bound(multiply(X_96,X_97),identity)
| least_upper_bound(multiply(X_96,X_97),identity) != positive_part(multiply(X_96,X_97))
| multiply(X_96,least_upper_bound(X_97,inverse(X_96))) = positive_part(multiply(X_96,X_97)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_96,least_upper_bound(X_97,inverse(X_96))),positive_part(multiply(X_96,X_97))) ),[0],$fot(least_upper_bound(multiply(X_96,X_97),identity))]]) ).
cnf(refute_0_679,plain,
( multiply(X_96,least_upper_bound(X_97,inverse(X_96))) != least_upper_bound(multiply(X_96,X_97),identity)
| multiply(X_96,least_upper_bound(X_97,inverse(X_96))) = positive_part(multiply(X_96,X_97)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_96,X_97),identity),positive_part(multiply(X_96,X_97))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
multiply(X_96,least_upper_bound(X_97,inverse(X_96))) = positive_part(multiply(X_96,X_97)),
inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(X_97,inverse(X_96))),least_upper_bound(multiply(X_96,X_97),identity)) )],[refute_0_672,refute_0_679]) ).
cnf(refute_0_681,plain,
multiply(X_69,least_upper_bound(X_210,inverse(X_69))) = positive_part(multiply(X_69,X_210)),
inference(subst,[],[refute_0_680:[bind(X_96,$fot(X_69)),bind(X_97,$fot(X_210))]]) ).
cnf(refute_0_682,plain,
( multiply(X_69,least_upper_bound(X_210,inverse(X_69))) != positive_part(multiply(X_69,X_210))
| inverse(least_upper_bound(X_210,inverse(X_69))) != multiply(inverse(multiply(X_69,least_upper_bound(X_210,inverse(X_69)))),X_69)
| inverse(least_upper_bound(X_210,inverse(X_69))) = multiply(inverse(positive_part(multiply(X_69,X_210))),X_69) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_210,inverse(X_69))),multiply(inverse(multiply(X_69,least_upper_bound(X_210,inverse(X_69)))),X_69)) ),[1,0,0],$fot(positive_part(multiply(X_69,X_210)))]]) ).
cnf(refute_0_683,plain,
( inverse(least_upper_bound(X_210,inverse(X_69))) != multiply(inverse(multiply(X_69,least_upper_bound(X_210,inverse(X_69)))),X_69)
| inverse(least_upper_bound(X_210,inverse(X_69))) = multiply(inverse(positive_part(multiply(X_69,X_210))),X_69) ),
inference(resolve,[$cnf( $equal(multiply(X_69,least_upper_bound(X_210,inverse(X_69))),positive_part(multiply(X_69,X_210))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
inverse(least_upper_bound(X_210,inverse(X_69))) = multiply(inverse(positive_part(multiply(X_69,X_210))),X_69),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_210,inverse(X_69))),multiply(inverse(multiply(X_69,least_upper_bound(X_210,inverse(X_69)))),X_69)) )],[refute_0_667,refute_0_683]) ).
cnf(refute_0_685,plain,
( inverse(least_upper_bound(X_210,inverse(X_69))) != multiply(inverse(positive_part(multiply(X_69,X_210))),X_69)
| multiply(inverse(positive_part(multiply(X_69,X_210))),X_69) = inverse(least_upper_bound(X_210,inverse(X_69))) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(X_210,inverse(X_69))))),bind(Y0,$fot(multiply(inverse(positive_part(multiply(X_69,X_210))),X_69)))]]) ).
cnf(refute_0_686,plain,
multiply(inverse(positive_part(multiply(X_69,X_210))),X_69) = inverse(least_upper_bound(X_210,inverse(X_69))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_210,inverse(X_69))),multiply(inverse(positive_part(multiply(X_69,X_210))),X_69)) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
multiply(inverse(positive_part(multiply(X_328,X_329))),X_328) = inverse(least_upper_bound(X_329,inverse(X_328))),
inference(subst,[],[refute_0_686:[bind(X_210,$fot(X_329)),bind(X_69,$fot(X_328))]]) ).
cnf(refute_0_688,plain,
inverse(multiply(inverse(X_63),X_75)) = multiply(inverse(X_75),inverse(inverse(X_63))),
inference(subst,[],[refute_0_657:[bind(X_58,$fot(inverse(X_63))),bind(X_59,$fot(X_75))]]) ).
cnf(refute_0_689,plain,
inverse(inverse(X_63)) = multiply(inverse(inverse(X_63)),identity),
inference(subst,[],[refute_0_215:[bind(X_61,$fot(inverse(inverse(X_63))))]]) ).
cnf(refute_0_690,plain,
multiply(X_63,identity) = multiply(inverse(inverse(X_63)),identity),
inference(subst,[],[refute_0_209:[bind(X_60,$fot(X_63)),bind(X_61,$fot(identity))]]) ).
cnf(refute_0_691,plain,
( multiply(X_63,identity) != multiply(inverse(inverse(X_63)),identity)
| multiply(inverse(inverse(X_63)),identity) = multiply(X_63,identity) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(multiply(X_63,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_63)),identity)))]]) ).
cnf(refute_0_692,plain,
multiply(inverse(inverse(X_63)),identity) = multiply(X_63,identity),
inference(resolve,[$cnf( $equal(multiply(X_63,identity),multiply(inverse(inverse(X_63)),identity)) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
( multiply(inverse(inverse(X_63)),identity) != multiply(X_63,identity)
| inverse(inverse(X_63)) != multiply(inverse(inverse(X_63)),identity)
| inverse(inverse(X_63)) = multiply(X_63,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_63)),multiply(inverse(inverse(X_63)),identity)) ),[1],$fot(multiply(X_63,identity))]]) ).
cnf(refute_0_694,plain,
( inverse(inverse(X_63)) != multiply(inverse(inverse(X_63)),identity)
| inverse(inverse(X_63)) = multiply(X_63,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_63)),identity),multiply(X_63,identity)) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
inverse(inverse(X_63)) = multiply(X_63,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_63)),multiply(inverse(inverse(X_63)),identity)) )],[refute_0_689,refute_0_694]) ).
cnf(refute_0_696,plain,
multiply(X_63,identity) = X_63,
inference(subst,[],[refute_0_339:[bind(X_61,$fot(X_63))]]) ).
cnf(refute_0_697,plain,
( multiply(X_63,identity) != X_63
| inverse(inverse(X_63)) != multiply(X_63,identity)
| inverse(inverse(X_63)) = X_63 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_63)),multiply(X_63,identity)) ),[1],$fot(X_63)]]) ).
cnf(refute_0_698,plain,
( inverse(inverse(X_63)) != multiply(X_63,identity)
| inverse(inverse(X_63)) = X_63 ),
inference(resolve,[$cnf( $equal(multiply(X_63,identity),X_63) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
inverse(inverse(X_63)) = X_63,
inference(resolve,[$cnf( $equal(inverse(inverse(X_63)),multiply(X_63,identity)) )],[refute_0_695,refute_0_698]) ).
cnf(refute_0_700,plain,
( inverse(multiply(inverse(X_63),X_75)) != multiply(inverse(X_75),inverse(inverse(X_63)))
| inverse(inverse(X_63)) != X_63
| inverse(multiply(inverse(X_63),X_75)) = multiply(inverse(X_75),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_63),X_75)),multiply(inverse(X_75),inverse(inverse(X_63)))) ),[1,1],$fot(X_63)]]) ).
cnf(refute_0_701,plain,
( inverse(multiply(inverse(X_63),X_75)) != multiply(inverse(X_75),inverse(inverse(X_63)))
| inverse(multiply(inverse(X_63),X_75)) = multiply(inverse(X_75),X_63) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_63)),X_63) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
inverse(multiply(inverse(X_63),X_75)) = multiply(inverse(X_75),X_63),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_63),X_75)),multiply(inverse(X_75),inverse(inverse(X_63)))) )],[refute_0_688,refute_0_701]) ).
cnf(refute_0_703,plain,
inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) = multiply(inverse(positive_part(multiply(X_328,X_329))),X_328),
inference(subst,[],[refute_0_702:[bind(X_63,$fot(X_328)),bind(X_75,$fot(positive_part(multiply(X_328,X_329))))]]) ).
cnf(refute_0_704,plain,
( multiply(inverse(positive_part(multiply(X_328,X_329))),X_328) != inverse(least_upper_bound(X_329,inverse(X_328)))
| inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) != multiply(inverse(positive_part(multiply(X_328,X_329))),X_328)
| inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) = inverse(least_upper_bound(X_329,inverse(X_328))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))))),bind(Y0,$fot(multiply(inverse(positive_part(multiply(X_328,X_329))),X_328))),bind(Z0,$fot(inverse(least_upper_bound(X_329,inverse(X_328)))))]]) ).
cnf(refute_0_705,plain,
( multiply(inverse(positive_part(multiply(X_328,X_329))),X_328) != inverse(least_upper_bound(X_329,inverse(X_328)))
| inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) = inverse(least_upper_bound(X_329,inverse(X_328))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))),multiply(inverse(positive_part(multiply(X_328,X_329))),X_328)) )],[refute_0_703,refute_0_704]) ).
cnf(refute_0_706,plain,
inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) = inverse(least_upper_bound(X_329,inverse(X_328))),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(multiply(X_328,X_329))),X_328),inverse(least_upper_bound(X_329,inverse(X_328)))) )],[refute_0_687,refute_0_705]) ).
cnf(refute_0_707,plain,
( inverse(multiply(X_58,X_59)) != multiply(inverse(X_59),inverse(X_58))
| multiply(inverse(X_59),inverse(X_58)) = inverse(multiply(X_58,X_59)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(multiply(X_58,X_59)))),bind(Y0,$fot(multiply(inverse(X_59),inverse(X_58))))]]) ).
cnf(refute_0_708,plain,
multiply(inverse(X_59),inverse(X_58)) = inverse(multiply(X_58,X_59)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_58,X_59)),multiply(inverse(X_59),inverse(X_58))) )],[refute_0_657,refute_0_707]) ).
cnf(refute_0_709,plain,
multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) = inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))),
inference(subst,[],[refute_0_708:[bind(X_58,$fot(inverse(X_328))),bind(X_59,$fot(positive_part(multiply(X_328,X_329))))]]) ).
cnf(refute_0_710,plain,
( multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) != inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329))))
| inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) != inverse(least_upper_bound(X_329,inverse(X_328)))
| multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) = inverse(least_upper_bound(X_329,inverse(X_328))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))))),bind(Y0,$fot(inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))))),bind(Z0,$fot(inverse(least_upper_bound(X_329,inverse(X_328)))))]]) ).
cnf(refute_0_711,plain,
( inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))) != inverse(least_upper_bound(X_329,inverse(X_328)))
| multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) = inverse(least_upper_bound(X_329,inverse(X_328))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))),inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329))))) )],[refute_0_709,refute_0_710]) ).
cnf(refute_0_712,plain,
multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) = inverse(least_upper_bound(X_329,inverse(X_328))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_328),positive_part(multiply(X_328,X_329)))),inverse(least_upper_bound(X_329,inverse(X_328)))) )],[refute_0_706,refute_0_711]) ).
cnf(refute_0_713,plain,
( multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))) != inverse(least_upper_bound(X_329,inverse(X_328)))
| inverse(least_upper_bound(inverse(X_328),X_329)) != multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))
| inverse(least_upper_bound(inverse(X_328),X_329)) = inverse(least_upper_bound(X_329,inverse(X_328))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_328),X_329)),multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))) ),[1],$fot(inverse(least_upper_bound(X_329,inverse(X_328))))]]) ).
cnf(refute_0_714,plain,
( inverse(least_upper_bound(inverse(X_328),X_329)) != multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))
| inverse(least_upper_bound(inverse(X_328),X_329)) = inverse(least_upper_bound(X_329,inverse(X_328))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328))),inverse(least_upper_bound(X_329,inverse(X_328)))) )],[refute_0_712,refute_0_713]) ).
cnf(refute_0_715,plain,
inverse(least_upper_bound(inverse(X_328),X_329)) = inverse(least_upper_bound(X_329,inverse(X_328))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_328),X_329)),multiply(inverse(positive_part(multiply(X_328,X_329))),inverse(inverse(X_328)))) )],[refute_0_666,refute_0_714]) ).
cnf(refute_0_716,plain,
( inverse(least_upper_bound(inverse(X_328),X_329)) != inverse(least_upper_bound(X_329,inverse(X_328)))
| inverse(least_upper_bound(X_329,inverse(X_328))) = inverse(least_upper_bound(inverse(X_328),X_329)) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(inverse(least_upper_bound(inverse(X_328),X_329)))),bind(Y0,$fot(inverse(least_upper_bound(X_329,inverse(X_328)))))]]) ).
cnf(refute_0_717,plain,
inverse(least_upper_bound(X_329,inverse(X_328))) = inverse(least_upper_bound(inverse(X_328),X_329)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_328),X_329)),inverse(least_upper_bound(X_329,inverse(X_328)))) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))) = inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))),
inference(subst,[],[refute_0_717:[bind(X_328,$fot(positive_part(X_332))),bind(X_329,$fot(negative_part(inverse(X_332))))]]) ).
cnf(refute_0_719,plain,
( inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))) != inverse(negative_part(inverse(X_332)))
| inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))) != inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))))
| inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))) = inverse(negative_part(inverse(X_332))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))))),bind(Y0,$fot(inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))))),bind(Z0,$fot(inverse(negative_part(inverse(X_332)))))]]) ).
cnf(refute_0_720,plain,
( inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))) != inverse(negative_part(inverse(X_332)))
| inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))) = inverse(negative_part(inverse(X_332))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332))))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))) = inverse(negative_part(inverse(X_332))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(positive_part(X_332)),negative_part(inverse(X_332)))),inverse(negative_part(inverse(X_332)))) )],[refute_0_651,refute_0_720]) ).
cnf(refute_0_722,plain,
multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))))]]) ).
cnf(refute_0_723,plain,
( multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) != multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))
| inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))) != inverse(negative_part(inverse(X_332)))
| multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))) ),[1,0],$fot(inverse(negative_part(inverse(X_332))))]]) ).
cnf(refute_0_724,plain,
( inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))) != inverse(negative_part(inverse(X_332)))
| multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),inverse(negative_part(inverse(X_332)))) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
( multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) != multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))
| multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) != multiply(inverse(negative_part(inverse(X_332))),identity)
| multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),identity) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))))),bind(Y0,$fot(multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))))),bind(Z0,$fot(multiply(inverse(negative_part(inverse(X_332))),identity)))]]) ).
cnf(refute_0_727,plain,
( multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) != multiply(inverse(negative_part(inverse(X_332))),identity)
| multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = multiply(inverse(negative_part(inverse(X_332))),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(inverse(X_332))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),multiply(inverse(negative_part(inverse(X_332))),identity)) )],[refute_0_345,refute_0_727]) ).
cnf(refute_0_729,plain,
( multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) != multiply(inverse(negative_part(inverse(X_332))),identity)
| multiply(inverse(negative_part(inverse(X_332))),identity) != inverse(negative_part(inverse(X_332)))
| multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = inverse(negative_part(inverse(X_332))) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))))),bind(Y0,$fot(multiply(inverse(negative_part(inverse(X_332))),identity))),bind(Z0,$fot(inverse(negative_part(inverse(X_332)))))]]) ).
cnf(refute_0_730,plain,
( multiply(inverse(negative_part(inverse(X_332))),identity) != inverse(negative_part(inverse(X_332)))
| multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = inverse(negative_part(inverse(X_332))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),multiply(inverse(negative_part(inverse(X_332))),identity)) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) = inverse(negative_part(inverse(X_332))),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(inverse(X_332))),identity),inverse(negative_part(inverse(X_332)))) )],[refute_0_340,refute_0_730]) ).
cnf(refute_0_732,plain,
( multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))) != inverse(negative_part(inverse(X_332)))
| positive_part(X_332) != multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))
| positive_part(X_332) = inverse(negative_part(inverse(X_332))) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(X_332),multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))) ),[1],$fot(inverse(negative_part(inverse(X_332))))]]) ).
cnf(refute_0_733,plain,
( positive_part(X_332) != multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))
| positive_part(X_332) = inverse(negative_part(inverse(X_332))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332))))),inverse(negative_part(inverse(X_332)))) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
positive_part(X_332) = inverse(negative_part(inverse(X_332))),
inference(resolve,[$cnf( $equal(positive_part(X_332),multiply(inverse(least_upper_bound(negative_part(inverse(X_332)),inverse(positive_part(X_332)))),positive_part(negative_part(least_upper_bound(X_332,inverse(X_332)))))) )],[refute_0_337,refute_0_733]) ).
cnf(refute_0_735,plain,
( positive_part(X_332) != inverse(negative_part(inverse(X_332)))
| inverse(negative_part(inverse(X_332))) = positive_part(X_332) ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(positive_part(X_332))),bind(Y0,$fot(inverse(negative_part(inverse(X_332)))))]]) ).
cnf(refute_0_736,plain,
inverse(negative_part(inverse(X_332))) = positive_part(X_332),
inference(resolve,[$cnf( $equal(positive_part(X_332),inverse(negative_part(inverse(X_332)))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
inverse(negative_part(inverse(X_59))) = positive_part(X_59),
inference(subst,[],[refute_0_736:[bind(X_332,$fot(X_59))]]) ).
cnf(refute_0_738,plain,
multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) = multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)),
introduced(tautology,[refl,[$fot(multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)))]]) ).
cnf(refute_0_739,plain,
( multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) != multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59))
| inverse(negative_part(inverse(X_59))) != positive_part(X_59)
| multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) = multiply(positive_part(X_59),negative_part(X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)),multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59))) ),[1,0],$fot(positive_part(X_59))]]) ).
cnf(refute_0_740,plain,
( inverse(negative_part(inverse(X_59))) != positive_part(X_59)
| multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) = multiply(positive_part(X_59),negative_part(X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)),multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59))) )],[refute_0_738,refute_0_739]) ).
cnf(refute_0_741,plain,
multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) = multiply(positive_part(X_59),negative_part(X_59)),
inference(resolve,[$cnf( $equal(inverse(negative_part(inverse(X_59))),positive_part(X_59)) )],[refute_0_737,refute_0_740]) ).
cnf(refute_0_742,plain,
( X_59 != multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59))
| multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)) != multiply(positive_part(X_59),negative_part(X_59))
| X_59 = multiply(positive_part(X_59),negative_part(X_59)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_59,multiply(positive_part(X_59),negative_part(X_59))) ),[0],$fot(multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)))]]) ).
cnf(refute_0_743,plain,
( X_59 != multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59))
| X_59 = multiply(positive_part(X_59),negative_part(X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59)),multiply(positive_part(X_59),negative_part(X_59))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
X_59 = multiply(positive_part(X_59),negative_part(X_59)),
inference(resolve,[$cnf( $equal(X_59,multiply(inverse(negative_part(inverse(X_59))),negative_part(X_59))) )],[refute_0_46,refute_0_743]) ).
cnf(refute_0_745,plain,
( X_59 != multiply(positive_part(X_59),negative_part(X_59))
| multiply(positive_part(X_59),negative_part(X_59)) = X_59 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(X_59)),bind(Y0,$fot(multiply(positive_part(X_59),negative_part(X_59))))]]) ).
cnf(refute_0_746,plain,
multiply(positive_part(X_59),negative_part(X_59)) = X_59,
inference(resolve,[$cnf( $equal(X_59,multiply(positive_part(X_59),negative_part(X_59))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
multiply(positive_part(a),negative_part(a)) = a,
inference(subst,[],[refute_0_746:[bind(X_59,$fot(a))]]) ).
cnf(refute_0_748,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_749,plain,
( a != a
| a = multiply(positive_part(a),negative_part(a)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(a),negative_part(a)),a) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
a != a,
inference(resolve,[$cnf( $equal(a,multiply(positive_part(a),negative_part(a))) )],[refute_0_749,prove_lat4]) ).
cnf(refute_0_751,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_752,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_751,refute_0_750]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP167-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 10:17:44 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.86/5.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.86/5.06
% 4.86/5.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.94/5.12
%------------------------------------------------------------------------------