TSTP Solution File: GRP114-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 10:35:32 EDT 2022
% Result : Unsatisfiable 1.21s 1.43s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 198
% Syntax : Number of clauses : 795 ( 410 unt; 0 nHn; 389 RR)
% Number of literals : 1349 (1348 equ; 556 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 1077 ( 18 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(inverse_of_identity,axiom,
inverse(identity) = identity ).
cnf(inverse_involution,axiom,
inverse(inverse(X)) = X ).
cnf(inverse_product_lemma,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).
cnf(intersection_commutative,axiom,
intersection(X,Y) = intersection(Y,X) ).
cnf(union_commutative,axiom,
union(X,Y) = union(Y,X) ).
cnf(intersection_associative,axiom,
intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z) ).
cnf(union_associative,axiom,
union(X,union(Y,Z)) = union(union(X,Y),Z) ).
cnf(union_intersection_absorbtion,axiom,
union(intersection(X,Y),Y) = Y ).
cnf(intersection_union_absorbtion,axiom,
intersection(union(X,Y),Y) = Y ).
cnf(multiply_union1,axiom,
multiply(X,union(Y,Z)) = union(multiply(X,Y),multiply(X,Z)) ).
cnf(multiply_intersection1,axiom,
multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)) ).
cnf(multiply_union2,axiom,
multiply(union(Y,Z),X) = union(multiply(Y,X),multiply(Z,X)) ).
cnf(multiply_intersection2,axiom,
multiply(intersection(Y,Z),X) = intersection(multiply(Y,X),multiply(Z,X)) ).
cnf(positive_part,axiom,
positive_part(X) = union(X,identity) ).
cnf(negative_part,axiom,
negative_part(X) = intersection(X,identity) ).
cnf(prove_product,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a ).
cnf(refute_0_0,plain,
multiply(multiply(inverse(X_116),X_116),X_117) = multiply(inverse(X_116),multiply(X_116,X_117)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_116))),bind(Y,$fot(X_116)),bind(Z,$fot(X_117))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_116),X_116) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_116))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(inverse(X_116),X_116),X_117) != multiply(inverse(X_116),multiply(X_116,X_117))
| multiply(inverse(X_116),X_116) != identity
| multiply(identity,X_117) = multiply(inverse(X_116),multiply(X_116,X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_116),X_116),X_117),multiply(inverse(X_116),multiply(X_116,X_117))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_116),X_116),X_117) != multiply(inverse(X_116),multiply(X_116,X_117))
| multiply(identity,X_117) = multiply(inverse(X_116),multiply(X_116,X_117)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_116),X_116),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_117) = multiply(inverse(X_116),multiply(X_116,X_117)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_116),X_116),X_117),multiply(inverse(X_116),multiply(X_116,X_117))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_117) = X_117,
inference(subst,[],[left_identity:[bind(X,$fot(X_117))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_117) != X_117
| multiply(identity,X_117) != multiply(inverse(X_116),multiply(X_116,X_117))
| X_117 = multiply(inverse(X_116),multiply(X_116,X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_117),multiply(inverse(X_116),multiply(X_116,X_117))) ),[0],$fot(X_117)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_117) != multiply(inverse(X_116),multiply(X_116,X_117))
| X_117 = multiply(inverse(X_116),multiply(X_116,X_117)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_117),X_117) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_117 = multiply(inverse(X_116),multiply(X_116,X_117)),
inference(resolve,[$cnf( $equal(multiply(identity,X_117),multiply(inverse(X_116),multiply(X_116,X_117))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
X_119 = multiply(inverse(inverse(positive_part(X_119))),multiply(inverse(positive_part(X_119)),X_119)),
inference(subst,[],[refute_0_8:[bind(X_116,$fot(inverse(positive_part(X_119)))),bind(X_117,$fot(X_119))]]) ).
cnf(refute_0_10,plain,
inverse(multiply(inverse(X),X_29)) = multiply(inverse(X_29),inverse(inverse(X))),
inference(subst,[],[inverse_product_lemma:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_11,plain,
( inverse(multiply(inverse(X),X_29)) != multiply(inverse(X_29),inverse(inverse(X)))
| inverse(inverse(X)) != X
| inverse(multiply(inverse(X),X_29)) = multiply(inverse(X_29),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_29)),multiply(inverse(X_29),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_12,plain,
( inverse(multiply(inverse(X),X_29)) != multiply(inverse(X_29),inverse(inverse(X)))
| inverse(multiply(inverse(X),X_29)) = multiply(inverse(X_29),X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_11]) ).
cnf(refute_0_13,plain,
inverse(multiply(inverse(X),X_29)) = multiply(inverse(X_29),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_29)),multiply(inverse(X_29),inverse(inverse(X)))) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
inverse(multiply(inverse(X),positive_part(inverse(inverse(X))))) = multiply(inverse(positive_part(inverse(inverse(X)))),X),
inference(subst,[],[refute_0_13:[bind(X_29,$fot(positive_part(inverse(inverse(X)))))]]) ).
cnf(refute_0_15,plain,
multiply(X_38,union(X_39,inverse(X_38))) = union(multiply(X_38,X_39),multiply(X_38,inverse(X_38))),
inference(subst,[],[multiply_union1:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(inverse(X_38)))]]) ).
cnf(refute_0_16,plain,
multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).
cnf(refute_0_17,plain,
inverse(inverse(X_1)) = X_1,
inference(subst,[],[inverse_involution:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_18,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| inverse(inverse(X_1)) != X_1
| multiply(X_1,inverse(X_1)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_19,plain,
( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
| multiply(X_1,inverse(X_1)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(X_1,inverse(X_1)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(X_38,inverse(X_38)) = identity,
inference(subst,[],[refute_0_20:[bind(X_1,$fot(X_38))]]) ).
cnf(refute_0_22,plain,
( multiply(X_38,inverse(X_38)) != identity
| multiply(X_38,union(X_39,inverse(X_38))) != union(multiply(X_38,X_39),multiply(X_38,inverse(X_38)))
| multiply(X_38,union(X_39,inverse(X_38))) = union(multiply(X_38,X_39),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_38,union(X_39,inverse(X_38))),union(multiply(X_38,X_39),multiply(X_38,inverse(X_38)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_23,plain,
( multiply(X_38,union(X_39,inverse(X_38))) != union(multiply(X_38,X_39),multiply(X_38,inverse(X_38)))
| multiply(X_38,union(X_39,inverse(X_38))) = union(multiply(X_38,X_39),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(X_38)),identity) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_38,union(X_39,inverse(X_38))) = union(multiply(X_38,X_39),identity),
inference(resolve,[$cnf( $equal(multiply(X_38,union(X_39,inverse(X_38))),union(multiply(X_38,X_39),multiply(X_38,inverse(X_38)))) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_27,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( positive_part(X) != union(X,identity)
| union(X,identity) = positive_part(X) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(positive_part(X))),bind(Y0,$fot(union(X,identity)))]]) ).
cnf(refute_0_29,plain,
union(X,identity) = positive_part(X),
inference(resolve,[$cnf( $equal(positive_part(X),union(X,identity)) )],[positive_part,refute_0_28]) ).
cnf(refute_0_30,plain,
union(multiply(X_38,X_39),identity) = positive_part(multiply(X_38,X_39)),
inference(subst,[],[refute_0_29:[bind(X,$fot(multiply(X_38,X_39)))]]) ).
cnf(refute_0_31,plain,
( multiply(X_38,union(X_39,inverse(X_38))) != union(multiply(X_38,X_39),identity)
| union(multiply(X_38,X_39),identity) != positive_part(multiply(X_38,X_39))
| multiply(X_38,union(X_39,inverse(X_38))) = positive_part(multiply(X_38,X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_38,union(X_39,inverse(X_38))),positive_part(multiply(X_38,X_39))) ),[0],$fot(union(multiply(X_38,X_39),identity))]]) ).
cnf(refute_0_32,plain,
( multiply(X_38,union(X_39,inverse(X_38))) != union(multiply(X_38,X_39),identity)
| multiply(X_38,union(X_39,inverse(X_38))) = positive_part(multiply(X_38,X_39)) ),
inference(resolve,[$cnf( $equal(union(multiply(X_38,X_39),identity),positive_part(multiply(X_38,X_39))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_38,union(X_39,inverse(X_38))) = positive_part(multiply(X_38,X_39)),
inference(resolve,[$cnf( $equal(multiply(X_38,union(X_39,inverse(X_38))),union(multiply(X_38,X_39),identity)) )],[refute_0_24,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(X_41,union(identity,inverse(X_41))) = positive_part(multiply(X_41,identity)),
inference(subst,[],[refute_0_33:[bind(X_38,$fot(X_41)),bind(X_39,$fot(identity))]]) ).
cnf(refute_0_35,plain,
union(X,identity) = union(identity,X),
inference(subst,[],[union_commutative:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_36,plain,
( positive_part(X) != union(X,identity)
| union(X,identity) != union(identity,X)
| positive_part(X) = union(identity,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(positive_part(X),union(identity,X)) ),[0],$fot(union(X,identity))]]) ).
cnf(refute_0_37,plain,
( positive_part(X) != union(X,identity)
| positive_part(X) = union(identity,X) ),
inference(resolve,[$cnf( $equal(union(X,identity),union(identity,X)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
positive_part(X) = union(identity,X),
inference(resolve,[$cnf( $equal(positive_part(X),union(X,identity)) )],[positive_part,refute_0_37]) ).
cnf(refute_0_39,plain,
positive_part(inverse(X_41)) = union(identity,inverse(X_41)),
inference(subst,[],[refute_0_38:[bind(X,$fot(inverse(X_41)))]]) ).
cnf(refute_0_40,plain,
( positive_part(inverse(X_41)) != union(identity,inverse(X_41))
| union(identity,inverse(X_41)) = positive_part(inverse(X_41)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(positive_part(inverse(X_41)))),bind(Y0,$fot(union(identity,inverse(X_41))))]]) ).
cnf(refute_0_41,plain,
union(identity,inverse(X_41)) = positive_part(inverse(X_41)),
inference(resolve,[$cnf( $equal(positive_part(inverse(X_41)),union(identity,inverse(X_41))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( multiply(X_41,union(identity,inverse(X_41))) != positive_part(multiply(X_41,identity))
| union(identity,inverse(X_41)) != positive_part(inverse(X_41))
| multiply(X_41,positive_part(inverse(X_41))) = positive_part(multiply(X_41,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_41,union(identity,inverse(X_41))),positive_part(multiply(X_41,identity))) ),[0,1],$fot(positive_part(inverse(X_41)))]]) ).
cnf(refute_0_43,plain,
( multiply(X_41,union(identity,inverse(X_41))) != positive_part(multiply(X_41,identity))
| multiply(X_41,positive_part(inverse(X_41))) = positive_part(multiply(X_41,identity)) ),
inference(resolve,[$cnf( $equal(union(identity,inverse(X_41)),positive_part(inverse(X_41))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(X_41,positive_part(inverse(X_41))) = positive_part(multiply(X_41,identity)),
inference(resolve,[$cnf( $equal(multiply(X_41,union(identity,inverse(X_41))),positive_part(multiply(X_41,identity))) )],[refute_0_34,refute_0_43]) ).
cnf(refute_0_45,plain,
inverse(multiply(identity,X_29)) = multiply(inverse(X_29),inverse(identity)),
inference(subst,[],[inverse_product_lemma:[bind(X,$fot(identity)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_46,plain,
( inverse(multiply(identity,X_29)) != multiply(inverse(X_29),inverse(identity))
| inverse(identity) != identity
| inverse(multiply(identity,X_29)) = multiply(inverse(X_29),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_29)),multiply(inverse(X_29),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_47,plain,
( inverse(multiply(identity,X_29)) != multiply(inverse(X_29),inverse(identity))
| inverse(multiply(identity,X_29)) = multiply(inverse(X_29),identity) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[inverse_of_identity,refute_0_46]) ).
cnf(refute_0_48,plain,
inverse(multiply(identity,X_29)) = multiply(inverse(X_29),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_29)),multiply(inverse(X_29),inverse(identity))) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(identity,X_29) = X_29,
inference(subst,[],[left_identity:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_50,plain,
inverse(multiply(identity,X_29)) = inverse(multiply(identity,X_29)),
introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_29)))]]) ).
cnf(refute_0_51,plain,
( multiply(identity,X_29) != X_29
| inverse(multiply(identity,X_29)) != inverse(multiply(identity,X_29))
| inverse(multiply(identity,X_29)) = inverse(X_29) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_29)),inverse(multiply(identity,X_29))) ),[1,0],$fot(X_29)]]) ).
cnf(refute_0_52,plain,
( multiply(identity,X_29) != X_29
| inverse(multiply(identity,X_29)) = inverse(X_29) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_29)),inverse(multiply(identity,X_29))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
inverse(multiply(identity,X_29)) = inverse(X_29),
inference(resolve,[$cnf( $equal(multiply(identity,X_29),X_29) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
( inverse(multiply(identity,X_29)) != multiply(inverse(X_29),identity)
| inverse(multiply(identity,X_29)) != inverse(X_29)
| inverse(X_29) = multiply(inverse(X_29),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_29)),multiply(inverse(X_29),identity)) ),[0],$fot(inverse(X_29))]]) ).
cnf(refute_0_55,plain,
( inverse(multiply(identity,X_29)) != multiply(inverse(X_29),identity)
| inverse(X_29) = multiply(inverse(X_29),identity) ),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_29)),inverse(X_29)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
inverse(X_29) = multiply(inverse(X_29),identity),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_29)),multiply(inverse(X_29),identity)) )],[refute_0_48,refute_0_55]) ).
cnf(refute_0_57,plain,
inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
inference(subst,[],[refute_0_56:[bind(X_29,$fot(inverse(X)))]]) ).
cnf(refute_0_58,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_59,plain,
( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
| inverse(inverse(X)) = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_58]) ).
cnf(refute_0_60,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_57,refute_0_59]) ).
cnf(refute_0_61,plain,
( inverse(inverse(X)) != X
| inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) ),[0],$fot(X)]]) ).
cnf(refute_0_62,plain,
( inverse(inverse(X)) != multiply(X,identity)
| X = multiply(X,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_61]) ).
cnf(refute_0_63,plain,
X = multiply(X,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_60,refute_0_62]) ).
cnf(refute_0_64,plain,
( X != multiply(X,identity)
| multiply(X,identity) = X ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).
cnf(refute_0_65,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(X_41,identity) = X_41,
inference(subst,[],[refute_0_65:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_67,plain,
positive_part(multiply(X_41,identity)) = positive_part(multiply(X_41,identity)),
introduced(tautology,[refl,[$fot(positive_part(multiply(X_41,identity)))]]) ).
cnf(refute_0_68,plain,
( multiply(X_41,identity) != X_41
| positive_part(multiply(X_41,identity)) != positive_part(multiply(X_41,identity))
| positive_part(multiply(X_41,identity)) = positive_part(X_41) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(multiply(X_41,identity)),positive_part(multiply(X_41,identity))) ),[1,0],$fot(X_41)]]) ).
cnf(refute_0_69,plain,
( multiply(X_41,identity) != X_41
| positive_part(multiply(X_41,identity)) = positive_part(X_41) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(X_41,identity)),positive_part(multiply(X_41,identity))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
positive_part(multiply(X_41,identity)) = positive_part(X_41),
inference(resolve,[$cnf( $equal(multiply(X_41,identity),X_41) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( multiply(X_41,positive_part(inverse(X_41))) != positive_part(multiply(X_41,identity))
| positive_part(multiply(X_41,identity)) != positive_part(X_41)
| multiply(X_41,positive_part(inverse(X_41))) = positive_part(X_41) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_41,positive_part(inverse(X_41))),positive_part(X_41)) ),[0],$fot(positive_part(multiply(X_41,identity)))]]) ).
cnf(refute_0_72,plain,
( multiply(X_41,positive_part(inverse(X_41))) != positive_part(multiply(X_41,identity))
| multiply(X_41,positive_part(inverse(X_41))) = positive_part(X_41) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(X_41,identity)),positive_part(X_41)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(X_41,positive_part(inverse(X_41))) = positive_part(X_41),
inference(resolve,[$cnf( $equal(multiply(X_41,positive_part(inverse(X_41))),positive_part(multiply(X_41,identity))) )],[refute_0_44,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(X),positive_part(inverse(inverse(X)))) = positive_part(inverse(X)),
inference(subst,[],[refute_0_73:[bind(X_41,$fot(inverse(X)))]]) ).
cnf(refute_0_75,plain,
( multiply(inverse(X),positive_part(inverse(inverse(X)))) != positive_part(inverse(X))
| inverse(multiply(inverse(X),positive_part(inverse(inverse(X))))) != multiply(inverse(positive_part(inverse(inverse(X)))),X)
| inverse(positive_part(inverse(X))) = multiply(inverse(positive_part(inverse(inverse(X)))),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),positive_part(inverse(inverse(X))))),multiply(inverse(positive_part(inverse(inverse(X)))),X)) ),[0,0],$fot(positive_part(inverse(X)))]]) ).
cnf(refute_0_76,plain,
( inverse(multiply(inverse(X),positive_part(inverse(inverse(X))))) != multiply(inverse(positive_part(inverse(inverse(X)))),X)
| inverse(positive_part(inverse(X))) = multiply(inverse(positive_part(inverse(inverse(X)))),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),positive_part(inverse(inverse(X)))),positive_part(inverse(X))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
inverse(positive_part(inverse(X))) = multiply(inverse(positive_part(inverse(inverse(X)))),X),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),positive_part(inverse(inverse(X))))),multiply(inverse(positive_part(inverse(inverse(X)))),X)) )],[refute_0_14,refute_0_76]) ).
cnf(refute_0_78,plain,
positive_part(inverse(inverse(X))) = positive_part(inverse(inverse(X))),
introduced(tautology,[refl,[$fot(positive_part(inverse(inverse(X))))]]) ).
cnf(refute_0_79,plain,
( inverse(inverse(X)) != X
| positive_part(inverse(inverse(X))) != positive_part(inverse(inverse(X)))
| positive_part(inverse(inverse(X))) = positive_part(X) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(inverse(inverse(X))),positive_part(inverse(inverse(X)))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_80,plain,
( inverse(inverse(X)) != X
| positive_part(inverse(inverse(X))) = positive_part(X) ),
inference(resolve,[$cnf( $equal(positive_part(inverse(inverse(X))),positive_part(inverse(inverse(X)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
positive_part(inverse(inverse(X))) = positive_part(X),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_80]) ).
cnf(refute_0_82,plain,
inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(inverse(inverse(X)))),
introduced(tautology,[refl,[$fot(inverse(positive_part(inverse(inverse(X)))))]]) ).
cnf(refute_0_83,plain,
( inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(inverse(inverse(X))))
| positive_part(inverse(inverse(X))) != positive_part(X)
| inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(X)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(positive_part(inverse(inverse(X)))),inverse(positive_part(inverse(inverse(X))))) ),[1,0],$fot(positive_part(X))]]) ).
cnf(refute_0_84,plain,
( positive_part(inverse(inverse(X))) != positive_part(X)
| inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(inverse(X)))),inverse(positive_part(inverse(inverse(X))))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(positive_part(inverse(inverse(X))),positive_part(X)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(inverse(positive_part(inverse(inverse(X)))),X) = multiply(inverse(positive_part(inverse(inverse(X)))),X),
introduced(tautology,[refl,[$fot(multiply(inverse(positive_part(inverse(inverse(X)))),X))]]) ).
cnf(refute_0_87,plain,
( multiply(inverse(positive_part(inverse(inverse(X)))),X) != multiply(inverse(positive_part(inverse(inverse(X)))),X)
| inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(X))
| multiply(inverse(positive_part(inverse(inverse(X)))),X) = multiply(inverse(positive_part(X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(positive_part(inverse(inverse(X)))),X),multiply(inverse(positive_part(inverse(inverse(X)))),X)) ),[1,0],$fot(inverse(positive_part(X)))]]) ).
cnf(refute_0_88,plain,
( inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(X))
| multiply(inverse(positive_part(inverse(inverse(X)))),X) = multiply(inverse(positive_part(X)),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(inverse(inverse(X)))),X),multiply(inverse(positive_part(inverse(inverse(X)))),X)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(inverse(positive_part(inverse(inverse(X)))),X) = multiply(inverse(positive_part(X)),X),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(inverse(X)))),inverse(positive_part(X))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( multiply(inverse(positive_part(inverse(inverse(X)))),X) != multiply(inverse(positive_part(X)),X)
| inverse(positive_part(inverse(X))) != multiply(inverse(positive_part(inverse(inverse(X)))),X)
| inverse(positive_part(inverse(X))) = multiply(inverse(positive_part(X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(positive_part(inverse(X))),multiply(inverse(positive_part(inverse(inverse(X)))),X)) ),[1],$fot(multiply(inverse(positive_part(X)),X))]]) ).
cnf(refute_0_91,plain,
( inverse(positive_part(inverse(X))) != multiply(inverse(positive_part(inverse(inverse(X)))),X)
| inverse(positive_part(inverse(X))) = multiply(inverse(positive_part(X)),X) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(inverse(inverse(X)))),X),multiply(inverse(positive_part(X)),X)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
inverse(positive_part(inverse(X))) = multiply(inverse(positive_part(X)),X),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X))),multiply(inverse(positive_part(inverse(inverse(X)))),X)) )],[refute_0_77,refute_0_91]) ).
cnf(refute_0_93,plain,
inverse(positive_part(inverse(X_119))) = multiply(inverse(positive_part(X_119)),X_119),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_119))]]) ).
cnf(refute_0_94,plain,
( inverse(positive_part(inverse(X_119))) != multiply(inverse(positive_part(X_119)),X_119)
| multiply(inverse(positive_part(X_119)),X_119) = inverse(positive_part(inverse(X_119))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(positive_part(inverse(X_119))))),bind(Y0,$fot(multiply(inverse(positive_part(X_119)),X_119)))]]) ).
cnf(refute_0_95,plain,
multiply(inverse(positive_part(X_119)),X_119) = inverse(positive_part(inverse(X_119))),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X_119))),multiply(inverse(positive_part(X_119)),X_119)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( X_119 != multiply(inverse(inverse(positive_part(X_119))),multiply(inverse(positive_part(X_119)),X_119))
| multiply(inverse(positive_part(X_119)),X_119) != inverse(positive_part(inverse(X_119)))
| X_119 = multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_119,multiply(inverse(inverse(positive_part(X_119))),multiply(inverse(positive_part(X_119)),X_119))) ),[1,1],$fot(inverse(positive_part(inverse(X_119))))]]) ).
cnf(refute_0_97,plain,
( X_119 != multiply(inverse(inverse(positive_part(X_119))),multiply(inverse(positive_part(X_119)),X_119))
| X_119 = multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_119)),X_119),inverse(positive_part(inverse(X_119)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
X_119 = multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))),
inference(resolve,[$cnf( $equal(X_119,multiply(inverse(inverse(positive_part(X_119))),multiply(inverse(positive_part(X_119)),X_119))) )],[refute_0_9,refute_0_97]) ).
cnf(refute_0_99,plain,
inverse(multiply(X_28,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_28)),
inference(subst,[],[inverse_product_lemma:[bind(X,$fot(X_28)),bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_100,plain,
( inverse(multiply(X_28,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_28))
| inverse(inverse(X)) != X
| inverse(multiply(X_28,inverse(X))) = multiply(X,inverse(X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_28,inverse(X))),multiply(inverse(inverse(X)),inverse(X_28))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_101,plain,
( inverse(multiply(X_28,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_28))
| inverse(multiply(X_28,inverse(X))) = multiply(X,inverse(X_28)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_100]) ).
cnf(refute_0_102,plain,
inverse(multiply(X_28,inverse(X))) = multiply(X,inverse(X_28)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_28,inverse(X))),multiply(inverse(inverse(X)),inverse(X_28))) )],[refute_0_99,refute_0_101]) ).
cnf(refute_0_103,plain,
inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119)))) = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))),
inference(subst,[],[refute_0_102:[bind(X,$fot(positive_part(X_119))),bind(X_28,$fot(positive_part(inverse(X_119))))]]) ).
cnf(refute_0_104,plain,
( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
| multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).
cnf(refute_0_105,plain,
multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[inverse_product_lemma,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) = inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119)))),
inference(subst,[],[refute_0_105:[bind(X,$fot(positive_part(inverse(X_119)))),bind(Y,$fot(inverse(positive_part(X_119))))]]) ).
cnf(refute_0_107,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_108,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_27,refute_0_107]) ).
cnf(refute_0_109,plain,
( multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) != inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119))))
| inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119)))) != multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))
| multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))))),bind(Y0,$fot(inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119)))))),bind(Z0,$fot(multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))))]]) ).
cnf(refute_0_110,plain,
( inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119)))) != multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))
| multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))),inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119))))) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))),
inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(inverse(X_119)),inverse(positive_part(X_119)))),multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))) )],[refute_0_103,refute_0_110]) ).
cnf(refute_0_112,plain,
( X_119 != multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119))))
| multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))) != multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))
| X_119 = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_119,multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))) ),[0],$fot(multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))))]]) ).
cnf(refute_0_113,plain,
( X_119 != multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119))))
| X_119 = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119)))),multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
X_119 = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))),
inference(resolve,[$cnf( $equal(X_119,multiply(inverse(inverse(positive_part(X_119))),inverse(positive_part(inverse(X_119))))) )],[refute_0_98,refute_0_113]) ).
cnf(refute_0_115,plain,
multiply(X_52,intersection(X_53,inverse(X_52))) = intersection(multiply(X_52,X_53),multiply(X_52,inverse(X_52))),
inference(subst,[],[multiply_intersection1:[bind(X,$fot(X_52)),bind(Y,$fot(X_53)),bind(Z,$fot(inverse(X_52)))]]) ).
cnf(refute_0_116,plain,
multiply(X_52,inverse(X_52)) = identity,
inference(subst,[],[refute_0_20:[bind(X_1,$fot(X_52))]]) ).
cnf(refute_0_117,plain,
( multiply(X_52,intersection(X_53,inverse(X_52))) != intersection(multiply(X_52,X_53),multiply(X_52,inverse(X_52)))
| multiply(X_52,inverse(X_52)) != identity
| multiply(X_52,intersection(X_53,inverse(X_52))) = intersection(multiply(X_52,X_53),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_52,intersection(X_53,inverse(X_52))),intersection(multiply(X_52,X_53),multiply(X_52,inverse(X_52)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_118,plain,
( multiply(X_52,intersection(X_53,inverse(X_52))) != intersection(multiply(X_52,X_53),multiply(X_52,inverse(X_52)))
| multiply(X_52,intersection(X_53,inverse(X_52))) = intersection(multiply(X_52,X_53),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_52,inverse(X_52)),identity) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
multiply(X_52,intersection(X_53,inverse(X_52))) = intersection(multiply(X_52,X_53),identity),
inference(resolve,[$cnf( $equal(multiply(X_52,intersection(X_53,inverse(X_52))),intersection(multiply(X_52,X_53),multiply(X_52,inverse(X_52)))) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
( negative_part(X) != intersection(X,identity)
| intersection(X,identity) = negative_part(X) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(intersection(X,identity)))]]) ).
cnf(refute_0_121,plain,
intersection(X,identity) = negative_part(X),
inference(resolve,[$cnf( $equal(negative_part(X),intersection(X,identity)) )],[negative_part,refute_0_120]) ).
cnf(refute_0_122,plain,
intersection(multiply(X_52,X_53),identity) = negative_part(multiply(X_52,X_53)),
inference(subst,[],[refute_0_121:[bind(X,$fot(multiply(X_52,X_53)))]]) ).
cnf(refute_0_123,plain,
( multiply(X_52,intersection(X_53,inverse(X_52))) != intersection(multiply(X_52,X_53),identity)
| intersection(multiply(X_52,X_53),identity) != negative_part(multiply(X_52,X_53))
| multiply(X_52,intersection(X_53,inverse(X_52))) = negative_part(multiply(X_52,X_53)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_52,intersection(X_53,inverse(X_52))),negative_part(multiply(X_52,X_53))) ),[0],$fot(intersection(multiply(X_52,X_53),identity))]]) ).
cnf(refute_0_124,plain,
( multiply(X_52,intersection(X_53,inverse(X_52))) != intersection(multiply(X_52,X_53),identity)
| multiply(X_52,intersection(X_53,inverse(X_52))) = negative_part(multiply(X_52,X_53)) ),
inference(resolve,[$cnf( $equal(intersection(multiply(X_52,X_53),identity),negative_part(multiply(X_52,X_53))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
multiply(X_52,intersection(X_53,inverse(X_52))) = negative_part(multiply(X_52,X_53)),
inference(resolve,[$cnf( $equal(multiply(X_52,intersection(X_53,inverse(X_52))),intersection(multiply(X_52,X_53),identity)) )],[refute_0_119,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(X_55,intersection(identity,inverse(X_55))) = negative_part(multiply(X_55,identity)),
inference(subst,[],[refute_0_125:[bind(X_52,$fot(X_55)),bind(X_53,$fot(identity))]]) ).
cnf(refute_0_127,plain,
intersection(X,identity) = intersection(identity,X),
inference(subst,[],[intersection_commutative:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_128,plain,
( intersection(X,identity) != intersection(identity,X)
| negative_part(X) != intersection(X,identity)
| negative_part(X) = intersection(identity,X) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(X),intersection(X,identity)) ),[1],$fot(intersection(identity,X))]]) ).
cnf(refute_0_129,plain,
( negative_part(X) != intersection(X,identity)
| negative_part(X) = intersection(identity,X) ),
inference(resolve,[$cnf( $equal(intersection(X,identity),intersection(identity,X)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
negative_part(X) = intersection(identity,X),
inference(resolve,[$cnf( $equal(negative_part(X),intersection(X,identity)) )],[negative_part,refute_0_129]) ).
cnf(refute_0_131,plain,
negative_part(inverse(X_55)) = intersection(identity,inverse(X_55)),
inference(subst,[],[refute_0_130:[bind(X,$fot(inverse(X_55)))]]) ).
cnf(refute_0_132,plain,
( negative_part(inverse(X_55)) != intersection(identity,inverse(X_55))
| intersection(identity,inverse(X_55)) = negative_part(inverse(X_55)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(inverse(X_55)))),bind(Y0,$fot(intersection(identity,inverse(X_55))))]]) ).
cnf(refute_0_133,plain,
intersection(identity,inverse(X_55)) = negative_part(inverse(X_55)),
inference(resolve,[$cnf( $equal(negative_part(inverse(X_55)),intersection(identity,inverse(X_55))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( multiply(X_55,intersection(identity,inverse(X_55))) != negative_part(multiply(X_55,identity))
| intersection(identity,inverse(X_55)) != negative_part(inverse(X_55))
| multiply(X_55,negative_part(inverse(X_55))) = negative_part(multiply(X_55,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,intersection(identity,inverse(X_55))),negative_part(multiply(X_55,identity))) ),[0,1],$fot(negative_part(inverse(X_55)))]]) ).
cnf(refute_0_135,plain,
( multiply(X_55,intersection(identity,inverse(X_55))) != negative_part(multiply(X_55,identity))
| multiply(X_55,negative_part(inverse(X_55))) = negative_part(multiply(X_55,identity)) ),
inference(resolve,[$cnf( $equal(intersection(identity,inverse(X_55)),negative_part(inverse(X_55))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
multiply(X_55,negative_part(inverse(X_55))) = negative_part(multiply(X_55,identity)),
inference(resolve,[$cnf( $equal(multiply(X_55,intersection(identity,inverse(X_55))),negative_part(multiply(X_55,identity))) )],[refute_0_126,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(X_55,identity) = X_55,
inference(subst,[],[refute_0_65:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_138,plain,
negative_part(multiply(X_55,identity)) = negative_part(multiply(X_55,identity)),
introduced(tautology,[refl,[$fot(negative_part(multiply(X_55,identity)))]]) ).
cnf(refute_0_139,plain,
( multiply(X_55,identity) != X_55
| negative_part(multiply(X_55,identity)) != negative_part(multiply(X_55,identity))
| negative_part(multiply(X_55,identity)) = negative_part(X_55) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(multiply(X_55,identity)),negative_part(multiply(X_55,identity))) ),[1,0],$fot(X_55)]]) ).
cnf(refute_0_140,plain,
( multiply(X_55,identity) != X_55
| negative_part(multiply(X_55,identity)) = negative_part(X_55) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(X_55,identity)),negative_part(multiply(X_55,identity))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
negative_part(multiply(X_55,identity)) = negative_part(X_55),
inference(resolve,[$cnf( $equal(multiply(X_55,identity),X_55) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( multiply(X_55,negative_part(inverse(X_55))) != negative_part(multiply(X_55,identity))
| negative_part(multiply(X_55,identity)) != negative_part(X_55)
| multiply(X_55,negative_part(inverse(X_55))) = negative_part(X_55) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_55,negative_part(inverse(X_55))),negative_part(X_55)) ),[0],$fot(negative_part(multiply(X_55,identity)))]]) ).
cnf(refute_0_143,plain,
( multiply(X_55,negative_part(inverse(X_55))) != negative_part(multiply(X_55,identity))
| multiply(X_55,negative_part(inverse(X_55))) = negative_part(X_55) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(X_55,identity)),negative_part(X_55)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
multiply(X_55,negative_part(inverse(X_55))) = negative_part(X_55),
inference(resolve,[$cnf( $equal(multiply(X_55,negative_part(inverse(X_55))),negative_part(multiply(X_55,identity))) )],[refute_0_136,refute_0_143]) ).
cnf(refute_0_145,plain,
inverse(multiply(positive_part(X_109),inverse(X_109))) = multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))),
inference(subst,[],[inverse_product_lemma:[bind(X,$fot(positive_part(X_109))),bind(Y,$fot(inverse(X_109)))]]) ).
cnf(refute_0_146,plain,
multiply(union(X_61,inverse(X_60)),X_60) = union(multiply(X_61,X_60),multiply(inverse(X_60),X_60)),
inference(subst,[],[multiply_union2:[bind(X,$fot(X_60)),bind(Y,$fot(X_61)),bind(Z,$fot(inverse(X_60)))]]) ).
cnf(refute_0_147,plain,
multiply(inverse(X_60),X_60) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_60))]]) ).
cnf(refute_0_148,plain,
( multiply(inverse(X_60),X_60) != identity
| multiply(union(X_61,inverse(X_60)),X_60) != union(multiply(X_61,X_60),multiply(inverse(X_60),X_60))
| multiply(union(X_61,inverse(X_60)),X_60) = union(multiply(X_61,X_60),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(X_61,inverse(X_60)),X_60),union(multiply(X_61,X_60),multiply(inverse(X_60),X_60))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_149,plain,
( multiply(union(X_61,inverse(X_60)),X_60) != union(multiply(X_61,X_60),multiply(inverse(X_60),X_60))
| multiply(union(X_61,inverse(X_60)),X_60) = union(multiply(X_61,X_60),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_60),X_60),identity) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(union(X_61,inverse(X_60)),X_60) = union(multiply(X_61,X_60),identity),
inference(resolve,[$cnf( $equal(multiply(union(X_61,inverse(X_60)),X_60),union(multiply(X_61,X_60),multiply(inverse(X_60),X_60))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
union(multiply(X_61,X_60),identity) = positive_part(multiply(X_61,X_60)),
inference(subst,[],[refute_0_29:[bind(X,$fot(multiply(X_61,X_60)))]]) ).
cnf(refute_0_152,plain,
( multiply(union(X_61,inverse(X_60)),X_60) != union(multiply(X_61,X_60),identity)
| union(multiply(X_61,X_60),identity) != positive_part(multiply(X_61,X_60))
| multiply(union(X_61,inverse(X_60)),X_60) = positive_part(multiply(X_61,X_60)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(union(X_61,inverse(X_60)),X_60),positive_part(multiply(X_61,X_60))) ),[0],$fot(union(multiply(X_61,X_60),identity))]]) ).
cnf(refute_0_153,plain,
( multiply(union(X_61,inverse(X_60)),X_60) != union(multiply(X_61,X_60),identity)
| multiply(union(X_61,inverse(X_60)),X_60) = positive_part(multiply(X_61,X_60)) ),
inference(resolve,[$cnf( $equal(union(multiply(X_61,X_60),identity),positive_part(multiply(X_61,X_60))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(union(X_61,inverse(X_60)),X_60) = positive_part(multiply(X_61,X_60)),
inference(resolve,[$cnf( $equal(multiply(union(X_61,inverse(X_60)),X_60),union(multiply(X_61,X_60),identity)) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
multiply(union(identity,inverse(X_72)),X_72) = positive_part(multiply(identity,X_72)),
inference(subst,[],[refute_0_154:[bind(X_60,$fot(X_72)),bind(X_61,$fot(identity))]]) ).
cnf(refute_0_156,plain,
positive_part(inverse(X_72)) = union(identity,inverse(X_72)),
inference(subst,[],[refute_0_38:[bind(X,$fot(inverse(X_72)))]]) ).
cnf(refute_0_157,plain,
( positive_part(inverse(X_72)) != union(identity,inverse(X_72))
| union(identity,inverse(X_72)) = positive_part(inverse(X_72)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(positive_part(inverse(X_72)))),bind(Y0,$fot(union(identity,inverse(X_72))))]]) ).
cnf(refute_0_158,plain,
union(identity,inverse(X_72)) = positive_part(inverse(X_72)),
inference(resolve,[$cnf( $equal(positive_part(inverse(X_72)),union(identity,inverse(X_72))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( multiply(union(identity,inverse(X_72)),X_72) != positive_part(multiply(identity,X_72))
| union(identity,inverse(X_72)) != positive_part(inverse(X_72))
| multiply(positive_part(inverse(X_72)),X_72) = positive_part(multiply(identity,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(identity,inverse(X_72)),X_72),positive_part(multiply(identity,X_72))) ),[0,0],$fot(positive_part(inverse(X_72)))]]) ).
cnf(refute_0_160,plain,
( multiply(union(identity,inverse(X_72)),X_72) != positive_part(multiply(identity,X_72))
| multiply(positive_part(inverse(X_72)),X_72) = positive_part(multiply(identity,X_72)) ),
inference(resolve,[$cnf( $equal(union(identity,inverse(X_72)),positive_part(inverse(X_72))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
multiply(positive_part(inverse(X_72)),X_72) = positive_part(multiply(identity,X_72)),
inference(resolve,[$cnf( $equal(multiply(union(identity,inverse(X_72)),X_72),positive_part(multiply(identity,X_72))) )],[refute_0_155,refute_0_160]) ).
cnf(refute_0_162,plain,
multiply(identity,X_72) = X_72,
inference(subst,[],[left_identity:[bind(X,$fot(X_72))]]) ).
cnf(refute_0_163,plain,
positive_part(multiply(identity,X_72)) = positive_part(multiply(identity,X_72)),
introduced(tautology,[refl,[$fot(positive_part(multiply(identity,X_72)))]]) ).
cnf(refute_0_164,plain,
( multiply(identity,X_72) != X_72
| positive_part(multiply(identity,X_72)) != positive_part(multiply(identity,X_72))
| positive_part(multiply(identity,X_72)) = positive_part(X_72) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(multiply(identity,X_72)),positive_part(multiply(identity,X_72))) ),[1,0],$fot(X_72)]]) ).
cnf(refute_0_165,plain,
( multiply(identity,X_72) != X_72
| positive_part(multiply(identity,X_72)) = positive_part(X_72) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(identity,X_72)),positive_part(multiply(identity,X_72))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
positive_part(multiply(identity,X_72)) = positive_part(X_72),
inference(resolve,[$cnf( $equal(multiply(identity,X_72),X_72) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
( multiply(positive_part(inverse(X_72)),X_72) != positive_part(multiply(identity,X_72))
| positive_part(multiply(identity,X_72)) != positive_part(X_72)
| multiply(positive_part(inverse(X_72)),X_72) = positive_part(X_72) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(inverse(X_72)),X_72),positive_part(X_72)) ),[0],$fot(positive_part(multiply(identity,X_72)))]]) ).
cnf(refute_0_168,plain,
( multiply(positive_part(inverse(X_72)),X_72) != positive_part(multiply(identity,X_72))
| multiply(positive_part(inverse(X_72)),X_72) = positive_part(X_72) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(identity,X_72)),positive_part(X_72)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(positive_part(inverse(X_72)),X_72) = positive_part(X_72),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_72)),X_72),positive_part(multiply(identity,X_72))) )],[refute_0_161,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(positive_part(inverse(inverse(X))),inverse(X)) = positive_part(inverse(X)),
inference(subst,[],[refute_0_169:[bind(X_72,$fot(inverse(X)))]]) ).
cnf(refute_0_171,plain,
( multiply(positive_part(inverse(inverse(X))),inverse(X)) != positive_part(inverse(X))
| inverse(inverse(X)) != X
| multiply(positive_part(X),inverse(X)) = positive_part(inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(inverse(X))),inverse(X)),positive_part(inverse(X))) ),[0,0,0],$fot(X)]]) ).
cnf(refute_0_172,plain,
( multiply(positive_part(inverse(inverse(X))),inverse(X)) != positive_part(inverse(X))
| multiply(positive_part(X),inverse(X)) = positive_part(inverse(X)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(positive_part(X),inverse(X)) = positive_part(inverse(X)),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(inverse(X))),inverse(X)),positive_part(inverse(X))) )],[refute_0_170,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(positive_part(X_109),inverse(X_109)) = positive_part(inverse(X_109)),
inference(subst,[],[refute_0_173:[bind(X,$fot(X_109))]]) ).
cnf(refute_0_175,plain,
( multiply(positive_part(X_109),inverse(X_109)) != positive_part(inverse(X_109))
| inverse(multiply(positive_part(X_109),inverse(X_109))) != multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))
| inverse(positive_part(inverse(X_109))) = multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(positive_part(X_109),inverse(X_109))),multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))) ),[0,0],$fot(positive_part(inverse(X_109)))]]) ).
cnf(refute_0_176,plain,
( inverse(multiply(positive_part(X_109),inverse(X_109))) != multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))
| inverse(positive_part(inverse(X_109))) = multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_109),inverse(X_109)),positive_part(inverse(X_109))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
inverse(positive_part(inverse(X_109))) = multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))),
inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(X_109),inverse(X_109))),multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))) )],[refute_0_145,refute_0_176]) ).
cnf(refute_0_178,plain,
inverse(multiply(positive_part(X_109),inverse(X_109))) = multiply(X_109,inverse(positive_part(X_109))),
inference(subst,[],[refute_0_102:[bind(X,$fot(X_109)),bind(X_28,$fot(positive_part(X_109)))]]) ).
cnf(refute_0_179,plain,
multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) = inverse(multiply(positive_part(X_109),inverse(X_109))),
inference(subst,[],[refute_0_105:[bind(X,$fot(positive_part(X_109))),bind(Y,$fot(inverse(X_109)))]]) ).
cnf(refute_0_180,plain,
( multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) != inverse(multiply(positive_part(X_109),inverse(X_109)))
| inverse(multiply(positive_part(X_109),inverse(X_109))) != multiply(X_109,inverse(positive_part(X_109)))
| multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) = multiply(X_109,inverse(positive_part(X_109))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))))),bind(Y0,$fot(inverse(multiply(positive_part(X_109),inverse(X_109))))),bind(Z0,$fot(multiply(X_109,inverse(positive_part(X_109)))))]]) ).
cnf(refute_0_181,plain,
( inverse(multiply(positive_part(X_109),inverse(X_109))) != multiply(X_109,inverse(positive_part(X_109)))
| multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) = multiply(X_109,inverse(positive_part(X_109))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))),inverse(multiply(positive_part(X_109),inverse(X_109)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) = multiply(X_109,inverse(positive_part(X_109))),
inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(X_109),inverse(X_109))),multiply(X_109,inverse(positive_part(X_109)))) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))) != multiply(X_109,inverse(positive_part(X_109)))
| inverse(positive_part(inverse(X_109))) != multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))
| inverse(positive_part(inverse(X_109))) = multiply(X_109,inverse(positive_part(X_109))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(positive_part(inverse(X_109))),multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))) ),[1],$fot(multiply(X_109,inverse(positive_part(X_109))))]]) ).
cnf(refute_0_184,plain,
( inverse(positive_part(inverse(X_109))) != multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))
| inverse(positive_part(inverse(X_109))) = multiply(X_109,inverse(positive_part(X_109))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_109)),inverse(positive_part(X_109))),multiply(X_109,inverse(positive_part(X_109)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
inverse(positive_part(inverse(X_109))) = multiply(X_109,inverse(positive_part(X_109))),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X_109))),multiply(inverse(inverse(X_109)),inverse(positive_part(X_109)))) )],[refute_0_177,refute_0_184]) ).
cnf(refute_0_186,plain,
( inverse(positive_part(inverse(X_109))) != multiply(X_109,inverse(positive_part(X_109)))
| multiply(X_109,inverse(positive_part(X_109))) = inverse(positive_part(inverse(X_109))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(positive_part(inverse(X_109))))),bind(Y0,$fot(multiply(X_109,inverse(positive_part(X_109)))))]]) ).
cnf(refute_0_187,plain,
multiply(X_109,inverse(positive_part(X_109))) = inverse(positive_part(inverse(X_109))),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X_109))),multiply(X_109,inverse(positive_part(X_109)))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(X_55,inverse(positive_part(X_55))) = inverse(positive_part(inverse(X_55))),
inference(subst,[],[refute_0_187:[bind(X_109,$fot(X_55))]]) ).
cnf(refute_0_189,plain,
multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) = multiply(inverse(X_116),multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))))),
inference(subst,[],[refute_0_8:[bind(X_117,$fot(multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))))]]) ).
cnf(refute_0_190,plain,
multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))) = negative_part(multiply(X_115,X_116)),
inference(subst,[],[refute_0_144:[bind(X_55,$fot(multiply(X_115,X_116)))]]) ).
cnf(refute_0_191,plain,
multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))) = multiply(X_115,multiply(X_116,negative_part(inverse(multiply(X_115,X_116))))),
inference(subst,[],[associativity:[bind(X,$fot(X_115)),bind(Y,$fot(X_116)),bind(Z,$fot(negative_part(inverse(multiply(X_115,X_116)))))]]) ).
cnf(refute_0_192,plain,
( multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))) != multiply(X_115,multiply(X_116,negative_part(inverse(multiply(X_115,X_116)))))
| multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))) != negative_part(multiply(X_115,X_116))
| multiply(X_115,multiply(X_116,negative_part(inverse(multiply(X_115,X_116))))) = negative_part(multiply(X_115,X_116)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))),negative_part(multiply(X_115,X_116))) ),[0],$fot(multiply(X_115,multiply(X_116,negative_part(inverse(multiply(X_115,X_116))))))]]) ).
cnf(refute_0_193,plain,
( multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))) != negative_part(multiply(X_115,X_116))
| multiply(X_115,multiply(X_116,negative_part(inverse(multiply(X_115,X_116))))) = negative_part(multiply(X_115,X_116)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))),multiply(X_115,multiply(X_116,negative_part(inverse(multiply(X_115,X_116)))))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(X_115,multiply(X_116,negative_part(inverse(multiply(X_115,X_116))))) = negative_part(multiply(X_115,X_116)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_115,X_116),negative_part(inverse(multiply(X_115,X_116)))),negative_part(multiply(X_115,X_116))) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))) = negative_part(multiply(X_116,X_163)),
inference(subst,[],[refute_0_194:[bind(X_115,$fot(X_116)),bind(X_116,$fot(X_163))]]) ).
cnf(refute_0_196,plain,
( multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))) != negative_part(multiply(X_116,X_163))
| multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) != multiply(inverse(X_116),multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))))
| multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) = multiply(inverse(X_116),negative_part(multiply(X_116,X_163))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))),multiply(inverse(X_116),multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))))) ),[1,1],$fot(negative_part(multiply(X_116,X_163)))]]) ).
cnf(refute_0_197,plain,
( multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) != multiply(inverse(X_116),multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))))
| multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) = multiply(inverse(X_116),negative_part(multiply(X_116,X_163))) ),
inference(resolve,[$cnf( $equal(multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))),negative_part(multiply(X_116,X_163))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) = multiply(inverse(X_116),negative_part(multiply(X_116,X_163))),
inference(resolve,[$cnf( $equal(multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))),multiply(inverse(X_116),multiply(X_116,multiply(X_163,negative_part(inverse(multiply(X_116,X_163))))))) )],[refute_0_189,refute_0_197]) ).
cnf(refute_0_199,plain,
intersection(inverse(X_118),X_54) = multiply(inverse(X_118),multiply(X_118,intersection(inverse(X_118),X_54))),
inference(subst,[],[refute_0_8:[bind(X_116,$fot(X_118)),bind(X_117,$fot(intersection(inverse(X_118),X_54)))]]) ).
cnf(refute_0_200,plain,
multiply(X_52,intersection(inverse(X_52),X_54)) = intersection(multiply(X_52,inverse(X_52)),multiply(X_52,X_54)),
inference(subst,[],[multiply_intersection1:[bind(X,$fot(X_52)),bind(Y,$fot(inverse(X_52))),bind(Z,$fot(X_54))]]) ).
cnf(refute_0_201,plain,
( multiply(X_52,intersection(inverse(X_52),X_54)) != intersection(multiply(X_52,inverse(X_52)),multiply(X_52,X_54))
| multiply(X_52,inverse(X_52)) != identity
| multiply(X_52,intersection(inverse(X_52),X_54)) = intersection(identity,multiply(X_52,X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_52,intersection(inverse(X_52),X_54)),intersection(multiply(X_52,inverse(X_52)),multiply(X_52,X_54))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_202,plain,
( multiply(X_52,intersection(inverse(X_52),X_54)) != intersection(multiply(X_52,inverse(X_52)),multiply(X_52,X_54))
| multiply(X_52,intersection(inverse(X_52),X_54)) = intersection(identity,multiply(X_52,X_54)) ),
inference(resolve,[$cnf( $equal(multiply(X_52,inverse(X_52)),identity) )],[refute_0_116,refute_0_201]) ).
cnf(refute_0_203,plain,
multiply(X_52,intersection(inverse(X_52),X_54)) = intersection(identity,multiply(X_52,X_54)),
inference(resolve,[$cnf( $equal(multiply(X_52,intersection(inverse(X_52),X_54)),intersection(multiply(X_52,inverse(X_52)),multiply(X_52,X_54))) )],[refute_0_200,refute_0_202]) ).
cnf(refute_0_204,plain,
( negative_part(X) != intersection(identity,X)
| intersection(identity,X) = negative_part(X) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(intersection(identity,X)))]]) ).
cnf(refute_0_205,plain,
intersection(identity,X) = negative_part(X),
inference(resolve,[$cnf( $equal(negative_part(X),intersection(identity,X)) )],[refute_0_130,refute_0_204]) ).
cnf(refute_0_206,plain,
intersection(identity,multiply(X_52,X_54)) = negative_part(multiply(X_52,X_54)),
inference(subst,[],[refute_0_205:[bind(X,$fot(multiply(X_52,X_54)))]]) ).
cnf(refute_0_207,plain,
( multiply(X_52,intersection(inverse(X_52),X_54)) != intersection(identity,multiply(X_52,X_54))
| intersection(identity,multiply(X_52,X_54)) != negative_part(multiply(X_52,X_54))
| multiply(X_52,intersection(inverse(X_52),X_54)) = negative_part(multiply(X_52,X_54)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_52,intersection(inverse(X_52),X_54)),negative_part(multiply(X_52,X_54))) ),[0],$fot(intersection(identity,multiply(X_52,X_54)))]]) ).
cnf(refute_0_208,plain,
( multiply(X_52,intersection(inverse(X_52),X_54)) != intersection(identity,multiply(X_52,X_54))
| multiply(X_52,intersection(inverse(X_52),X_54)) = negative_part(multiply(X_52,X_54)) ),
inference(resolve,[$cnf( $equal(intersection(identity,multiply(X_52,X_54)),negative_part(multiply(X_52,X_54))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
multiply(X_52,intersection(inverse(X_52),X_54)) = negative_part(multiply(X_52,X_54)),
inference(resolve,[$cnf( $equal(multiply(X_52,intersection(inverse(X_52),X_54)),intersection(identity,multiply(X_52,X_54))) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
multiply(X_118,intersection(inverse(X_118),X_54)) = negative_part(multiply(X_118,X_54)),
inference(subst,[],[refute_0_209:[bind(X_52,$fot(X_118))]]) ).
cnf(refute_0_211,plain,
( multiply(X_118,intersection(inverse(X_118),X_54)) != negative_part(multiply(X_118,X_54))
| intersection(inverse(X_118),X_54) != multiply(inverse(X_118),multiply(X_118,intersection(inverse(X_118),X_54)))
| intersection(inverse(X_118),X_54) = multiply(inverse(X_118),negative_part(multiply(X_118,X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(inverse(X_118),X_54),multiply(inverse(X_118),multiply(X_118,intersection(inverse(X_118),X_54)))) ),[1,1],$fot(negative_part(multiply(X_118,X_54)))]]) ).
cnf(refute_0_212,plain,
( intersection(inverse(X_118),X_54) != multiply(inverse(X_118),multiply(X_118,intersection(inverse(X_118),X_54)))
| intersection(inverse(X_118),X_54) = multiply(inverse(X_118),negative_part(multiply(X_118,X_54))) ),
inference(resolve,[$cnf( $equal(multiply(X_118,intersection(inverse(X_118),X_54)),negative_part(multiply(X_118,X_54))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
intersection(inverse(X_118),X_54) = multiply(inverse(X_118),negative_part(multiply(X_118,X_54))),
inference(resolve,[$cnf( $equal(intersection(inverse(X_118),X_54),multiply(inverse(X_118),multiply(X_118,intersection(inverse(X_118),X_54)))) )],[refute_0_199,refute_0_212]) ).
cnf(refute_0_214,plain,
( intersection(inverse(X_118),X_54) != multiply(inverse(X_118),negative_part(multiply(X_118,X_54)))
| multiply(inverse(X_118),negative_part(multiply(X_118,X_54))) = intersection(inverse(X_118),X_54) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(intersection(inverse(X_118),X_54))),bind(Y0,$fot(multiply(inverse(X_118),negative_part(multiply(X_118,X_54)))))]]) ).
cnf(refute_0_215,plain,
multiply(inverse(X_118),negative_part(multiply(X_118,X_54))) = intersection(inverse(X_118),X_54),
inference(resolve,[$cnf( $equal(intersection(inverse(X_118),X_54),multiply(inverse(X_118),negative_part(multiply(X_118,X_54)))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(inverse(X_116),negative_part(multiply(X_116,X_163))) = intersection(inverse(X_116),X_163),
inference(subst,[],[refute_0_215:[bind(X_118,$fot(X_116)),bind(X_54,$fot(X_163))]]) ).
cnf(refute_0_217,plain,
( multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) != multiply(inverse(X_116),negative_part(multiply(X_116,X_163)))
| multiply(inverse(X_116),negative_part(multiply(X_116,X_163))) != intersection(inverse(X_116),X_163)
| multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) = intersection(inverse(X_116),X_163) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))),intersection(inverse(X_116),X_163)) ),[0],$fot(multiply(inverse(X_116),negative_part(multiply(X_116,X_163))))]]) ).
cnf(refute_0_218,plain,
( multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) != multiply(inverse(X_116),negative_part(multiply(X_116,X_163)))
| multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) = intersection(inverse(X_116),X_163) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_116),negative_part(multiply(X_116,X_163))),intersection(inverse(X_116),X_163)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))) = intersection(inverse(X_116),X_163),
inference(resolve,[$cnf( $equal(multiply(X_163,negative_part(inverse(multiply(X_116,X_163)))),multiply(inverse(X_116),negative_part(multiply(X_116,X_163)))) )],[refute_0_198,refute_0_218]) ).
cnf(refute_0_220,plain,
multiply(negative_part(inverse(X)),negative_part(inverse(multiply(positive_part(X),negative_part(inverse(X)))))) = intersection(inverse(positive_part(X)),negative_part(inverse(X))),
inference(subst,[],[refute_0_219:[bind(X_116,$fot(positive_part(X))),bind(X_163,$fot(negative_part(inverse(X))))]]) ).
cnf(refute_0_221,plain,
multiply(union(X_61,X_62),negative_part(inverse(X_62))) = union(multiply(X_61,negative_part(inverse(X_62))),multiply(X_62,negative_part(inverse(X_62)))),
inference(subst,[],[multiply_union2:[bind(X,$fot(negative_part(inverse(X_62)))),bind(Y,$fot(X_61)),bind(Z,$fot(X_62))]]) ).
cnf(refute_0_222,plain,
multiply(X_62,negative_part(inverse(X_62))) = negative_part(X_62),
inference(subst,[],[refute_0_144:[bind(X_55,$fot(X_62))]]) ).
cnf(refute_0_223,plain,
( multiply(X_62,negative_part(inverse(X_62))) != negative_part(X_62)
| multiply(union(X_61,X_62),negative_part(inverse(X_62))) != union(multiply(X_61,negative_part(inverse(X_62))),multiply(X_62,negative_part(inverse(X_62))))
| multiply(union(X_61,X_62),negative_part(inverse(X_62))) = union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(X_61,X_62),negative_part(inverse(X_62))),union(multiply(X_61,negative_part(inverse(X_62))),multiply(X_62,negative_part(inverse(X_62))))) ),[1,1],$fot(negative_part(X_62))]]) ).
cnf(refute_0_224,plain,
( multiply(union(X_61,X_62),negative_part(inverse(X_62))) != union(multiply(X_61,negative_part(inverse(X_62))),multiply(X_62,negative_part(inverse(X_62))))
| multiply(union(X_61,X_62),negative_part(inverse(X_62))) = union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62)) ),
inference(resolve,[$cnf( $equal(multiply(X_62,negative_part(inverse(X_62))),negative_part(X_62)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
multiply(union(X_61,X_62),negative_part(inverse(X_62))) = union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62)),
inference(resolve,[$cnf( $equal(multiply(union(X_61,X_62),negative_part(inverse(X_62))),union(multiply(X_61,negative_part(inverse(X_62))),multiply(X_62,negative_part(inverse(X_62))))) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( union(X,Y) != union(Y,X)
| union(Y,X) = union(X,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(union(X,Y))),bind(Y0,$fot(union(Y,X)))]]) ).
cnf(refute_0_227,plain,
union(Y,X) = union(X,Y),
inference(resolve,[$cnf( $equal(union(X,Y),union(Y,X)) )],[union_commutative,refute_0_226]) ).
cnf(refute_0_228,plain,
union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62)) = union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62)))),
inference(subst,[],[refute_0_227:[bind(X,$fot(negative_part(X_62))),bind(Y,$fot(multiply(X_61,negative_part(inverse(X_62)))))]]) ).
cnf(refute_0_229,plain,
( multiply(union(X_61,X_62),negative_part(inverse(X_62))) != union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62))
| union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62)) != union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62))))
| multiply(union(X_61,X_62),negative_part(inverse(X_62))) = union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(union(X_61,X_62),negative_part(inverse(X_62))),union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62))))) ),[0],$fot(union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62)))]]) ).
cnf(refute_0_230,plain,
( multiply(union(X_61,X_62),negative_part(inverse(X_62))) != union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62))
| multiply(union(X_61,X_62),negative_part(inverse(X_62))) = union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62)))) ),
inference(resolve,[$cnf( $equal(union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62)),union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62))))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
multiply(union(X_61,X_62),negative_part(inverse(X_62))) = union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62)))),
inference(resolve,[$cnf( $equal(multiply(union(X_61,X_62),negative_part(inverse(X_62))),union(multiply(X_61,negative_part(inverse(X_62))),negative_part(X_62))) )],[refute_0_225,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))),
inference(subst,[],[refute_0_231:[bind(X_61,$fot(negative_part(X))),bind(X_62,$fot(negative_part(inverse(X))))]]) ).
cnf(refute_0_233,plain,
multiply(union(X_61,identity),X_60) = union(multiply(X_61,X_60),multiply(identity,X_60)),
inference(subst,[],[multiply_union2:[bind(X,$fot(X_60)),bind(Y,$fot(X_61)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_234,plain,
multiply(identity,X_60) = X_60,
inference(subst,[],[left_identity:[bind(X,$fot(X_60))]]) ).
cnf(refute_0_235,plain,
( multiply(identity,X_60) != X_60
| multiply(union(X_61,identity),X_60) != union(multiply(X_61,X_60),multiply(identity,X_60))
| multiply(union(X_61,identity),X_60) = union(multiply(X_61,X_60),X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(X_61,identity),X_60),union(multiply(X_61,X_60),multiply(identity,X_60))) ),[1,1],$fot(X_60)]]) ).
cnf(refute_0_236,plain,
( multiply(union(X_61,identity),X_60) != union(multiply(X_61,X_60),multiply(identity,X_60))
| multiply(union(X_61,identity),X_60) = union(multiply(X_61,X_60),X_60) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_60),X_60) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
multiply(union(X_61,identity),X_60) = union(multiply(X_61,X_60),X_60),
inference(resolve,[$cnf( $equal(multiply(union(X_61,identity),X_60),union(multiply(X_61,X_60),multiply(identity,X_60))) )],[refute_0_233,refute_0_236]) ).
cnf(refute_0_238,plain,
union(X_61,identity) = positive_part(X_61),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_239,plain,
multiply(union(X_61,identity),X_60) = multiply(union(X_61,identity),X_60),
introduced(tautology,[refl,[$fot(multiply(union(X_61,identity),X_60))]]) ).
cnf(refute_0_240,plain,
( multiply(union(X_61,identity),X_60) != multiply(union(X_61,identity),X_60)
| union(X_61,identity) != positive_part(X_61)
| multiply(union(X_61,identity),X_60) = multiply(positive_part(X_61),X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(X_61,identity),X_60),multiply(union(X_61,identity),X_60)) ),[1,0],$fot(positive_part(X_61))]]) ).
cnf(refute_0_241,plain,
( union(X_61,identity) != positive_part(X_61)
| multiply(union(X_61,identity),X_60) = multiply(positive_part(X_61),X_60) ),
inference(resolve,[$cnf( $equal(multiply(union(X_61,identity),X_60),multiply(union(X_61,identity),X_60)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
multiply(union(X_61,identity),X_60) = multiply(positive_part(X_61),X_60),
inference(resolve,[$cnf( $equal(union(X_61,identity),positive_part(X_61)) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
( multiply(union(X_61,identity),X_60) != multiply(positive_part(X_61),X_60)
| multiply(union(X_61,identity),X_60) != union(multiply(X_61,X_60),X_60)
| multiply(positive_part(X_61),X_60) = union(multiply(X_61,X_60),X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(X_61,identity),X_60),union(multiply(X_61,X_60),X_60)) ),[0],$fot(multiply(positive_part(X_61),X_60))]]) ).
cnf(refute_0_244,plain,
( multiply(union(X_61,identity),X_60) != union(multiply(X_61,X_60),X_60)
| multiply(positive_part(X_61),X_60) = union(multiply(X_61,X_60),X_60) ),
inference(resolve,[$cnf( $equal(multiply(union(X_61,identity),X_60),multiply(positive_part(X_61),X_60)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
union(multiply(X_61,X_60),X_60) = union(X_60,multiply(X_61,X_60)),
inference(subst,[],[refute_0_227:[bind(X,$fot(X_60)),bind(Y,$fot(multiply(X_61,X_60)))]]) ).
cnf(refute_0_246,plain,
( multiply(positive_part(X_61),X_60) != union(multiply(X_61,X_60),X_60)
| union(multiply(X_61,X_60),X_60) != union(X_60,multiply(X_61,X_60))
| multiply(positive_part(X_61),X_60) = union(X_60,multiply(X_61,X_60)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(X_61),X_60),union(X_60,multiply(X_61,X_60))) ),[0],$fot(union(multiply(X_61,X_60),X_60))]]) ).
cnf(refute_0_247,plain,
( multiply(positive_part(X_61),X_60) != union(multiply(X_61,X_60),X_60)
| multiply(positive_part(X_61),X_60) = union(X_60,multiply(X_61,X_60)) ),
inference(resolve,[$cnf( $equal(union(multiply(X_61,X_60),X_60),union(X_60,multiply(X_61,X_60))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
( multiply(union(X_61,identity),X_60) != union(multiply(X_61,X_60),X_60)
| multiply(positive_part(X_61),X_60) = union(X_60,multiply(X_61,X_60)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_61),X_60),union(multiply(X_61,X_60),X_60)) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
multiply(positive_part(X_61),X_60) = union(X_60,multiply(X_61,X_60)),
inference(resolve,[$cnf( $equal(multiply(union(X_61,identity),X_60),union(multiply(X_61,X_60),X_60)) )],[refute_0_237,refute_0_248]) ).
cnf(refute_0_250,plain,
multiply(positive_part(inverse(X)),negative_part(X)) = union(negative_part(X),multiply(inverse(X),negative_part(X))),
inference(subst,[],[refute_0_249:[bind(X_60,$fot(negative_part(X))),bind(X_61,$fot(inverse(X)))]]) ).
cnf(refute_0_251,plain,
multiply(inverse(X),negative_part(inverse(inverse(X)))) = negative_part(inverse(X)),
inference(subst,[],[refute_0_144:[bind(X_55,$fot(inverse(X)))]]) ).
cnf(refute_0_252,plain,
( multiply(inverse(X),negative_part(inverse(inverse(X)))) != negative_part(inverse(X))
| inverse(inverse(X)) != X
| multiply(inverse(X),negative_part(X)) = negative_part(inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(inverse(X)))),negative_part(inverse(X))) ),[0,1,0],$fot(X)]]) ).
cnf(refute_0_253,plain,
( multiply(inverse(X),negative_part(inverse(inverse(X)))) != negative_part(inverse(X))
| multiply(inverse(X),negative_part(X)) = negative_part(inverse(X)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_252]) ).
cnf(refute_0_254,plain,
multiply(inverse(X),negative_part(X)) = negative_part(inverse(X)),
inference(resolve,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(inverse(X)))),negative_part(inverse(X))) )],[refute_0_251,refute_0_253]) ).
cnf(refute_0_255,plain,
( multiply(inverse(X),negative_part(X)) != negative_part(inverse(X))
| multiply(positive_part(inverse(X)),negative_part(X)) != union(negative_part(X),multiply(inverse(X),negative_part(X)))
| multiply(positive_part(inverse(X)),negative_part(X)) = union(negative_part(X),negative_part(inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(X)),union(negative_part(X),multiply(inverse(X),negative_part(X)))) ),[1,1],$fot(negative_part(inverse(X)))]]) ).
cnf(refute_0_256,plain,
( multiply(positive_part(inverse(X)),negative_part(X)) != union(negative_part(X),multiply(inverse(X),negative_part(X)))
| multiply(positive_part(inverse(X)),negative_part(X)) = union(negative_part(X),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),negative_part(X)),negative_part(inverse(X))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(positive_part(inverse(X)),negative_part(X)) = union(negative_part(X),negative_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(X)),union(negative_part(X),multiply(inverse(X),negative_part(X)))) )],[refute_0_250,refute_0_256]) ).
cnf(refute_0_258,plain,
multiply(multiply(positive_part(X),inverse(X)),X_117) = multiply(positive_part(X),multiply(inverse(X),X_117)),
inference(subst,[],[associativity:[bind(X,$fot(positive_part(X))),bind(Y,$fot(inverse(X))),bind(Z,$fot(X_117))]]) ).
cnf(refute_0_259,plain,
( multiply(multiply(positive_part(X),inverse(X)),X_117) != multiply(positive_part(X),multiply(inverse(X),X_117))
| multiply(positive_part(X),inverse(X)) != positive_part(inverse(X))
| multiply(positive_part(inverse(X)),X_117) = multiply(positive_part(X),multiply(inverse(X),X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(positive_part(X),inverse(X)),X_117),multiply(positive_part(X),multiply(inverse(X),X_117))) ),[0,0],$fot(positive_part(inverse(X)))]]) ).
cnf(refute_0_260,plain,
( multiply(multiply(positive_part(X),inverse(X)),X_117) != multiply(positive_part(X),multiply(inverse(X),X_117))
| multiply(positive_part(inverse(X)),X_117) = multiply(positive_part(X),multiply(inverse(X),X_117)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X),inverse(X)),positive_part(inverse(X))) )],[refute_0_173,refute_0_259]) ).
cnf(refute_0_261,plain,
multiply(positive_part(inverse(X)),X_117) = multiply(positive_part(X),multiply(inverse(X),X_117)),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),inverse(X)),X_117),multiply(positive_part(X),multiply(inverse(X),X_117))) )],[refute_0_258,refute_0_260]) ).
cnf(refute_0_262,plain,
multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(X_138),multiply(inverse(X_138),negative_part(inverse(inverse(X_138))))),
inference(subst,[],[refute_0_261:[bind(X,$fot(X_138)),bind(X_117,$fot(negative_part(inverse(inverse(X_138)))))]]) ).
cnf(refute_0_263,plain,
multiply(inverse(X_138),negative_part(inverse(inverse(X_138)))) = negative_part(inverse(X_138)),
inference(subst,[],[refute_0_144:[bind(X_55,$fot(inverse(X_138)))]]) ).
cnf(refute_0_264,plain,
( multiply(inverse(X_138),negative_part(inverse(inverse(X_138)))) != negative_part(inverse(X_138))
| multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) != multiply(positive_part(X_138),multiply(inverse(X_138),negative_part(inverse(inverse(X_138)))))
| multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(X_138),negative_part(inverse(X_138))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),multiply(positive_part(X_138),multiply(inverse(X_138),negative_part(inverse(inverse(X_138)))))) ),[1,1],$fot(negative_part(inverse(X_138)))]]) ).
cnf(refute_0_265,plain,
( multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) != multiply(positive_part(X_138),multiply(inverse(X_138),negative_part(inverse(inverse(X_138)))))
| multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(X_138),negative_part(inverse(X_138))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_138),negative_part(inverse(inverse(X_138)))),negative_part(inverse(X_138))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(X_138),negative_part(inverse(X_138))),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),multiply(positive_part(X_138),multiply(inverse(X_138),negative_part(inverse(inverse(X_138)))))) )],[refute_0_262,refute_0_265]) ).
cnf(refute_0_267,plain,
inverse(inverse(X_138)) = X_138,
inference(subst,[],[inverse_involution:[bind(X,$fot(X_138))]]) ).
cnf(refute_0_268,plain,
negative_part(inverse(inverse(X_138))) = negative_part(inverse(inverse(X_138))),
introduced(tautology,[refl,[$fot(negative_part(inverse(inverse(X_138))))]]) ).
cnf(refute_0_269,plain,
( inverse(inverse(X_138)) != X_138
| negative_part(inverse(inverse(X_138))) != negative_part(inverse(inverse(X_138)))
| negative_part(inverse(inverse(X_138))) = negative_part(X_138) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(inverse(inverse(X_138))),negative_part(inverse(inverse(X_138)))) ),[1,0],$fot(X_138)]]) ).
cnf(refute_0_270,plain,
( inverse(inverse(X_138)) != X_138
| negative_part(inverse(inverse(X_138))) = negative_part(X_138) ),
inference(resolve,[$cnf( $equal(negative_part(inverse(inverse(X_138))),negative_part(inverse(inverse(X_138)))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
negative_part(inverse(inverse(X_138))) = negative_part(X_138),
inference(resolve,[$cnf( $equal(inverse(inverse(X_138)),X_138) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),
introduced(tautology,[refl,[$fot(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))))]]) ).
cnf(refute_0_273,plain,
( multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) != multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138))))
| negative_part(inverse(inverse(X_138))) != negative_part(X_138)
| multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(inverse(X_138)),negative_part(X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138))))) ),[1,1],$fot(negative_part(X_138))]]) ).
cnf(refute_0_274,plain,
( negative_part(inverse(inverse(X_138))) != negative_part(X_138)
| multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(inverse(X_138)),negative_part(X_138)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138))))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) = multiply(positive_part(inverse(X_138)),negative_part(X_138)),
inference(resolve,[$cnf( $equal(negative_part(inverse(inverse(X_138))),negative_part(X_138)) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
( multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) != multiply(positive_part(X_138),negative_part(inverse(X_138)))
| multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) != multiply(positive_part(inverse(X_138)),negative_part(X_138))
| multiply(positive_part(inverse(X_138)),negative_part(X_138)) = multiply(positive_part(X_138),negative_part(inverse(X_138))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),multiply(positive_part(X_138),negative_part(inverse(X_138)))) ),[0],$fot(multiply(positive_part(inverse(X_138)),negative_part(X_138)))]]) ).
cnf(refute_0_277,plain,
( multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))) != multiply(positive_part(X_138),negative_part(inverse(X_138)))
| multiply(positive_part(inverse(X_138)),negative_part(X_138)) = multiply(positive_part(X_138),negative_part(inverse(X_138))) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),multiply(positive_part(inverse(X_138)),negative_part(X_138))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
multiply(positive_part(inverse(X_138)),negative_part(X_138)) = multiply(positive_part(X_138),negative_part(inverse(X_138))),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_138)),negative_part(inverse(inverse(X_138)))),multiply(positive_part(X_138),negative_part(inverse(X_138)))) )],[refute_0_266,refute_0_277]) ).
cnf(refute_0_279,plain,
multiply(positive_part(inverse(X)),negative_part(X)) = multiply(positive_part(X),negative_part(inverse(X))),
inference(subst,[],[refute_0_278:[bind(X_138,$fot(X))]]) ).
cnf(refute_0_280,plain,
( multiply(positive_part(inverse(X)),negative_part(X)) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(positive_part(inverse(X)),negative_part(X)) != union(negative_part(X),negative_part(inverse(X)))
| multiply(positive_part(X),negative_part(inverse(X))) = union(negative_part(X),negative_part(inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(X)),union(negative_part(X),negative_part(inverse(X)))) ),[0],$fot(multiply(positive_part(X),negative_part(inverse(X))))]]) ).
cnf(refute_0_281,plain,
( multiply(positive_part(inverse(X)),negative_part(X)) != union(negative_part(X),negative_part(inverse(X)))
| multiply(positive_part(X),negative_part(inverse(X))) = union(negative_part(X),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(X)),multiply(positive_part(X),negative_part(inverse(X)))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
multiply(positive_part(X),negative_part(inverse(X))) = union(negative_part(X),negative_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(X)),union(negative_part(X),negative_part(inverse(X)))) )],[refute_0_257,refute_0_281]) ).
cnf(refute_0_283,plain,
( multiply(positive_part(X),negative_part(inverse(X))) != union(negative_part(X),negative_part(inverse(X)))
| union(negative_part(X),negative_part(inverse(X))) = multiply(positive_part(X),negative_part(inverse(X))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(positive_part(X),negative_part(inverse(X))))),bind(Y0,$fot(union(negative_part(X),negative_part(inverse(X)))))]]) ).
cnf(refute_0_284,plain,
union(negative_part(X),negative_part(inverse(X))) = multiply(positive_part(X),negative_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(positive_part(X),negative_part(inverse(X))),union(negative_part(X),negative_part(inverse(X)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))
| union(negative_part(X),negative_part(inverse(X))) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))) ),[0,0],$fot(multiply(positive_part(X),negative_part(inverse(X))))]]) ).
cnf(refute_0_286,plain,
( multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) ),
inference(resolve,[$cnf( $equal(union(negative_part(X),negative_part(inverse(X))),multiply(positive_part(X),negative_part(inverse(X)))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))),
inference(resolve,[$cnf( $equal(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))) )],[refute_0_232,refute_0_286]) ).
cnf(refute_0_288,plain,
multiply(positive_part(inverse(X)),identity) = positive_part(inverse(X)),
inference(subst,[],[refute_0_65:[bind(X,$fot(positive_part(inverse(X))))]]) ).
cnf(refute_0_289,plain,
multiply(inverse(negative_part(X_14)),negative_part(negative_part(X_14))) = negative_part(inverse(negative_part(X_14))),
inference(subst,[],[refute_0_254:[bind(X,$fot(negative_part(X_14)))]]) ).
cnf(refute_0_290,plain,
( intersection(X,Y) != intersection(Y,X)
| intersection(Y,X) = intersection(X,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(intersection(X,Y))),bind(Y0,$fot(intersection(Y,X)))]]) ).
cnf(refute_0_291,plain,
intersection(Y,X) = intersection(X,Y),
inference(resolve,[$cnf( $equal(intersection(X,Y),intersection(Y,X)) )],[intersection_commutative,refute_0_290]) ).
cnf(refute_0_292,plain,
intersection(union(X,Y),Y) = intersection(Y,union(X,Y)),
inference(subst,[],[refute_0_291:[bind(X,$fot(Y)),bind(Y,$fot(union(X,Y)))]]) ).
cnf(refute_0_293,plain,
( intersection(union(X,Y),Y) != Y
| intersection(union(X,Y),Y) != intersection(Y,union(X,Y))
| intersection(Y,union(X,Y)) = Y ),
introduced(tautology,[equality,[$cnf( $equal(intersection(union(X,Y),Y),Y) ),[0],$fot(intersection(Y,union(X,Y)))]]) ).
cnf(refute_0_294,plain,
( intersection(union(X,Y),Y) != Y
| intersection(Y,union(X,Y)) = Y ),
inference(resolve,[$cnf( $equal(intersection(union(X,Y),Y),intersection(Y,union(X,Y))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
intersection(Y,union(X,Y)) = Y,
inference(resolve,[$cnf( $equal(intersection(union(X,Y),Y),Y) )],[intersection_union_absorbtion,refute_0_294]) ).
cnf(refute_0_296,plain,
intersection(X_19,union(identity,X_19)) = X_19,
inference(subst,[],[refute_0_295:[bind(X,$fot(identity)),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_297,plain,
positive_part(X_19) = union(identity,X_19),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_298,plain,
( positive_part(X_19) != union(identity,X_19)
| union(identity,X_19) = positive_part(X_19) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(positive_part(X_19))),bind(Y0,$fot(union(identity,X_19)))]]) ).
cnf(refute_0_299,plain,
union(identity,X_19) = positive_part(X_19),
inference(resolve,[$cnf( $equal(positive_part(X_19),union(identity,X_19)) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
( intersection(X_19,union(identity,X_19)) != X_19
| union(identity,X_19) != positive_part(X_19)
| intersection(X_19,positive_part(X_19)) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(intersection(X_19,union(identity,X_19)),X_19) ),[0,1],$fot(positive_part(X_19))]]) ).
cnf(refute_0_301,plain,
( intersection(X_19,union(identity,X_19)) != X_19
| intersection(X_19,positive_part(X_19)) = X_19 ),
inference(resolve,[$cnf( $equal(union(identity,X_19),positive_part(X_19)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
intersection(X_19,positive_part(X_19)) = X_19,
inference(resolve,[$cnf( $equal(intersection(X_19,union(identity,X_19)),X_19) )],[refute_0_296,refute_0_301]) ).
cnf(refute_0_303,plain,
intersection(negative_part(X_14),positive_part(negative_part(X_14))) = negative_part(X_14),
inference(subst,[],[refute_0_302:[bind(X_19,$fot(negative_part(X_14)))]]) ).
cnf(refute_0_304,plain,
positive_part(intersection(X_14,identity)) = union(identity,intersection(X_14,identity)),
inference(subst,[],[refute_0_38:[bind(X,$fot(intersection(X_14,identity)))]]) ).
cnf(refute_0_305,plain,
union(intersection(X,Y),Y) = union(Y,intersection(X,Y)),
inference(subst,[],[refute_0_227:[bind(X,$fot(Y)),bind(Y,$fot(intersection(X,Y)))]]) ).
cnf(refute_0_306,plain,
( union(intersection(X,Y),Y) != Y
| union(intersection(X,Y),Y) != union(Y,intersection(X,Y))
| union(Y,intersection(X,Y)) = Y ),
introduced(tautology,[equality,[$cnf( $equal(union(intersection(X,Y),Y),Y) ),[0],$fot(union(Y,intersection(X,Y)))]]) ).
cnf(refute_0_307,plain,
( union(intersection(X,Y),Y) != Y
| union(Y,intersection(X,Y)) = Y ),
inference(resolve,[$cnf( $equal(union(intersection(X,Y),Y),union(Y,intersection(X,Y))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
union(Y,intersection(X,Y)) = Y,
inference(resolve,[$cnf( $equal(union(intersection(X,Y),Y),Y) )],[union_intersection_absorbtion,refute_0_307]) ).
cnf(refute_0_309,plain,
union(identity,intersection(X_14,identity)) = identity,
inference(subst,[],[refute_0_308:[bind(X,$fot(X_14)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_310,plain,
( positive_part(intersection(X_14,identity)) != union(identity,intersection(X_14,identity))
| union(identity,intersection(X_14,identity)) != identity
| positive_part(intersection(X_14,identity)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(positive_part(intersection(X_14,identity)),identity) ),[0],$fot(union(identity,intersection(X_14,identity)))]]) ).
cnf(refute_0_311,plain,
( positive_part(intersection(X_14,identity)) != union(identity,intersection(X_14,identity))
| positive_part(intersection(X_14,identity)) = identity ),
inference(resolve,[$cnf( $equal(union(identity,intersection(X_14,identity)),identity) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
positive_part(intersection(X_14,identity)) = identity,
inference(resolve,[$cnf( $equal(positive_part(intersection(X_14,identity)),union(identity,intersection(X_14,identity))) )],[refute_0_304,refute_0_311]) ).
cnf(refute_0_313,plain,
intersection(X_14,identity) = negative_part(X_14),
inference(subst,[],[refute_0_121:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_314,plain,
positive_part(intersection(X_14,identity)) = positive_part(intersection(X_14,identity)),
introduced(tautology,[refl,[$fot(positive_part(intersection(X_14,identity)))]]) ).
cnf(refute_0_315,plain,
( intersection(X_14,identity) != negative_part(X_14)
| positive_part(intersection(X_14,identity)) != positive_part(intersection(X_14,identity))
| positive_part(intersection(X_14,identity)) = positive_part(negative_part(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(intersection(X_14,identity)),positive_part(intersection(X_14,identity))) ),[1,0],$fot(negative_part(X_14))]]) ).
cnf(refute_0_316,plain,
( intersection(X_14,identity) != negative_part(X_14)
| positive_part(intersection(X_14,identity)) = positive_part(negative_part(X_14)) ),
inference(resolve,[$cnf( $equal(positive_part(intersection(X_14,identity)),positive_part(intersection(X_14,identity))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
positive_part(intersection(X_14,identity)) = positive_part(negative_part(X_14)),
inference(resolve,[$cnf( $equal(intersection(X_14,identity),negative_part(X_14)) )],[refute_0_313,refute_0_316]) ).
cnf(refute_0_318,plain,
( positive_part(intersection(X_14,identity)) != identity
| positive_part(intersection(X_14,identity)) != positive_part(negative_part(X_14))
| positive_part(negative_part(X_14)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(intersection(X_14,identity)),identity) ),[0],$fot(positive_part(negative_part(X_14)))]]) ).
cnf(refute_0_319,plain,
( positive_part(intersection(X_14,identity)) != identity
| positive_part(negative_part(X_14)) = identity ),
inference(resolve,[$cnf( $equal(positive_part(intersection(X_14,identity)),positive_part(negative_part(X_14))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
positive_part(negative_part(X_14)) = identity,
inference(resolve,[$cnf( $equal(positive_part(intersection(X_14,identity)),identity) )],[refute_0_312,refute_0_319]) ).
cnf(refute_0_321,plain,
( intersection(negative_part(X_14),positive_part(negative_part(X_14))) != negative_part(X_14)
| positive_part(negative_part(X_14)) != identity
| intersection(negative_part(X_14),identity) = negative_part(X_14) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(negative_part(X_14),positive_part(negative_part(X_14))),negative_part(X_14)) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_322,plain,
( intersection(negative_part(X_14),positive_part(negative_part(X_14))) != negative_part(X_14)
| intersection(negative_part(X_14),identity) = negative_part(X_14) ),
inference(resolve,[$cnf( $equal(positive_part(negative_part(X_14)),identity) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
intersection(negative_part(X_14),identity) = negative_part(X_14),
inference(resolve,[$cnf( $equal(intersection(negative_part(X_14),positive_part(negative_part(X_14))),negative_part(X_14)) )],[refute_0_303,refute_0_322]) ).
cnf(refute_0_324,plain,
intersection(negative_part(X_14),identity) = negative_part(negative_part(X_14)),
inference(subst,[],[refute_0_121:[bind(X,$fot(negative_part(X_14)))]]) ).
cnf(refute_0_325,plain,
( intersection(negative_part(X_14),identity) != negative_part(X_14)
| intersection(negative_part(X_14),identity) != negative_part(negative_part(X_14))
| negative_part(negative_part(X_14)) = negative_part(X_14) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(negative_part(X_14),identity),negative_part(X_14)) ),[0],$fot(negative_part(negative_part(X_14)))]]) ).
cnf(refute_0_326,plain,
( intersection(negative_part(X_14),identity) != negative_part(X_14)
| negative_part(negative_part(X_14)) = negative_part(X_14) ),
inference(resolve,[$cnf( $equal(intersection(negative_part(X_14),identity),negative_part(negative_part(X_14))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
negative_part(negative_part(X_14)) = negative_part(X_14),
inference(resolve,[$cnf( $equal(intersection(negative_part(X_14),identity),negative_part(X_14)) )],[refute_0_323,refute_0_326]) ).
cnf(refute_0_328,plain,
( multiply(inverse(negative_part(X_14)),negative_part(negative_part(X_14))) != negative_part(inverse(negative_part(X_14)))
| negative_part(negative_part(X_14)) != negative_part(X_14)
| multiply(inverse(negative_part(X_14)),negative_part(X_14)) = negative_part(inverse(negative_part(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(negative_part(X_14)),negative_part(negative_part(X_14))),negative_part(inverse(negative_part(X_14)))) ),[0,1],$fot(negative_part(X_14))]]) ).
cnf(refute_0_329,plain,
( multiply(inverse(negative_part(X_14)),negative_part(negative_part(X_14))) != negative_part(inverse(negative_part(X_14)))
| multiply(inverse(negative_part(X_14)),negative_part(X_14)) = negative_part(inverse(negative_part(X_14))) ),
inference(resolve,[$cnf( $equal(negative_part(negative_part(X_14)),negative_part(X_14)) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
multiply(inverse(negative_part(X_14)),negative_part(X_14)) = negative_part(inverse(negative_part(X_14))),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(X_14)),negative_part(negative_part(X_14))),negative_part(inverse(negative_part(X_14)))) )],[refute_0_289,refute_0_329]) ).
cnf(refute_0_331,plain,
multiply(inverse(negative_part(X_14)),negative_part(X_14)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(negative_part(X_14)))]]) ).
cnf(refute_0_332,plain,
( multiply(inverse(negative_part(X_14)),negative_part(X_14)) != identity
| multiply(inverse(negative_part(X_14)),negative_part(X_14)) != negative_part(inverse(negative_part(X_14)))
| identity = negative_part(inverse(negative_part(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(negative_part(X_14)),negative_part(X_14)),negative_part(inverse(negative_part(X_14)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_333,plain,
( multiply(inverse(negative_part(X_14)),negative_part(X_14)) != negative_part(inverse(negative_part(X_14)))
| identity = negative_part(inverse(negative_part(X_14))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(X_14)),negative_part(X_14)),identity) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
identity = negative_part(inverse(negative_part(X_14))),
inference(resolve,[$cnf( $equal(multiply(inverse(negative_part(X_14)),negative_part(X_14)),negative_part(inverse(negative_part(X_14)))) )],[refute_0_330,refute_0_333]) ).
cnf(refute_0_335,plain,
( identity != negative_part(inverse(negative_part(X_14)))
| negative_part(inverse(negative_part(X_14))) = identity ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(identity)),bind(Y0,$fot(negative_part(inverse(negative_part(X_14)))))]]) ).
cnf(refute_0_336,plain,
negative_part(inverse(negative_part(X_14))) = identity,
inference(resolve,[$cnf( $equal(identity,negative_part(inverse(negative_part(X_14)))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
negative_part(inverse(negative_part(inverse(X)))) = identity,
inference(subst,[],[refute_0_336:[bind(X_14,$fot(inverse(X)))]]) ).
cnf(refute_0_338,plain,
multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))),
introduced(tautology,[refl,[$fot(multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))]]) ).
cnf(refute_0_339,plain,
( multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) != multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))
| negative_part(inverse(negative_part(inverse(X)))) != identity
| multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(inverse(X)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_340,plain,
( negative_part(inverse(negative_part(inverse(X)))) != identity
| multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(inverse(X)),identity) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(inverse(X)),identity),
inference(resolve,[$cnf( $equal(negative_part(inverse(negative_part(inverse(X)))),identity) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
( multiply(positive_part(inverse(X)),identity) != positive_part(inverse(X))
| multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) != multiply(positive_part(inverse(X)),identity)
| multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) = positive_part(inverse(X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))),bind(Y0,$fot(multiply(positive_part(inverse(X)),identity))),bind(Z0,$fot(positive_part(inverse(X))))]]) ).
cnf(refute_0_343,plain,
( multiply(positive_part(inverse(X)),identity) != positive_part(inverse(X))
| multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) = positive_part(inverse(X)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))),multiply(positive_part(inverse(X)),identity)) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) = positive_part(inverse(X)),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X)),identity),positive_part(inverse(X))) )],[refute_0_288,refute_0_343]) ).
cnf(refute_0_345,plain,
multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) = multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),
introduced(tautology,[refl,[$fot(multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))))]]) ).
cnf(refute_0_346,plain,
( multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) != multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))
| multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) != positive_part(inverse(X))
| multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) = multiply(negative_part(X),positive_part(inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))) ),[1,1],$fot(positive_part(inverse(X)))]]) ).
cnf(refute_0_347,plain,
( multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))) != positive_part(inverse(X))
| multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) = multiply(negative_part(X),positive_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) = multiply(negative_part(X),positive_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))),positive_part(inverse(X))) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
multiply(union(negative_part(X_143),negative_part(inverse(X_143))),X) = union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)),
inference(subst,[],[multiply_union2:[bind(Y,$fot(negative_part(X_143))),bind(Z,$fot(negative_part(inverse(X_143))))]]) ).
cnf(refute_0_350,plain,
multiply(positive_part(X_143),negative_part(inverse(X_143))) = union(negative_part(X_143),negative_part(inverse(X_143))),
inference(subst,[],[refute_0_282:[bind(X,$fot(X_143))]]) ).
cnf(refute_0_351,plain,
( multiply(positive_part(X_143),negative_part(inverse(X_143))) != union(negative_part(X_143),negative_part(inverse(X_143)))
| union(negative_part(X_143),negative_part(inverse(X_143))) = multiply(positive_part(X_143),negative_part(inverse(X_143))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(positive_part(X_143),negative_part(inverse(X_143))))),bind(Y0,$fot(union(negative_part(X_143),negative_part(inverse(X_143)))))]]) ).
cnf(refute_0_352,plain,
union(negative_part(X_143),negative_part(inverse(X_143))) = multiply(positive_part(X_143),negative_part(inverse(X_143))),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_143),negative_part(inverse(X_143))),union(negative_part(X_143),negative_part(inverse(X_143)))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
( multiply(union(negative_part(X_143),negative_part(inverse(X_143))),X) != union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))
| union(negative_part(X_143),negative_part(inverse(X_143))) != multiply(positive_part(X_143),negative_part(inverse(X_143)))
| multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) = union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(negative_part(X_143),negative_part(inverse(X_143))),X),union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))) ),[0,0],$fot(multiply(positive_part(X_143),negative_part(inverse(X_143))))]]) ).
cnf(refute_0_354,plain,
( multiply(union(negative_part(X_143),negative_part(inverse(X_143))),X) != union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))
| multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) = union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) ),
inference(resolve,[$cnf( $equal(union(negative_part(X_143),negative_part(inverse(X_143))),multiply(positive_part(X_143),negative_part(inverse(X_143)))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) = union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)),
inference(resolve,[$cnf( $equal(multiply(union(negative_part(X_143),negative_part(inverse(X_143))),X),union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))) )],[refute_0_349,refute_0_354]) ).
cnf(refute_0_356,plain,
multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) = multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)),
inference(subst,[],[associativity:[bind(X,$fot(positive_part(X_143))),bind(Y,$fot(negative_part(inverse(X_143)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_357,plain,
( multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) != multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X))
| multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) != union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))
| multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) = union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X),union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))) ),[0],$fot(multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)))]]) ).
cnf(refute_0_358,plain,
( multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) != union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))
| multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) = union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X),multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
( multiply(positive_part(X_61),X_60) != union(X_60,multiply(X_61,X_60))
| union(X_60,multiply(X_61,X_60)) = multiply(positive_part(X_61),X_60) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(positive_part(X_61),X_60))),bind(Y0,$fot(union(X_60,multiply(X_61,X_60))))]]) ).
cnf(refute_0_360,plain,
union(X_60,multiply(X_61,X_60)) = multiply(positive_part(X_61),X_60),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_61),X_60),union(X_60,multiply(X_61,X_60))) )],[refute_0_249,refute_0_359]) ).
cnf(refute_0_361,plain,
union(X,multiply(inverse(X_143),X)) = multiply(positive_part(inverse(X_143)),X),
inference(subst,[],[refute_0_360:[bind(X_60,$fot(X)),bind(X_61,$fot(inverse(X_143)))]]) ).
cnf(refute_0_362,plain,
multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))) = multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))),
introduced(tautology,[refl,[$fot(multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))))]]) ).
cnf(refute_0_363,plain,
( multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))) != multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X)))
| union(X,multiply(inverse(X_143),X)) != multiply(positive_part(inverse(X_143)),X)
| multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))),multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X)))) ),[1,1],$fot(multiply(positive_part(inverse(X_143)),X))]]) ).
cnf(refute_0_364,plain,
( union(X,multiply(inverse(X_143),X)) != multiply(positive_part(inverse(X_143)),X)
| multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))),multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X)))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)),
inference(resolve,[$cnf( $equal(union(X,multiply(inverse(X_143),X)),multiply(positive_part(inverse(X_143)),X)) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) = union(multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)),multiply(negative_part(inverse(X_122)),Z)),
inference(subst,[],[multiply_union1:[bind(X,$fot(negative_part(inverse(X_122)))),bind(Y,$fot(multiply(X_122,X_123)))]]) ).
cnf(refute_0_367,plain,
multiply(multiply(negative_part(inverse(X_116)),X_116),X_117) = multiply(negative_part(inverse(X_116)),multiply(X_116,X_117)),
inference(subst,[],[associativity:[bind(X,$fot(negative_part(inverse(X_116)))),bind(Y,$fot(X_116)),bind(Z,$fot(X_117))]]) ).
cnf(refute_0_368,plain,
multiply(intersection(X_64,inverse(X_63)),X_63) = intersection(multiply(X_64,X_63),multiply(inverse(X_63),X_63)),
inference(subst,[],[multiply_intersection2:[bind(X,$fot(X_63)),bind(Y,$fot(X_64)),bind(Z,$fot(inverse(X_63)))]]) ).
cnf(refute_0_369,plain,
multiply(inverse(X_63),X_63) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_370,plain,
( multiply(intersection(X_64,inverse(X_63)),X_63) != intersection(multiply(X_64,X_63),multiply(inverse(X_63),X_63))
| multiply(inverse(X_63),X_63) != identity
| multiply(intersection(X_64,inverse(X_63)),X_63) = intersection(multiply(X_64,X_63),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(intersection(X_64,inverse(X_63)),X_63),intersection(multiply(X_64,X_63),multiply(inverse(X_63),X_63))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_371,plain,
( multiply(intersection(X_64,inverse(X_63)),X_63) != intersection(multiply(X_64,X_63),multiply(inverse(X_63),X_63))
| multiply(intersection(X_64,inverse(X_63)),X_63) = intersection(multiply(X_64,X_63),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_63),X_63),identity) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
multiply(intersection(X_64,inverse(X_63)),X_63) = intersection(multiply(X_64,X_63),identity),
inference(resolve,[$cnf( $equal(multiply(intersection(X_64,inverse(X_63)),X_63),intersection(multiply(X_64,X_63),multiply(inverse(X_63),X_63))) )],[refute_0_368,refute_0_371]) ).
cnf(refute_0_373,plain,
intersection(multiply(X_64,X_63),identity) = negative_part(multiply(X_64,X_63)),
inference(subst,[],[refute_0_121:[bind(X,$fot(multiply(X_64,X_63)))]]) ).
cnf(refute_0_374,plain,
( multiply(intersection(X_64,inverse(X_63)),X_63) != intersection(multiply(X_64,X_63),identity)
| intersection(multiply(X_64,X_63),identity) != negative_part(multiply(X_64,X_63))
| multiply(intersection(X_64,inverse(X_63)),X_63) = negative_part(multiply(X_64,X_63)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(intersection(X_64,inverse(X_63)),X_63),negative_part(multiply(X_64,X_63))) ),[0],$fot(intersection(multiply(X_64,X_63),identity))]]) ).
cnf(refute_0_375,plain,
( multiply(intersection(X_64,inverse(X_63)),X_63) != intersection(multiply(X_64,X_63),identity)
| multiply(intersection(X_64,inverse(X_63)),X_63) = negative_part(multiply(X_64,X_63)) ),
inference(resolve,[$cnf( $equal(intersection(multiply(X_64,X_63),identity),negative_part(multiply(X_64,X_63))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
multiply(intersection(X_64,inverse(X_63)),X_63) = negative_part(multiply(X_64,X_63)),
inference(resolve,[$cnf( $equal(multiply(intersection(X_64,inverse(X_63)),X_63),intersection(multiply(X_64,X_63),identity)) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
multiply(intersection(identity,inverse(X_66)),X_66) = negative_part(multiply(identity,X_66)),
inference(subst,[],[refute_0_376:[bind(X_63,$fot(X_66)),bind(X_64,$fot(identity))]]) ).
cnf(refute_0_378,plain,
negative_part(inverse(X_66)) = intersection(identity,inverse(X_66)),
inference(subst,[],[refute_0_130:[bind(X,$fot(inverse(X_66)))]]) ).
cnf(refute_0_379,plain,
( negative_part(inverse(X_66)) != intersection(identity,inverse(X_66))
| intersection(identity,inverse(X_66)) = negative_part(inverse(X_66)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(inverse(X_66)))),bind(Y0,$fot(intersection(identity,inverse(X_66))))]]) ).
cnf(refute_0_380,plain,
intersection(identity,inverse(X_66)) = negative_part(inverse(X_66)),
inference(resolve,[$cnf( $equal(negative_part(inverse(X_66)),intersection(identity,inverse(X_66))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
( multiply(intersection(identity,inverse(X_66)),X_66) != negative_part(multiply(identity,X_66))
| intersection(identity,inverse(X_66)) != negative_part(inverse(X_66))
| multiply(negative_part(inverse(X_66)),X_66) = negative_part(multiply(identity,X_66)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(intersection(identity,inverse(X_66)),X_66),negative_part(multiply(identity,X_66))) ),[0,0],$fot(negative_part(inverse(X_66)))]]) ).
cnf(refute_0_382,plain,
( multiply(intersection(identity,inverse(X_66)),X_66) != negative_part(multiply(identity,X_66))
| multiply(negative_part(inverse(X_66)),X_66) = negative_part(multiply(identity,X_66)) ),
inference(resolve,[$cnf( $equal(intersection(identity,inverse(X_66)),negative_part(inverse(X_66))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
multiply(negative_part(inverse(X_66)),X_66) = negative_part(multiply(identity,X_66)),
inference(resolve,[$cnf( $equal(multiply(intersection(identity,inverse(X_66)),X_66),negative_part(multiply(identity,X_66))) )],[refute_0_377,refute_0_382]) ).
cnf(refute_0_384,plain,
multiply(identity,X_66) = X_66,
inference(subst,[],[left_identity:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_385,plain,
negative_part(multiply(identity,X_66)) = negative_part(multiply(identity,X_66)),
introduced(tautology,[refl,[$fot(negative_part(multiply(identity,X_66)))]]) ).
cnf(refute_0_386,plain,
( multiply(identity,X_66) != X_66
| negative_part(multiply(identity,X_66)) != negative_part(multiply(identity,X_66))
| negative_part(multiply(identity,X_66)) = negative_part(X_66) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(multiply(identity,X_66)),negative_part(multiply(identity,X_66))) ),[1,0],$fot(X_66)]]) ).
cnf(refute_0_387,plain,
( multiply(identity,X_66) != X_66
| negative_part(multiply(identity,X_66)) = negative_part(X_66) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(identity,X_66)),negative_part(multiply(identity,X_66))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
negative_part(multiply(identity,X_66)) = negative_part(X_66),
inference(resolve,[$cnf( $equal(multiply(identity,X_66),X_66) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
( multiply(negative_part(inverse(X_66)),X_66) != negative_part(multiply(identity,X_66))
| negative_part(multiply(identity,X_66)) != negative_part(X_66)
| multiply(negative_part(inverse(X_66)),X_66) = negative_part(X_66) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(inverse(X_66)),X_66),negative_part(X_66)) ),[0],$fot(negative_part(multiply(identity,X_66)))]]) ).
cnf(refute_0_390,plain,
( multiply(negative_part(inverse(X_66)),X_66) != negative_part(multiply(identity,X_66))
| multiply(negative_part(inverse(X_66)),X_66) = negative_part(X_66) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(identity,X_66)),negative_part(X_66)) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
multiply(negative_part(inverse(X_66)),X_66) = negative_part(X_66),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_66)),X_66),negative_part(multiply(identity,X_66))) )],[refute_0_383,refute_0_390]) ).
cnf(refute_0_392,plain,
multiply(negative_part(inverse(X_116)),X_116) = negative_part(X_116),
inference(subst,[],[refute_0_391:[bind(X_66,$fot(X_116))]]) ).
cnf(refute_0_393,plain,
( multiply(multiply(negative_part(inverse(X_116)),X_116),X_117) != multiply(negative_part(inverse(X_116)),multiply(X_116,X_117))
| multiply(negative_part(inverse(X_116)),X_116) != negative_part(X_116)
| multiply(negative_part(X_116),X_117) = multiply(negative_part(inverse(X_116)),multiply(X_116,X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(negative_part(inverse(X_116)),X_116),X_117),multiply(negative_part(inverse(X_116)),multiply(X_116,X_117))) ),[0,0],$fot(negative_part(X_116))]]) ).
cnf(refute_0_394,plain,
( multiply(multiply(negative_part(inverse(X_116)),X_116),X_117) != multiply(negative_part(inverse(X_116)),multiply(X_116,X_117))
| multiply(negative_part(X_116),X_117) = multiply(negative_part(inverse(X_116)),multiply(X_116,X_117)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_116)),X_116),negative_part(X_116)) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
multiply(negative_part(X_116),X_117) = multiply(negative_part(inverse(X_116)),multiply(X_116,X_117)),
inference(resolve,[$cnf( $equal(multiply(multiply(negative_part(inverse(X_116)),X_116),X_117),multiply(negative_part(inverse(X_116)),multiply(X_116,X_117))) )],[refute_0_367,refute_0_394]) ).
cnf(refute_0_396,plain,
multiply(negative_part(X_122),X_123) = multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)),
inference(subst,[],[refute_0_395:[bind(X_116,$fot(X_122)),bind(X_117,$fot(X_123))]]) ).
cnf(refute_0_397,plain,
( multiply(negative_part(X_122),X_123) != multiply(negative_part(inverse(X_122)),multiply(X_122,X_123))
| multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)) = multiply(negative_part(X_122),X_123) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(negative_part(X_122),X_123))),bind(Y0,$fot(multiply(negative_part(inverse(X_122)),multiply(X_122,X_123))))]]) ).
cnf(refute_0_398,plain,
multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)) = multiply(negative_part(X_122),X_123),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),multiply(X_122,X_123))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
( multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)) != multiply(negative_part(X_122),X_123)
| multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) != union(multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)),multiply(negative_part(inverse(X_122)),Z))
| multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) = union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)),union(multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)),multiply(negative_part(inverse(X_122)),Z))) ),[1,0],$fot(multiply(negative_part(X_122),X_123))]]) ).
cnf(refute_0_400,plain,
( multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) != union(multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)),multiply(negative_part(inverse(X_122)),Z))
| multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) = union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)),multiply(negative_part(X_122),X_123)) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) = union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)),union(multiply(negative_part(inverse(X_122)),multiply(X_122,X_123)),multiply(negative_part(inverse(X_122)),Z))) )],[refute_0_366,refute_0_400]) ).
cnf(refute_0_402,plain,
multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) = union(multiply(negative_part(X_136),Y),multiply(negative_part(X_136),multiply(inverse(X_136),X_137))),
inference(subst,[],[multiply_union1:[bind(X,$fot(negative_part(X_136))),bind(Z,$fot(multiply(inverse(X_136),X_137)))]]) ).
cnf(refute_0_403,plain,
multiply(multiply(negative_part(X),inverse(X)),X_117) = multiply(negative_part(X),multiply(inverse(X),X_117)),
inference(subst,[],[associativity:[bind(X,$fot(negative_part(X))),bind(Y,$fot(inverse(X))),bind(Z,$fot(X_117))]]) ).
cnf(refute_0_404,plain,
multiply(negative_part(inverse(inverse(X))),inverse(X)) = negative_part(inverse(X)),
inference(subst,[],[refute_0_391:[bind(X_66,$fot(inverse(X)))]]) ).
cnf(refute_0_405,plain,
( multiply(negative_part(inverse(inverse(X))),inverse(X)) != negative_part(inverse(X))
| inverse(inverse(X)) != X
| multiply(negative_part(X),inverse(X)) = negative_part(inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(inverse(X))),inverse(X)),negative_part(inverse(X))) ),[0,0,0],$fot(X)]]) ).
cnf(refute_0_406,plain,
( multiply(negative_part(inverse(inverse(X))),inverse(X)) != negative_part(inverse(X))
| multiply(negative_part(X),inverse(X)) = negative_part(inverse(X)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_405]) ).
cnf(refute_0_407,plain,
multiply(negative_part(X),inverse(X)) = negative_part(inverse(X)),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(inverse(X))),inverse(X)),negative_part(inverse(X))) )],[refute_0_404,refute_0_406]) ).
cnf(refute_0_408,plain,
( multiply(multiply(negative_part(X),inverse(X)),X_117) != multiply(negative_part(X),multiply(inverse(X),X_117))
| multiply(negative_part(X),inverse(X)) != negative_part(inverse(X))
| multiply(negative_part(inverse(X)),X_117) = multiply(negative_part(X),multiply(inverse(X),X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(negative_part(X),inverse(X)),X_117),multiply(negative_part(X),multiply(inverse(X),X_117))) ),[0,0],$fot(negative_part(inverse(X)))]]) ).
cnf(refute_0_409,plain,
( multiply(multiply(negative_part(X),inverse(X)),X_117) != multiply(negative_part(X),multiply(inverse(X),X_117))
| multiply(negative_part(inverse(X)),X_117) = multiply(negative_part(X),multiply(inverse(X),X_117)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(X),inverse(X)),negative_part(inverse(X))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
multiply(negative_part(inverse(X)),X_117) = multiply(negative_part(X),multiply(inverse(X),X_117)),
inference(resolve,[$cnf( $equal(multiply(multiply(negative_part(X),inverse(X)),X_117),multiply(negative_part(X),multiply(inverse(X),X_117))) )],[refute_0_403,refute_0_409]) ).
cnf(refute_0_411,plain,
multiply(negative_part(inverse(X_136)),X_137) = multiply(negative_part(X_136),multiply(inverse(X_136),X_137)),
inference(subst,[],[refute_0_410:[bind(X,$fot(X_136)),bind(X_117,$fot(X_137))]]) ).
cnf(refute_0_412,plain,
( multiply(negative_part(inverse(X_136)),X_137) != multiply(negative_part(X_136),multiply(inverse(X_136),X_137))
| multiply(negative_part(X_136),multiply(inverse(X_136),X_137)) = multiply(negative_part(inverse(X_136)),X_137) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(negative_part(inverse(X_136)),X_137))),bind(Y0,$fot(multiply(negative_part(X_136),multiply(inverse(X_136),X_137))))]]) ).
cnf(refute_0_413,plain,
multiply(negative_part(X_136),multiply(inverse(X_136),X_137)) = multiply(negative_part(inverse(X_136)),X_137),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_136)),X_137),multiply(negative_part(X_136),multiply(inverse(X_136),X_137))) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
( multiply(negative_part(X_136),multiply(inverse(X_136),X_137)) != multiply(negative_part(inverse(X_136)),X_137)
| multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) != union(multiply(negative_part(X_136),Y),multiply(negative_part(X_136),multiply(inverse(X_136),X_137)))
| multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) = union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))),union(multiply(negative_part(X_136),Y),multiply(negative_part(X_136),multiply(inverse(X_136),X_137)))) ),[1,1],$fot(multiply(negative_part(inverse(X_136)),X_137))]]) ).
cnf(refute_0_415,plain,
( multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) != union(multiply(negative_part(X_136),Y),multiply(negative_part(X_136),multiply(inverse(X_136),X_137)))
| multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) = union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_136),multiply(inverse(X_136),X_137)),multiply(negative_part(inverse(X_136)),X_137)) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) = union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137)),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))),union(multiply(negative_part(X_136),Y),multiply(negative_part(X_136),multiply(inverse(X_136),X_137)))) )],[refute_0_402,refute_0_415]) ).
cnf(refute_0_417,plain,
( multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) != union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))
| union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) = multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)))),bind(Y0,$fot(union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))))]]) ).
cnf(refute_0_418,plain,
union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) = multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)),union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))) )],[refute_0_401,refute_0_417]) ).
cnf(refute_0_419,plain,
union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137)) = multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137)),
inference(subst,[],[refute_0_418:[bind(Z,$fot(X_137)),bind(X_122,$fot(X_136)),bind(X_123,$fot(Y))]]) ).
cnf(refute_0_420,plain,
( multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) != union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137))
| union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137)) != multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137))
| multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) = multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))),multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137))) ),[0],$fot(union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137)))]]) ).
cnf(refute_0_421,plain,
( multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) != union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137))
| multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) = multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137)) ),
inference(resolve,[$cnf( $equal(union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137)),multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) = multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137)),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))),union(multiply(negative_part(X_136),Y),multiply(negative_part(inverse(X_136)),X_137))) )],[refute_0_416,refute_0_421]) ).
cnf(refute_0_423,plain,
( multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) != multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137))
| multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137)) = multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))))),bind(Y0,$fot(multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137))))]]) ).
cnf(refute_0_424,plain,
multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137)) = multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_136),union(Y,multiply(inverse(X_136),X_137))),multiply(negative_part(inverse(X_136)),union(multiply(X_136,Y),X_137))) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) = multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))),
inference(subst,[],[refute_0_424:[bind(Y,$fot(X_123)),bind(X_136,$fot(X_122)),bind(X_137,$fot(Z))]]) ).
cnf(refute_0_426,plain,
( multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) != multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z)))
| multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) != union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))
| multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))) = union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)),union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))) ),[0],$fot(multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))))]]) ).
cnf(refute_0_427,plain,
( multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)) != union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))
| multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))) = union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)),multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z)))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))) = union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_122)),union(multiply(X_122,X_123),Z)),union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))) )],[refute_0_401,refute_0_427]) ).
cnf(refute_0_429,plain,
( multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))) != union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))
| union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) = multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))))),bind(Y0,$fot(union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))))]]) ).
cnf(refute_0_430,plain,
union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z)) = multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_122),union(X_123,multiply(inverse(X_122),Z))),union(multiply(negative_part(X_122),X_123),multiply(negative_part(inverse(X_122)),Z))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))),
inference(subst,[],[refute_0_430:[bind(Z,$fot(X)),bind(X_122,$fot(X_143)),bind(X_123,$fot(X))]]) ).
cnf(refute_0_432,plain,
( multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))) != multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X))
| union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) != multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X)))
| union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)))),bind(Y0,$fot(multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))))),bind(Z0,$fot(multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X))))]]) ).
cnf(refute_0_433,plain,
( multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))) != multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X))
| union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)) ),
inference(resolve,[$cnf( $equal(union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)),multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X)))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)),
inference(resolve,[$cnf( $equal(multiply(negative_part(X_143),union(X,multiply(inverse(X_143),X))),multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X))) )],[refute_0_365,refute_0_433]) ).
cnf(refute_0_435,plain,
( multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) != union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))
| union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)) != multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X))
| multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)),multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X))) ),[0],$fot(union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)))]]) ).
cnf(refute_0_436,plain,
( multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) != union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))
| multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)) ),
inference(resolve,[$cnf( $equal(union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X)),multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
( multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X) != union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))
| multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)),union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))) )],[refute_0_358,refute_0_436]) ).
cnf(refute_0_438,plain,
multiply(positive_part(X_143),multiply(negative_part(inverse(X_143)),X)) = multiply(negative_part(X_143),multiply(positive_part(inverse(X_143)),X)),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X_143),negative_part(inverse(X_143))),X),union(multiply(negative_part(X_143),X),multiply(negative_part(inverse(X_143)),X))) )],[refute_0_355,refute_0_437]) ).
cnf(refute_0_439,plain,
multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) = multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),
inference(subst,[],[refute_0_438:[bind(X,$fot(negative_part(inverse(negative_part(inverse(X)))))),bind(X_143,$fot(X))]]) ).
cnf(refute_0_440,plain,
multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),
inference(subst,[],[associativity:[bind(X,$fot(positive_part(X))),bind(Y,$fot(negative_part(inverse(X)))),bind(Z,$fot(negative_part(inverse(negative_part(inverse(X))))))]]) ).
cnf(refute_0_441,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))
| multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) != multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))),bind(Y0,$fot(multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))))),bind(Z0,$fot(multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))))]]) ).
cnf(refute_0_442,plain,
( multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) != multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),
inference(resolve,[$cnf( $equal(multiply(positive_part(X),multiply(negative_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))) )],[refute_0_439,refute_0_442]) ).
cnf(refute_0_444,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))
| multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) != multiply(negative_part(X),positive_part(inverse(X)))
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(negative_part(X),positive_part(inverse(X))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))),bind(Y0,$fot(multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))))),bind(Z0,$fot(multiply(negative_part(X),positive_part(inverse(X)))))]]) ).
cnf(refute_0_445,plain,
( multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))) != multiply(negative_part(X),positive_part(inverse(X)))
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(negative_part(X),positive_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X))))))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(negative_part(X),positive_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(negative_part(X),multiply(positive_part(inverse(X)),negative_part(inverse(negative_part(inverse(X)))))),multiply(negative_part(X),positive_part(inverse(X)))) )],[refute_0_348,refute_0_445]) ).
cnf(refute_0_447,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(negative_part(X),positive_part(inverse(X)))
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))
| multiply(negative_part(X),positive_part(inverse(X))) = union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))) ),[0],$fot(multiply(negative_part(X),positive_part(inverse(X))))]]) ).
cnf(refute_0_448,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))
| multiply(negative_part(X),positive_part(inverse(X))) = union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(negative_part(X),positive_part(inverse(X)))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
multiply(multiply(positive_part(X),negative_part(inverse(X))),identity) = multiply(positive_part(X),negative_part(inverse(X))),
inference(subst,[],[refute_0_65:[bind(X,$fot(multiply(positive_part(X),negative_part(inverse(X)))))]]) ).
cnf(refute_0_450,plain,
multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),
introduced(tautology,[refl,[$fot(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))]]) ).
cnf(refute_0_451,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))
| negative_part(inverse(negative_part(inverse(X)))) != identity
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_452,plain,
( negative_part(inverse(negative_part(inverse(X)))) != identity
| multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),identity) ),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),identity),
inference(resolve,[$cnf( $equal(negative_part(inverse(negative_part(inverse(X)))),identity) )],[refute_0_337,refute_0_452]) ).
cnf(refute_0_454,plain,
multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),
introduced(tautology,[refl,[$fot(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))]]) ).
cnf(refute_0_455,plain,
( multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))
| union(negative_part(X),negative_part(inverse(X))) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))) ),[1,0],$fot(multiply(positive_part(X),negative_part(inverse(X))))]]) ).
cnf(refute_0_456,plain,
( union(negative_part(X),negative_part(inverse(X))) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) ),
inference(resolve,[$cnf( $equal(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),
inference(resolve,[$cnf( $equal(union(negative_part(X),negative_part(inverse(X))),multiply(positive_part(X),negative_part(inverse(X)))) )],[refute_0_284,refute_0_456]) ).
cnf(refute_0_458,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(multiply(positive_part(X),negative_part(inverse(X))),identity)
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),identity) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))),bind(Y0,$fot(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))),bind(Z0,$fot(multiply(multiply(positive_part(X),negative_part(inverse(X))),identity)))]]) ).
cnf(refute_0_459,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(multiply(positive_part(X),negative_part(inverse(X))),identity)
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),identity) ),
inference(resolve,[$cnf( $equal(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(multiply(positive_part(X),negative_part(inverse(X))),identity),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(multiply(positive_part(X),negative_part(inverse(X))),identity)) )],[refute_0_453,refute_0_459]) ).
cnf(refute_0_461,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),identity) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(multiply(positive_part(X),negative_part(inverse(X))),identity)
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(X),negative_part(inverse(X))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))),bind(Y0,$fot(multiply(multiply(positive_part(X),negative_part(inverse(X))),identity))),bind(Z0,$fot(multiply(positive_part(X),negative_part(inverse(X)))))]]) ).
cnf(refute_0_462,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),identity) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(X),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(multiply(positive_part(X),negative_part(inverse(X))),identity)) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) = multiply(positive_part(X),negative_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),identity),multiply(positive_part(X),negative_part(inverse(X)))) )],[refute_0_449,refute_0_462]) ).
cnf(refute_0_464,plain,
( multiply(union(X_61,X_62),negative_part(inverse(X_62))) != union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62))))
| union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62)))) = multiply(union(X_61,X_62),negative_part(inverse(X_62))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(union(X_61,X_62),negative_part(inverse(X_62))))),bind(Y0,$fot(union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62))))))]]) ).
cnf(refute_0_465,plain,
union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62)))) = multiply(union(X_61,X_62),negative_part(inverse(X_62))),
inference(resolve,[$cnf( $equal(multiply(union(X_61,X_62),negative_part(inverse(X_62))),union(negative_part(X_62),multiply(X_61,negative_part(inverse(X_62))))) )],[refute_0_231,refute_0_464]) ).
cnf(refute_0_466,plain,
union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) = multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),
inference(subst,[],[refute_0_465:[bind(X_61,$fot(negative_part(X))),bind(X_62,$fot(negative_part(inverse(X))))]]) ).
cnf(refute_0_467,plain,
( multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(positive_part(X),negative_part(inverse(X)))
| union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) != multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))
| union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) = multiply(positive_part(X),negative_part(inverse(X))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))))),bind(Y0,$fot(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))))),bind(Z0,$fot(multiply(positive_part(X),negative_part(inverse(X)))))]]) ).
cnf(refute_0_468,plain,
( multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != multiply(positive_part(X),negative_part(inverse(X)))
| union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) = multiply(positive_part(X),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))),multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X)))))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) = multiply(positive_part(X),negative_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(union(negative_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),multiply(positive_part(X),negative_part(inverse(X)))) )],[refute_0_463,refute_0_468]) ).
cnf(refute_0_470,plain,
( multiply(negative_part(X),positive_part(inverse(X))) != union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))
| union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(negative_part(X),positive_part(inverse(X))) = multiply(positive_part(X),negative_part(inverse(X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(X),positive_part(inverse(X))),multiply(positive_part(X),negative_part(inverse(X)))) ),[0],$fot(union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))))]]) ).
cnf(refute_0_471,plain,
( multiply(negative_part(X),positive_part(inverse(X))) != union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))
| multiply(negative_part(X),positive_part(inverse(X))) = multiply(positive_part(X),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X)))))),multiply(positive_part(X),negative_part(inverse(X)))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
( multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))) != union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))
| multiply(negative_part(X),positive_part(inverse(X))) = multiply(positive_part(X),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(X),positive_part(inverse(X))),union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))) )],[refute_0_448,refute_0_471]) ).
cnf(refute_0_473,plain,
multiply(negative_part(X),positive_part(inverse(X))) = multiply(positive_part(X),negative_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(multiply(positive_part(X),negative_part(inverse(X))),negative_part(inverse(negative_part(inverse(X))))),union(negative_part(negative_part(inverse(X))),multiply(negative_part(X),negative_part(inverse(negative_part(inverse(X))))))) )],[refute_0_287,refute_0_472]) ).
cnf(refute_0_474,plain,
( multiply(negative_part(X),positive_part(inverse(X))) != multiply(positive_part(X),negative_part(inverse(X)))
| multiply(positive_part(X),negative_part(inverse(X))) = multiply(negative_part(X),positive_part(inverse(X))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiply(negative_part(X),positive_part(inverse(X))))),bind(Y0,$fot(multiply(positive_part(X),negative_part(inverse(X)))))]]) ).
cnf(refute_0_475,plain,
multiply(positive_part(X),negative_part(inverse(X))) = multiply(negative_part(X),positive_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(negative_part(X),positive_part(inverse(X))),multiply(positive_part(X),negative_part(inverse(X)))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
( multiply(negative_part(inverse(X)),negative_part(inverse(multiply(positive_part(X),negative_part(inverse(X)))))) != intersection(inverse(positive_part(X)),negative_part(inverse(X)))
| multiply(positive_part(X),negative_part(inverse(X))) != multiply(negative_part(X),positive_part(inverse(X)))
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = intersection(inverse(positive_part(X)),negative_part(inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(positive_part(X),negative_part(inverse(X)))))),intersection(inverse(positive_part(X)),negative_part(inverse(X)))) ),[0,1,0,0],$fot(multiply(negative_part(X),positive_part(inverse(X))))]]) ).
cnf(refute_0_477,plain,
( multiply(negative_part(inverse(X)),negative_part(inverse(multiply(positive_part(X),negative_part(inverse(X)))))) != intersection(inverse(positive_part(X)),negative_part(inverse(X)))
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = intersection(inverse(positive_part(X)),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X),negative_part(inverse(X))),multiply(negative_part(X),positive_part(inverse(X)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = intersection(inverse(positive_part(X)),negative_part(inverse(X))),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(positive_part(X),negative_part(inverse(X)))))),intersection(inverse(positive_part(X)),negative_part(inverse(X)))) )],[refute_0_220,refute_0_477]) ).
cnf(refute_0_479,plain,
multiply(negative_part(inverse(X)),identity) = negative_part(inverse(X)),
inference(subst,[],[refute_0_65:[bind(X,$fot(negative_part(inverse(X))))]]) ).
cnf(refute_0_480,plain,
multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),
inference(subst,[],[refute_0_473:[bind(X,$fot(multiply(negative_part(X_143),positive_part(inverse(X_143)))))]]) ).
cnf(refute_0_481,plain,
union(identity,union(X_132,X_133)) = union(union(identity,X_132),X_133),
inference(subst,[],[union_associative:[bind(X,$fot(identity)),bind(Y,$fot(X_132)),bind(Z,$fot(X_133))]]) ).
cnf(refute_0_482,plain,
positive_part(X_132) = union(identity,X_132),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_132))]]) ).
cnf(refute_0_483,plain,
( positive_part(X_132) != union(identity,X_132)
| union(identity,X_132) = positive_part(X_132) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(positive_part(X_132))),bind(Y0,$fot(union(identity,X_132)))]]) ).
cnf(refute_0_484,plain,
union(identity,X_132) = positive_part(X_132),
inference(resolve,[$cnf( $equal(positive_part(X_132),union(identity,X_132)) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
( union(identity,X_132) != positive_part(X_132)
| union(identity,union(X_132,X_133)) != union(union(identity,X_132),X_133)
| union(identity,union(X_132,X_133)) = union(positive_part(X_132),X_133) ),
introduced(tautology,[equality,[$cnf( $equal(union(identity,union(X_132,X_133)),union(union(identity,X_132),X_133)) ),[1,0],$fot(positive_part(X_132))]]) ).
cnf(refute_0_486,plain,
( union(identity,union(X_132,X_133)) != union(union(identity,X_132),X_133)
| union(identity,union(X_132,X_133)) = union(positive_part(X_132),X_133) ),
inference(resolve,[$cnf( $equal(union(identity,X_132),positive_part(X_132)) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
union(identity,union(X_132,X_133)) = union(positive_part(X_132),X_133),
inference(resolve,[$cnf( $equal(union(identity,union(X_132,X_133)),union(union(identity,X_132),X_133)) )],[refute_0_481,refute_0_486]) ).
cnf(refute_0_488,plain,
( positive_part(X) != union(identity,X)
| union(identity,X) = positive_part(X) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(positive_part(X))),bind(Y0,$fot(union(identity,X)))]]) ).
cnf(refute_0_489,plain,
union(identity,X) = positive_part(X),
inference(resolve,[$cnf( $equal(positive_part(X),union(identity,X)) )],[refute_0_38,refute_0_488]) ).
cnf(refute_0_490,plain,
union(identity,union(X_132,X_133)) = positive_part(union(X_132,X_133)),
inference(subst,[],[refute_0_489:[bind(X,$fot(union(X_132,X_133)))]]) ).
cnf(refute_0_491,plain,
( union(identity,union(X_132,X_133)) != positive_part(union(X_132,X_133))
| union(identity,union(X_132,X_133)) != union(positive_part(X_132),X_133)
| positive_part(union(X_132,X_133)) = union(positive_part(X_132),X_133) ),
introduced(tautology,[equality,[$cnf( $equal(union(identity,union(X_132,X_133)),union(positive_part(X_132),X_133)) ),[0],$fot(positive_part(union(X_132,X_133)))]]) ).
cnf(refute_0_492,plain,
( union(identity,union(X_132,X_133)) != union(positive_part(X_132),X_133)
| positive_part(union(X_132,X_133)) = union(positive_part(X_132),X_133) ),
inference(resolve,[$cnf( $equal(union(identity,union(X_132,X_133)),positive_part(union(X_132,X_133))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
positive_part(union(X_132,X_133)) = union(positive_part(X_132),X_133),
inference(resolve,[$cnf( $equal(union(identity,union(X_132,X_133)),union(positive_part(X_132),X_133)) )],[refute_0_487,refute_0_492]) ).
cnf(refute_0_494,plain,
positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) = union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))),
inference(subst,[],[refute_0_493:[bind(X_132,$fot(negative_part(X_143))),bind(X_133,$fot(negative_part(inverse(X_143))))]]) ).
cnf(refute_0_495,plain,
( positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) != union(positive_part(negative_part(X_143)),negative_part(inverse(X_143)))
| union(negative_part(X_143),negative_part(inverse(X_143))) != multiply(positive_part(X_143),negative_part(inverse(X_143)))
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))),union(positive_part(negative_part(X_143)),negative_part(inverse(X_143)))) ),[0,0],$fot(multiply(positive_part(X_143),negative_part(inverse(X_143))))]]) ).
cnf(refute_0_496,plain,
( positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) != union(positive_part(negative_part(X_143)),negative_part(inverse(X_143)))
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) ),
inference(resolve,[$cnf( $equal(union(negative_part(X_143),negative_part(inverse(X_143))),multiply(positive_part(X_143),negative_part(inverse(X_143)))) )],[refute_0_352,refute_0_495]) ).
cnf(refute_0_497,plain,
positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))),
inference(resolve,[$cnf( $equal(positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))),union(positive_part(negative_part(X_143)),negative_part(inverse(X_143)))) )],[refute_0_494,refute_0_496]) ).
cnf(refute_0_498,plain,
positive_part(negative_part(inverse(X_143))) = identity,
inference(subst,[],[refute_0_320:[bind(X_14,$fot(inverse(X_143)))]]) ).
cnf(refute_0_499,plain,
positive_part(union(negative_part(X_14),X_135)) = union(positive_part(negative_part(X_14)),X_135),
inference(subst,[],[refute_0_493:[bind(X_132,$fot(negative_part(X_14))),bind(X_133,$fot(X_135))]]) ).
cnf(refute_0_500,plain,
( positive_part(negative_part(X_14)) != identity
| positive_part(union(negative_part(X_14),X_135)) != union(positive_part(negative_part(X_14)),X_135)
| positive_part(union(negative_part(X_14),X_135)) = union(identity,X_135) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(union(negative_part(X_14),X_135)),union(positive_part(negative_part(X_14)),X_135)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_501,plain,
( positive_part(union(negative_part(X_14),X_135)) != union(positive_part(negative_part(X_14)),X_135)
| positive_part(union(negative_part(X_14),X_135)) = union(identity,X_135) ),
inference(resolve,[$cnf( $equal(positive_part(negative_part(X_14)),identity) )],[refute_0_320,refute_0_500]) ).
cnf(refute_0_502,plain,
positive_part(union(negative_part(X_14),X_135)) = union(identity,X_135),
inference(resolve,[$cnf( $equal(positive_part(union(negative_part(X_14),X_135)),union(positive_part(negative_part(X_14)),X_135)) )],[refute_0_499,refute_0_501]) ).
cnf(refute_0_503,plain,
union(identity,X_135) = positive_part(X_135),
inference(subst,[],[refute_0_489:[bind(X,$fot(X_135))]]) ).
cnf(refute_0_504,plain,
( positive_part(union(negative_part(X_14),X_135)) != union(identity,X_135)
| union(identity,X_135) != positive_part(X_135)
| positive_part(union(negative_part(X_14),X_135)) = positive_part(X_135) ),
introduced(tautology,[equality,[$cnf( ~ $equal(positive_part(union(negative_part(X_14),X_135)),positive_part(X_135)) ),[0],$fot(union(identity,X_135))]]) ).
cnf(refute_0_505,plain,
( positive_part(union(negative_part(X_14),X_135)) != union(identity,X_135)
| positive_part(union(negative_part(X_14),X_135)) = positive_part(X_135) ),
inference(resolve,[$cnf( $equal(union(identity,X_135),positive_part(X_135)) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
positive_part(union(negative_part(X_14),X_135)) = positive_part(X_135),
inference(resolve,[$cnf( $equal(positive_part(union(negative_part(X_14),X_135)),union(identity,X_135)) )],[refute_0_502,refute_0_505]) ).
cnf(refute_0_507,plain,
positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) = positive_part(negative_part(inverse(X_143))),
inference(subst,[],[refute_0_506:[bind(X_135,$fot(negative_part(inverse(X_143)))),bind(X_14,$fot(X_143))]]) ).
cnf(refute_0_508,plain,
( positive_part(negative_part(inverse(X_143))) != identity
| positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) != positive_part(negative_part(inverse(X_143)))
| positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) = identity ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))))),bind(Y0,$fot(positive_part(negative_part(inverse(X_143))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_509,plain,
( positive_part(negative_part(inverse(X_143))) != identity
| positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) = identity ),
inference(resolve,[$cnf( $equal(positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))),positive_part(negative_part(inverse(X_143)))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) = identity,
inference(resolve,[$cnf( $equal(positive_part(negative_part(inverse(X_143))),identity) )],[refute_0_498,refute_0_509]) ).
cnf(refute_0_511,plain,
( positive_part(union(X_132,X_133)) != union(positive_part(X_132),X_133)
| union(positive_part(X_132),X_133) = positive_part(union(X_132,X_133)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(positive_part(union(X_132,X_133)))),bind(Y0,$fot(union(positive_part(X_132),X_133)))]]) ).
cnf(refute_0_512,plain,
union(positive_part(X_132),X_133) = positive_part(union(X_132,X_133)),
inference(resolve,[$cnf( $equal(positive_part(union(X_132,X_133)),union(positive_part(X_132),X_133)) )],[refute_0_493,refute_0_511]) ).
cnf(refute_0_513,plain,
union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) = positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))),
inference(subst,[],[refute_0_512:[bind(X_132,$fot(negative_part(X_143))),bind(X_133,$fot(negative_part(inverse(X_143))))]]) ).
cnf(refute_0_514,plain,
( positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) != identity
| union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) != positive_part(union(negative_part(X_143),negative_part(inverse(X_143))))
| union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) = identity ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))))),bind(Y0,$fot(positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_515,plain,
( positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))) != identity
| union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) = identity ),
inference(resolve,[$cnf( $equal(union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))),positive_part(union(negative_part(X_143),negative_part(inverse(X_143))))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) = identity,
inference(resolve,[$cnf( $equal(positive_part(union(negative_part(X_143),negative_part(inverse(X_143)))),identity) )],[refute_0_510,refute_0_515]) ).
cnf(refute_0_517,plain,
( positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) != union(positive_part(negative_part(X_143)),negative_part(inverse(X_143)))
| union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))) != identity
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),identity) ),[0],$fot(union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))))]]) ).
cnf(refute_0_518,plain,
( positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) != union(positive_part(negative_part(X_143)),negative_part(inverse(X_143)))
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = identity ),
inference(resolve,[$cnf( $equal(union(positive_part(negative_part(X_143)),negative_part(inverse(X_143))),identity) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = identity,
inference(resolve,[$cnf( $equal(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),union(positive_part(negative_part(X_143)),negative_part(inverse(X_143)))) )],[refute_0_497,refute_0_518]) ).
cnf(refute_0_520,plain,
multiply(positive_part(X_143),negative_part(inverse(X_143))) = multiply(negative_part(X_143),positive_part(inverse(X_143))),
inference(subst,[],[refute_0_475:[bind(X,$fot(X_143))]]) ).
cnf(refute_0_521,plain,
positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),
introduced(tautology,[refl,[$fot(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))))]]) ).
cnf(refute_0_522,plain,
( multiply(positive_part(X_143),negative_part(inverse(X_143))) != multiply(negative_part(X_143),positive_part(inverse(X_143)))
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) != positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143))))
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143))))) ),[1,0],$fot(multiply(negative_part(X_143),positive_part(inverse(X_143))))]]) ).
cnf(refute_0_523,plain,
( multiply(positive_part(X_143),negative_part(inverse(X_143))) != multiply(negative_part(X_143),positive_part(inverse(X_143)))
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143))))) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) = positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_143),negative_part(inverse(X_143))),multiply(negative_part(X_143),positive_part(inverse(X_143)))) )],[refute_0_520,refute_0_523]) ).
cnf(refute_0_525,plain,
( positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) != identity
| positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) != positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143))))
| positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),identity) ),[0],$fot(positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))))]]) ).
cnf(refute_0_526,plain,
( positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))) != identity
| positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) = identity ),
inference(resolve,[$cnf( $equal(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143))))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) = identity,
inference(resolve,[$cnf( $equal(positive_part(multiply(positive_part(X_143),negative_part(inverse(X_143)))),identity) )],[refute_0_519,refute_0_526]) ).
cnf(refute_0_528,plain,
( multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) != identity
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_529,plain,
( multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),identity) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),
inference(resolve,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(positive_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) )],[refute_0_480,refute_0_529]) ).
cnf(refute_0_531,plain,
multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) = identity,
inference(subst,[],[refute_0_20:[bind(X_1,$fot(multiply(negative_part(X_143),positive_part(inverse(X_143)))))]]) ).
cnf(refute_0_532,plain,
multiply(positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),
inference(subst,[],[refute_0_173:[bind(X,$fot(multiply(positive_part(X_144),negative_part(inverse(X_144)))))]]) ).
cnf(refute_0_533,plain,
positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = identity,
inference(subst,[],[refute_0_519:[bind(X_143,$fot(X_144))]]) ).
cnf(refute_0_534,plain,
( multiply(positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != identity
| multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_535,plain,
( multiply(positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),identity) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),
inference(resolve,[$cnf( $equal(multiply(positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) )],[refute_0_532,refute_0_535]) ).
cnf(refute_0_537,plain,
multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))))]]) ).
cnf(refute_0_538,plain,
( multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))
| multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) ),[0],$fot(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))]]) ).
cnf(refute_0_539,plain,
( multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) )],[refute_0_536,refute_0_539]) ).
cnf(refute_0_541,plain,
multiply(positive_part(X_144),negative_part(inverse(X_144))) = multiply(negative_part(X_144),positive_part(inverse(X_144))),
inference(subst,[],[refute_0_475:[bind(X,$fot(X_144))]]) ).
cnf(refute_0_542,plain,
inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),
introduced(tautology,[refl,[$fot(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))]]) ).
cnf(refute_0_543,plain,
( multiply(positive_part(X_144),negative_part(inverse(X_144))) != multiply(negative_part(X_144),positive_part(inverse(X_144)))
| inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))
| inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),[1,0],$fot(multiply(negative_part(X_144),positive_part(inverse(X_144))))]]) ).
cnf(refute_0_544,plain,
( multiply(positive_part(X_144),negative_part(inverse(X_144))) != multiply(negative_part(X_144),positive_part(inverse(X_144)))
| inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_144),negative_part(inverse(X_144))),multiply(negative_part(X_144),positive_part(inverse(X_144)))) )],[refute_0_541,refute_0_544]) ).
cnf(refute_0_546,plain,
( inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))
| inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) ),[0],$fot(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))]]) ).
cnf(refute_0_547,plain,
( inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),
introduced(tautology,[refl,[$fot(positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))))]]) ).
cnf(refute_0_549,plain,
( inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))
| positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) ),[1,0],$fot(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))]]) ).
cnf(refute_0_550,plain,
( inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))
| positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) ),
inference(resolve,[$cnf( $equal(positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))),
inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) )],[refute_0_545,refute_0_550]) ).
cnf(refute_0_552,plain,
( inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))
| inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))),positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))) ),[0],$fot(positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))))]]) ).
cnf(refute_0_553,plain,
( inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) ),
inference(resolve,[$cnf( $equal(positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144))))),positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
( inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))
| inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) )],[refute_0_547,refute_0_553]) ).
cnf(refute_0_555,plain,
inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))),
inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))),positive_part(inverse(multiply(positive_part(X_144),negative_part(inverse(X_144)))))) )],[refute_0_540,refute_0_554]) ).
cnf(refute_0_556,plain,
( inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) != positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))
| positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) = inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))),bind(Y0,$fot(positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))))]]) ).
cnf(refute_0_557,plain,
positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144))))) = inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))),
inference(resolve,[$cnf( $equal(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))),positive_part(inverse(multiply(negative_part(X_144),positive_part(inverse(X_144)))))) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) = inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))),
inference(subst,[],[refute_0_557:[bind(X_144,$fot(X_143))]]) ).
cnf(refute_0_559,plain,
multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),
introduced(tautology,[refl,[$fot(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))]]) ).
cnf(refute_0_560,plain,
( multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) != inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))
| multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) ),[1,1],$fot(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))]]) ).
cnf(refute_0_561,plain,
( positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) != inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))
| multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))),
inference(resolve,[$cnf( $equal(positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) )],[refute_0_558,refute_0_561]) ).
cnf(refute_0_563,plain,
intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))) = multiply(positive_part(X_144),negative_part(inverse(X_144))),
inference(subst,[],[refute_0_302:[bind(X_19,$fot(multiply(positive_part(X_144),negative_part(inverse(X_144)))))]]) ).
cnf(refute_0_564,plain,
( intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != identity
| intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity) = multiply(positive_part(X_144),negative_part(inverse(X_144))) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))),multiply(positive_part(X_144),negative_part(inverse(X_144)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_565,plain,
( intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity) = multiply(positive_part(X_144),negative_part(inverse(X_144))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),identity) )],[refute_0_533,refute_0_564]) ).
cnf(refute_0_566,plain,
intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity) = multiply(positive_part(X_144),negative_part(inverse(X_144))),
inference(resolve,[$cnf( $equal(intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),positive_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))),multiply(positive_part(X_144),negative_part(inverse(X_144)))) )],[refute_0_563,refute_0_565]) ).
cnf(refute_0_567,plain,
intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity) = negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),
inference(subst,[],[refute_0_121:[bind(X,$fot(multiply(positive_part(X_144),negative_part(inverse(X_144)))))]]) ).
cnf(refute_0_568,plain,
( intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity) != negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))
| negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = multiply(positive_part(X_144),negative_part(inverse(X_144))) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity),multiply(positive_part(X_144),negative_part(inverse(X_144)))) ),[0],$fot(negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))))]]) ).
cnf(refute_0_569,plain,
( intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = multiply(positive_part(X_144),negative_part(inverse(X_144))) ),
inference(resolve,[$cnf( $equal(intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity),negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = multiply(positive_part(X_144),negative_part(inverse(X_144))),
inference(resolve,[$cnf( $equal(intersection(multiply(positive_part(X_144),negative_part(inverse(X_144))),identity),multiply(positive_part(X_144),negative_part(inverse(X_144)))) )],[refute_0_566,refute_0_569]) ).
cnf(refute_0_571,plain,
negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),
introduced(tautology,[refl,[$fot(negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))))]]) ).
cnf(refute_0_572,plain,
( multiply(positive_part(X_144),negative_part(inverse(X_144))) != multiply(negative_part(X_144),positive_part(inverse(X_144)))
| negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))
| negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))) ),[1,0],$fot(multiply(negative_part(X_144),positive_part(inverse(X_144))))]]) ).
cnf(refute_0_573,plain,
( multiply(positive_part(X_144),negative_part(inverse(X_144))) != multiply(negative_part(X_144),positive_part(inverse(X_144)))
| negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144))))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) = negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_144),negative_part(inverse(X_144))),multiply(negative_part(X_144),positive_part(inverse(X_144)))) )],[refute_0_541,refute_0_573]) ).
cnf(refute_0_575,plain,
( negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144))))
| negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = multiply(positive_part(X_144),negative_part(inverse(X_144))) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),multiply(positive_part(X_144),negative_part(inverse(X_144)))) ),[0],$fot(negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))))]]) ).
cnf(refute_0_576,plain,
( negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = multiply(positive_part(X_144),negative_part(inverse(X_144))) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144))))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
( multiply(positive_part(X_144),negative_part(inverse(X_144))) != multiply(negative_part(X_144),positive_part(inverse(X_144)))
| negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = multiply(negative_part(X_144),positive_part(inverse(X_144))) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))),multiply(positive_part(X_144),negative_part(inverse(X_144)))) ),[1],$fot(multiply(negative_part(X_144),positive_part(inverse(X_144))))]]) ).
cnf(refute_0_578,plain,
( negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = multiply(negative_part(X_144),positive_part(inverse(X_144))) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_144),negative_part(inverse(X_144))),multiply(negative_part(X_144),positive_part(inverse(X_144)))) )],[refute_0_541,refute_0_577]) ).
cnf(refute_0_579,plain,
( negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))) != multiply(positive_part(X_144),negative_part(inverse(X_144)))
| negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = multiply(negative_part(X_144),positive_part(inverse(X_144))) ),
inference(resolve,[$cnf( $equal(negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))),multiply(positive_part(X_144),negative_part(inverse(X_144)))) )],[refute_0_576,refute_0_578]) ).
cnf(refute_0_580,plain,
negative_part(multiply(negative_part(X_144),positive_part(inverse(X_144)))) = multiply(negative_part(X_144),positive_part(inverse(X_144))),
inference(resolve,[$cnf( $equal(negative_part(multiply(positive_part(X_144),negative_part(inverse(X_144)))),multiply(positive_part(X_144),negative_part(inverse(X_144)))) )],[refute_0_570,refute_0_579]) ).
cnf(refute_0_581,plain,
negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) = multiply(negative_part(X_143),positive_part(inverse(X_143))),
inference(subst,[],[refute_0_580:[bind(X_144,$fot(X_143))]]) ).
cnf(refute_0_582,plain,
multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),
introduced(tautology,[refl,[$fot(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))]]) ).
cnf(refute_0_583,plain,
( multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) != multiply(negative_part(X_143),positive_part(inverse(X_143)))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) ),[1,0],$fot(multiply(negative_part(X_143),positive_part(inverse(X_143))))]]) ).
cnf(refute_0_584,plain,
( negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))) != multiply(negative_part(X_143),positive_part(inverse(X_143)))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),
inference(resolve,[$cnf( $equal(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),multiply(negative_part(X_143),positive_part(inverse(X_143)))) )],[refute_0_581,refute_0_584]) ).
cnf(refute_0_586,plain,
( multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))),bind(Y0,$fot(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))),bind(Z0,$fot(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))]]) ).
cnf(refute_0_587,plain,
( multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))),
inference(resolve,[$cnf( $equal(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) )],[refute_0_562,refute_0_587]) ).
cnf(refute_0_589,plain,
( multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) != identity
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = identity ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))),bind(Y0,$fot(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_590,plain,
( multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) != identity
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = identity ),
inference(resolve,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(negative_part(X_143),positive_part(inverse(X_143))),inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))),identity) )],[refute_0_531,refute_0_590]) ).
cnf(refute_0_592,plain,
( multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != identity
| identity = multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_593,plain,
( multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| identity = multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),identity) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) = negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))),
inference(subst,[],[left_identity:[bind(X,$fot(negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))]]) ).
cnf(refute_0_595,plain,
( multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))
| identity != multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| identity = negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) ),[1],$fot(negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))]]) ).
cnf(refute_0_596,plain,
( identity != multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| identity = negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) ),
inference(resolve,[$cnf( $equal(multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
( multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) != multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))
| identity = negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) ),
inference(resolve,[$cnf( $equal(identity,multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) )],[refute_0_593,refute_0_596]) ).
cnf(refute_0_598,plain,
identity = negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))),
inference(resolve,[$cnf( $equal(multiply(negative_part(multiply(negative_part(X_143),positive_part(inverse(X_143)))),positive_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))),multiply(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))))) )],[refute_0_530,refute_0_597]) ).
cnf(refute_0_599,plain,
( identity != negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))
| negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) = identity ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(identity)),bind(Y0,$fot(negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))))]]) ).
cnf(refute_0_600,plain,
negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143))))) = identity,
inference(resolve,[$cnf( $equal(identity,negative_part(inverse(multiply(negative_part(X_143),positive_part(inverse(X_143)))))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X))))) = identity,
inference(subst,[],[refute_0_600:[bind(X_143,$fot(X))]]) ).
cnf(refute_0_602,plain,
multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))),
introduced(tautology,[refl,[$fot(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))))]]) ).
cnf(refute_0_603,plain,
( multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) != multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X))))))
| negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X))))) != identity
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = multiply(negative_part(inverse(X)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))),multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X))))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_604,plain,
( negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X))))) != identity
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = multiply(negative_part(inverse(X)),identity) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))),multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X))))))) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = multiply(negative_part(inverse(X)),identity),
inference(resolve,[$cnf( $equal(negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X))))),identity) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
( multiply(negative_part(inverse(X)),identity) != negative_part(inverse(X))
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) != multiply(negative_part(inverse(X)),identity)
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = negative_part(inverse(X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))))),bind(Y0,$fot(multiply(negative_part(inverse(X)),identity))),bind(Z0,$fot(negative_part(inverse(X))))]]) ).
cnf(refute_0_607,plain,
( multiply(negative_part(inverse(X)),identity) != negative_part(inverse(X))
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = negative_part(inverse(X)) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))),multiply(negative_part(inverse(X)),identity)) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) = negative_part(inverse(X)),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X)),identity),negative_part(inverse(X))) )],[refute_0_479,refute_0_607]) ).
cnf(refute_0_609,plain,
( multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) != intersection(inverse(positive_part(X)),negative_part(inverse(X)))
| multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) != negative_part(inverse(X))
| negative_part(inverse(X)) = intersection(inverse(positive_part(X)),negative_part(inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))),intersection(inverse(positive_part(X)),negative_part(inverse(X)))) ),[0],$fot(negative_part(inverse(X)))]]) ).
cnf(refute_0_610,plain,
( multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) != intersection(inverse(positive_part(X)),negative_part(inverse(X)))
| negative_part(inverse(X)) = intersection(inverse(positive_part(X)),negative_part(inverse(X))) ),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))),negative_part(inverse(X))) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
multiply(inverse(X),negative_part(inverse(multiply(positive_part(X),inverse(X))))) = intersection(inverse(positive_part(X)),inverse(X)),
inference(subst,[],[refute_0_219:[bind(X_116,$fot(positive_part(X))),bind(X_163,$fot(inverse(X)))]]) ).
cnf(refute_0_612,plain,
( multiply(inverse(X),negative_part(inverse(multiply(positive_part(X),inverse(X))))) != intersection(inverse(positive_part(X)),inverse(X))
| multiply(positive_part(X),inverse(X)) != positive_part(inverse(X))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = intersection(inverse(positive_part(X)),inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(multiply(positive_part(X),inverse(X))))),intersection(inverse(positive_part(X)),inverse(X))) ),[0,1,0,0],$fot(positive_part(inverse(X)))]]) ).
cnf(refute_0_613,plain,
( multiply(inverse(X),negative_part(inverse(multiply(positive_part(X),inverse(X))))) != intersection(inverse(positive_part(X)),inverse(X))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = intersection(inverse(positive_part(X)),inverse(X)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X),inverse(X)),positive_part(inverse(X))) )],[refute_0_173,refute_0_612]) ).
cnf(refute_0_614,plain,
multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = intersection(inverse(positive_part(X)),inverse(X)),
inference(resolve,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(multiply(positive_part(X),inverse(X))))),intersection(inverse(positive_part(X)),inverse(X))) )],[refute_0_611,refute_0_613]) ).
cnf(refute_0_615,plain,
multiply(inverse(X),inverse(positive_part(inverse(X)))) = inverse(positive_part(inverse(inverse(X)))),
inference(subst,[],[refute_0_187:[bind(X_109,$fot(inverse(X)))]]) ).
cnf(refute_0_616,plain,
( multiply(inverse(X),inverse(positive_part(inverse(X)))) != inverse(positive_part(inverse(inverse(X))))
| inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(X))
| multiply(inverse(X),inverse(positive_part(inverse(X)))) = inverse(positive_part(X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(inverse(X),inverse(positive_part(inverse(X)))))),bind(Y0,$fot(inverse(positive_part(inverse(inverse(X)))))),bind(Z0,$fot(inverse(positive_part(X))))]]) ).
cnf(refute_0_617,plain,
( inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(X))
| multiply(inverse(X),inverse(positive_part(inverse(X)))) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(positive_part(inverse(X)))),inverse(positive_part(inverse(inverse(X))))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
multiply(inverse(X),inverse(positive_part(inverse(X)))) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(inverse(X)))),inverse(positive_part(X))) )],[refute_0_85,refute_0_617]) ).
cnf(refute_0_619,plain,
intersection(inverse(positive_part(X_47)),positive_part(inverse(positive_part(X_47)))) = inverse(positive_part(X_47)),
inference(subst,[],[refute_0_302:[bind(X_19,$fot(inverse(positive_part(X_47))))]]) ).
cnf(refute_0_620,plain,
multiply(inverse(X_40),union(X_39,X_40)) = union(multiply(inverse(X_40),X_39),multiply(inverse(X_40),X_40)),
inference(subst,[],[multiply_union1:[bind(X,$fot(inverse(X_40))),bind(Y,$fot(X_39)),bind(Z,$fot(X_40))]]) ).
cnf(refute_0_621,plain,
multiply(inverse(X_40),X_40) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_622,plain,
( multiply(inverse(X_40),X_40) != identity
| multiply(inverse(X_40),union(X_39,X_40)) != union(multiply(inverse(X_40),X_39),multiply(inverse(X_40),X_40))
| multiply(inverse(X_40),union(X_39,X_40)) = union(multiply(inverse(X_40),X_39),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_40),union(X_39,X_40)),union(multiply(inverse(X_40),X_39),multiply(inverse(X_40),X_40))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_623,plain,
( multiply(inverse(X_40),union(X_39,X_40)) != union(multiply(inverse(X_40),X_39),multiply(inverse(X_40),X_40))
| multiply(inverse(X_40),union(X_39,X_40)) = union(multiply(inverse(X_40),X_39),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),X_40),identity) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
multiply(inverse(X_40),union(X_39,X_40)) = union(multiply(inverse(X_40),X_39),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),union(X_39,X_40)),union(multiply(inverse(X_40),X_39),multiply(inverse(X_40),X_40))) )],[refute_0_620,refute_0_623]) ).
cnf(refute_0_625,plain,
union(multiply(inverse(X_40),X_39),identity) = positive_part(multiply(inverse(X_40),X_39)),
inference(subst,[],[refute_0_29:[bind(X,$fot(multiply(inverse(X_40),X_39)))]]) ).
cnf(refute_0_626,plain,
( multiply(inverse(X_40),union(X_39,X_40)) != union(multiply(inverse(X_40),X_39),identity)
| union(multiply(inverse(X_40),X_39),identity) != positive_part(multiply(inverse(X_40),X_39))
| multiply(inverse(X_40),union(X_39,X_40)) = positive_part(multiply(inverse(X_40),X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_40),union(X_39,X_40)),positive_part(multiply(inverse(X_40),X_39))) ),[0],$fot(union(multiply(inverse(X_40),X_39),identity))]]) ).
cnf(refute_0_627,plain,
( multiply(inverse(X_40),union(X_39,X_40)) != union(multiply(inverse(X_40),X_39),identity)
| multiply(inverse(X_40),union(X_39,X_40)) = positive_part(multiply(inverse(X_40),X_39)) ),
inference(resolve,[$cnf( $equal(union(multiply(inverse(X_40),X_39),identity),positive_part(multiply(inverse(X_40),X_39))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
multiply(inverse(X_40),union(X_39,X_40)) = positive_part(multiply(inverse(X_40),X_39)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_40),union(X_39,X_40)),union(multiply(inverse(X_40),X_39),identity)) )],[refute_0_624,refute_0_627]) ).
cnf(refute_0_629,plain,
multiply(inverse(positive_part(X_44)),union(X_44,positive_part(X_44))) = positive_part(multiply(inverse(positive_part(X_44)),X_44)),
inference(subst,[],[refute_0_628:[bind(X_39,$fot(X_44)),bind(X_40,$fot(positive_part(X_44)))]]) ).
cnf(refute_0_630,plain,
union(positive_part(X),intersection(X,positive_part(X))) = positive_part(X),
inference(subst,[],[refute_0_308:[bind(Y,$fot(positive_part(X)))]]) ).
cnf(refute_0_631,plain,
intersection(X,positive_part(X)) = X,
inference(subst,[],[refute_0_302:[bind(X_19,$fot(X))]]) ).
cnf(refute_0_632,plain,
( intersection(X,positive_part(X)) != X
| union(positive_part(X),intersection(X,positive_part(X))) != positive_part(X)
| union(positive_part(X),X) = positive_part(X) ),
introduced(tautology,[equality,[$cnf( $equal(union(positive_part(X),intersection(X,positive_part(X))),positive_part(X)) ),[0,1],$fot(X)]]) ).
cnf(refute_0_633,plain,
( union(positive_part(X),intersection(X,positive_part(X))) != positive_part(X)
| union(positive_part(X),X) = positive_part(X) ),
inference(resolve,[$cnf( $equal(intersection(X,positive_part(X)),X) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
union(positive_part(X),X) = positive_part(X),
inference(resolve,[$cnf( $equal(union(positive_part(X),intersection(X,positive_part(X))),positive_part(X)) )],[refute_0_630,refute_0_633]) ).
cnf(refute_0_635,plain,
union(positive_part(X),X) = union(X,positive_part(X)),
inference(subst,[],[refute_0_227:[bind(Y,$fot(positive_part(X)))]]) ).
cnf(refute_0_636,plain,
( union(positive_part(X),X) != positive_part(X)
| union(positive_part(X),X) != union(X,positive_part(X))
| union(X,positive_part(X)) = positive_part(X) ),
introduced(tautology,[equality,[$cnf( $equal(union(positive_part(X),X),positive_part(X)) ),[0],$fot(union(X,positive_part(X)))]]) ).
cnf(refute_0_637,plain,
( union(positive_part(X),X) != positive_part(X)
| union(X,positive_part(X)) = positive_part(X) ),
inference(resolve,[$cnf( $equal(union(positive_part(X),X),union(X,positive_part(X))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
union(X,positive_part(X)) = positive_part(X),
inference(resolve,[$cnf( $equal(union(positive_part(X),X),positive_part(X)) )],[refute_0_634,refute_0_637]) ).
cnf(refute_0_639,plain,
union(X_44,positive_part(X_44)) = positive_part(X_44),
inference(subst,[],[refute_0_638:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_640,plain,
( multiply(inverse(positive_part(X_44)),union(X_44,positive_part(X_44))) != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| union(X_44,positive_part(X_44)) != positive_part(X_44)
| multiply(inverse(positive_part(X_44)),positive_part(X_44)) = positive_part(multiply(inverse(positive_part(X_44)),X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(positive_part(X_44)),union(X_44,positive_part(X_44))),positive_part(multiply(inverse(positive_part(X_44)),X_44))) ),[0,1],$fot(positive_part(X_44))]]) ).
cnf(refute_0_641,plain,
( multiply(inverse(positive_part(X_44)),union(X_44,positive_part(X_44))) != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| multiply(inverse(positive_part(X_44)),positive_part(X_44)) = positive_part(multiply(inverse(positive_part(X_44)),X_44)) ),
inference(resolve,[$cnf( $equal(union(X_44,positive_part(X_44)),positive_part(X_44)) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
multiply(inverse(positive_part(X_44)),positive_part(X_44)) = positive_part(multiply(inverse(positive_part(X_44)),X_44)),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_44)),union(X_44,positive_part(X_44))),positive_part(multiply(inverse(positive_part(X_44)),X_44))) )],[refute_0_629,refute_0_641]) ).
cnf(refute_0_643,plain,
multiply(inverse(positive_part(X_44)),positive_part(X_44)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(positive_part(X_44)))]]) ).
cnf(refute_0_644,plain,
( multiply(inverse(positive_part(X_44)),positive_part(X_44)) != identity
| multiply(inverse(positive_part(X_44)),positive_part(X_44)) != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| identity = positive_part(multiply(inverse(positive_part(X_44)),X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(positive_part(X_44)),positive_part(X_44)),positive_part(multiply(inverse(positive_part(X_44)),X_44))) ),[0],$fot(identity)]]) ).
cnf(refute_0_645,plain,
( multiply(inverse(positive_part(X_44)),positive_part(X_44)) != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| identity = positive_part(multiply(inverse(positive_part(X_44)),X_44)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_44)),positive_part(X_44)),identity) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
( inverse(positive_part(inverse(X))) != multiply(inverse(positive_part(X)),X)
| multiply(inverse(positive_part(X)),X) = inverse(positive_part(inverse(X))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(positive_part(inverse(X))))),bind(Y0,$fot(multiply(inverse(positive_part(X)),X)))]]) ).
cnf(refute_0_647,plain,
multiply(inverse(positive_part(X)),X) = inverse(positive_part(inverse(X))),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X))),multiply(inverse(positive_part(X)),X)) )],[refute_0_92,refute_0_646]) ).
cnf(refute_0_648,plain,
multiply(inverse(positive_part(X_44)),X_44) = inverse(positive_part(inverse(X_44))),
inference(subst,[],[refute_0_647:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_649,plain,
positive_part(multiply(inverse(positive_part(X_44)),X_44)) = positive_part(multiply(inverse(positive_part(X_44)),X_44)),
introduced(tautology,[refl,[$fot(positive_part(multiply(inverse(positive_part(X_44)),X_44)))]]) ).
cnf(refute_0_650,plain,
( multiply(inverse(positive_part(X_44)),X_44) != inverse(positive_part(inverse(X_44)))
| positive_part(multiply(inverse(positive_part(X_44)),X_44)) != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| positive_part(multiply(inverse(positive_part(X_44)),X_44)) = positive_part(inverse(positive_part(inverse(X_44)))) ),
introduced(tautology,[equality,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_44)),X_44)),positive_part(multiply(inverse(positive_part(X_44)),X_44))) ),[1,0],$fot(inverse(positive_part(inverse(X_44))))]]) ).
cnf(refute_0_651,plain,
( multiply(inverse(positive_part(X_44)),X_44) != inverse(positive_part(inverse(X_44)))
| positive_part(multiply(inverse(positive_part(X_44)),X_44)) = positive_part(inverse(positive_part(inverse(X_44)))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_44)),X_44)),positive_part(multiply(inverse(positive_part(X_44)),X_44))) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
positive_part(multiply(inverse(positive_part(X_44)),X_44)) = positive_part(inverse(positive_part(inverse(X_44)))),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_44)),X_44),inverse(positive_part(inverse(X_44)))) )],[refute_0_648,refute_0_651]) ).
cnf(refute_0_653,plain,
( identity != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| positive_part(multiply(inverse(positive_part(X_44)),X_44)) != positive_part(inverse(positive_part(inverse(X_44))))
| identity = positive_part(inverse(positive_part(inverse(X_44)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,positive_part(inverse(positive_part(inverse(X_44))))) ),[0],$fot(positive_part(multiply(inverse(positive_part(X_44)),X_44)))]]) ).
cnf(refute_0_654,plain,
( identity != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| identity = positive_part(inverse(positive_part(inverse(X_44)))) ),
inference(resolve,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_44)),X_44)),positive_part(inverse(positive_part(inverse(X_44))))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
( multiply(inverse(positive_part(X_44)),positive_part(X_44)) != positive_part(multiply(inverse(positive_part(X_44)),X_44))
| identity = positive_part(inverse(positive_part(inverse(X_44)))) ),
inference(resolve,[$cnf( $equal(identity,positive_part(multiply(inverse(positive_part(X_44)),X_44))) )],[refute_0_645,refute_0_654]) ).
cnf(refute_0_656,plain,
identity = positive_part(inverse(positive_part(inverse(X_44)))),
inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_44)),positive_part(X_44)),positive_part(multiply(inverse(positive_part(X_44)),X_44))) )],[refute_0_642,refute_0_655]) ).
cnf(refute_0_657,plain,
identity = positive_part(inverse(positive_part(inverse(inverse(X))))),
inference(subst,[],[refute_0_656:[bind(X_44,$fot(inverse(X)))]]) ).
cnf(refute_0_658,plain,
( identity != positive_part(inverse(positive_part(inverse(inverse(X)))))
| inverse(inverse(X)) != X
| identity = positive_part(inverse(positive_part(X))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,positive_part(inverse(positive_part(inverse(inverse(X)))))) ),[1,0,0,0],$fot(X)]]) ).
cnf(refute_0_659,plain,
( identity != positive_part(inverse(positive_part(inverse(inverse(X)))))
| identity = positive_part(inverse(positive_part(X))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[inverse_involution,refute_0_658]) ).
cnf(refute_0_660,plain,
identity = positive_part(inverse(positive_part(X))),
inference(resolve,[$cnf( $equal(identity,positive_part(inverse(positive_part(inverse(inverse(X)))))) )],[refute_0_657,refute_0_659]) ).
cnf(refute_0_661,plain,
identity = positive_part(inverse(positive_part(X_47))),
inference(subst,[],[refute_0_660:[bind(X,$fot(X_47))]]) ).
cnf(refute_0_662,plain,
( identity != positive_part(inverse(positive_part(X_47)))
| positive_part(inverse(positive_part(X_47))) = identity ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(identity)),bind(Y0,$fot(positive_part(inverse(positive_part(X_47)))))]]) ).
cnf(refute_0_663,plain,
positive_part(inverse(positive_part(X_47))) = identity,
inference(resolve,[$cnf( $equal(identity,positive_part(inverse(positive_part(X_47)))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
( intersection(inverse(positive_part(X_47)),positive_part(inverse(positive_part(X_47)))) != inverse(positive_part(X_47))
| positive_part(inverse(positive_part(X_47))) != identity
| intersection(inverse(positive_part(X_47)),identity) = inverse(positive_part(X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(inverse(positive_part(X_47)),positive_part(inverse(positive_part(X_47)))),inverse(positive_part(X_47))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_665,plain,
( intersection(inverse(positive_part(X_47)),positive_part(inverse(positive_part(X_47)))) != inverse(positive_part(X_47))
| intersection(inverse(positive_part(X_47)),identity) = inverse(positive_part(X_47)) ),
inference(resolve,[$cnf( $equal(positive_part(inverse(positive_part(X_47))),identity) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
intersection(inverse(positive_part(X_47)),identity) = inverse(positive_part(X_47)),
inference(resolve,[$cnf( $equal(intersection(inverse(positive_part(X_47)),positive_part(inverse(positive_part(X_47)))),inverse(positive_part(X_47))) )],[refute_0_619,refute_0_665]) ).
cnf(refute_0_667,plain,
intersection(inverse(positive_part(X_47)),identity) = negative_part(inverse(positive_part(X_47))),
inference(subst,[],[refute_0_121:[bind(X,$fot(inverse(positive_part(X_47))))]]) ).
cnf(refute_0_668,plain,
( intersection(inverse(positive_part(X_47)),identity) != inverse(positive_part(X_47))
| intersection(inverse(positive_part(X_47)),identity) != negative_part(inverse(positive_part(X_47)))
| negative_part(inverse(positive_part(X_47))) = inverse(positive_part(X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(inverse(positive_part(X_47)),identity),inverse(positive_part(X_47))) ),[0],$fot(negative_part(inverse(positive_part(X_47))))]]) ).
cnf(refute_0_669,plain,
( intersection(inverse(positive_part(X_47)),identity) != inverse(positive_part(X_47))
| negative_part(inverse(positive_part(X_47))) = inverse(positive_part(X_47)) ),
inference(resolve,[$cnf( $equal(intersection(inverse(positive_part(X_47)),identity),negative_part(inverse(positive_part(X_47)))) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
negative_part(inverse(positive_part(X_47))) = inverse(positive_part(X_47)),
inference(resolve,[$cnf( $equal(intersection(inverse(positive_part(X_47)),identity),inverse(positive_part(X_47))) )],[refute_0_666,refute_0_669]) ).
cnf(refute_0_671,plain,
negative_part(inverse(positive_part(inverse(X)))) = inverse(positive_part(inverse(X))),
inference(subst,[],[refute_0_670:[bind(X_47,$fot(inverse(X)))]]) ).
cnf(refute_0_672,plain,
multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))),
introduced(tautology,[refl,[$fot(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))))]]) ).
cnf(refute_0_673,plain,
( multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) != multiply(inverse(X),negative_part(inverse(positive_part(inverse(X)))))
| negative_part(inverse(positive_part(inverse(X)))) != inverse(positive_part(inverse(X)))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = multiply(inverse(X),inverse(positive_part(inverse(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))),multiply(inverse(X),negative_part(inverse(positive_part(inverse(X)))))) ),[1,1],$fot(inverse(positive_part(inverse(X))))]]) ).
cnf(refute_0_674,plain,
( negative_part(inverse(positive_part(inverse(X)))) != inverse(positive_part(inverse(X)))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = multiply(inverse(X),inverse(positive_part(inverse(X)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))),multiply(inverse(X),negative_part(inverse(positive_part(inverse(X)))))) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = multiply(inverse(X),inverse(positive_part(inverse(X)))),
inference(resolve,[$cnf( $equal(negative_part(inverse(positive_part(inverse(X)))),inverse(positive_part(inverse(X)))) )],[refute_0_671,refute_0_674]) ).
cnf(refute_0_676,plain,
( multiply(inverse(X),inverse(positive_part(inverse(X)))) != inverse(positive_part(X))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) != multiply(inverse(X),inverse(positive_part(inverse(X))))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = inverse(positive_part(X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))))),bind(Y0,$fot(multiply(inverse(X),inverse(positive_part(inverse(X)))))),bind(Z0,$fot(inverse(positive_part(X))))]]) ).
cnf(refute_0_677,plain,
( multiply(inverse(X),inverse(positive_part(inverse(X)))) != inverse(positive_part(X))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))),multiply(inverse(X),inverse(positive_part(inverse(X))))) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(positive_part(inverse(X)))),inverse(positive_part(X))) )],[refute_0_618,refute_0_677]) ).
cnf(refute_0_679,plain,
( multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) != intersection(inverse(positive_part(X)),inverse(X))
| multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) != inverse(positive_part(X))
| inverse(positive_part(X)) = intersection(inverse(positive_part(X)),inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))),intersection(inverse(positive_part(X)),inverse(X))) ),[0],$fot(inverse(positive_part(X)))]]) ).
cnf(refute_0_680,plain,
( multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) != intersection(inverse(positive_part(X)),inverse(X))
| inverse(positive_part(X)) = intersection(inverse(positive_part(X)),inverse(X)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))),inverse(positive_part(X))) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
intersection(inverse(positive_part(X)),inverse(X)) = intersection(inverse(X),inverse(positive_part(X))),
inference(subst,[],[refute_0_291:[bind(X,$fot(inverse(X))),bind(Y,$fot(inverse(positive_part(X))))]]) ).
cnf(refute_0_682,plain,
( intersection(inverse(positive_part(X)),inverse(X)) != intersection(inverse(X),inverse(positive_part(X)))
| inverse(positive_part(X)) != intersection(inverse(positive_part(X)),inverse(X))
| inverse(positive_part(X)) = intersection(inverse(X),inverse(positive_part(X))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(positive_part(X)),intersection(inverse(positive_part(X)),inverse(X))) ),[1],$fot(intersection(inverse(X),inverse(positive_part(X))))]]) ).
cnf(refute_0_683,plain,
( inverse(positive_part(X)) != intersection(inverse(positive_part(X)),inverse(X))
| inverse(positive_part(X)) = intersection(inverse(X),inverse(positive_part(X))) ),
inference(resolve,[$cnf( $equal(intersection(inverse(positive_part(X)),inverse(X)),intersection(inverse(X),inverse(positive_part(X)))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
( multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))) != intersection(inverse(positive_part(X)),inverse(X))
| inverse(positive_part(X)) = intersection(inverse(X),inverse(positive_part(X))) ),
inference(resolve,[$cnf( $equal(inverse(positive_part(X)),intersection(inverse(positive_part(X)),inverse(X))) )],[refute_0_680,refute_0_683]) ).
cnf(refute_0_685,plain,
inverse(positive_part(X)) = intersection(inverse(X),inverse(positive_part(X))),
inference(resolve,[$cnf( $equal(multiply(inverse(X),negative_part(inverse(positive_part(inverse(X))))),intersection(inverse(positive_part(X)),inverse(X))) )],[refute_0_614,refute_0_684]) ).
cnf(refute_0_686,plain,
( inverse(positive_part(X)) != intersection(inverse(X),inverse(positive_part(X)))
| intersection(inverse(X),inverse(positive_part(X))) = inverse(positive_part(X)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(inverse(positive_part(X)))),bind(Y0,$fot(intersection(inverse(X),inverse(positive_part(X)))))]]) ).
cnf(refute_0_687,plain,
intersection(inverse(X),inverse(positive_part(X))) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(inverse(positive_part(X)),intersection(inverse(X),inverse(positive_part(X)))) )],[refute_0_685,refute_0_686]) ).
cnf(refute_0_688,plain,
negative_part(intersection(X_126,X_127)) = intersection(intersection(X_126,X_127),identity),
inference(subst,[],[negative_part:[bind(X,$fot(intersection(X_126,X_127)))]]) ).
cnf(refute_0_689,plain,
intersection(X_126,intersection(X_127,identity)) = intersection(intersection(X_126,X_127),identity),
inference(subst,[],[intersection_associative:[bind(X,$fot(X_126)),bind(Y,$fot(X_127)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_690,plain,
( intersection(X_126,intersection(X_127,identity)) != intersection(intersection(X_126,X_127),identity)
| intersection(intersection(X_126,X_127),identity) = intersection(X_126,intersection(X_127,identity)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(intersection(X_126,intersection(X_127,identity)))),bind(Y0,$fot(intersection(intersection(X_126,X_127),identity)))]]) ).
cnf(refute_0_691,plain,
intersection(intersection(X_126,X_127),identity) = intersection(X_126,intersection(X_127,identity)),
inference(resolve,[$cnf( $equal(intersection(X_126,intersection(X_127,identity)),intersection(intersection(X_126,X_127),identity)) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
( intersection(intersection(X_126,X_127),identity) != intersection(X_126,intersection(X_127,identity))
| negative_part(intersection(X_126,X_127)) != intersection(intersection(X_126,X_127),identity)
| negative_part(intersection(X_126,X_127)) = intersection(X_126,intersection(X_127,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(intersection(X_126,X_127)),intersection(intersection(X_126,X_127),identity)) ),[1],$fot(intersection(X_126,intersection(X_127,identity)))]]) ).
cnf(refute_0_693,plain,
( negative_part(intersection(X_126,X_127)) != intersection(intersection(X_126,X_127),identity)
| negative_part(intersection(X_126,X_127)) = intersection(X_126,intersection(X_127,identity)) ),
inference(resolve,[$cnf( $equal(intersection(intersection(X_126,X_127),identity),intersection(X_126,intersection(X_127,identity))) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
negative_part(intersection(X_126,X_127)) = intersection(X_126,intersection(X_127,identity)),
inference(resolve,[$cnf( $equal(negative_part(intersection(X_126,X_127)),intersection(intersection(X_126,X_127),identity)) )],[refute_0_688,refute_0_693]) ).
cnf(refute_0_695,plain,
intersection(X_127,identity) = negative_part(X_127),
inference(subst,[],[refute_0_121:[bind(X,$fot(X_127))]]) ).
cnf(refute_0_696,plain,
intersection(X_126,intersection(X_127,identity)) = intersection(X_126,intersection(X_127,identity)),
introduced(tautology,[refl,[$fot(intersection(X_126,intersection(X_127,identity)))]]) ).
cnf(refute_0_697,plain,
( intersection(X_126,intersection(X_127,identity)) != intersection(X_126,intersection(X_127,identity))
| intersection(X_127,identity) != negative_part(X_127)
| intersection(X_126,intersection(X_127,identity)) = intersection(X_126,negative_part(X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(X_126,intersection(X_127,identity)),intersection(X_126,intersection(X_127,identity))) ),[1,1],$fot(negative_part(X_127))]]) ).
cnf(refute_0_698,plain,
( intersection(X_127,identity) != negative_part(X_127)
| intersection(X_126,intersection(X_127,identity)) = intersection(X_126,negative_part(X_127)) ),
inference(resolve,[$cnf( $equal(intersection(X_126,intersection(X_127,identity)),intersection(X_126,intersection(X_127,identity))) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
intersection(X_126,intersection(X_127,identity)) = intersection(X_126,negative_part(X_127)),
inference(resolve,[$cnf( $equal(intersection(X_127,identity),negative_part(X_127)) )],[refute_0_695,refute_0_698]) ).
cnf(refute_0_700,plain,
( intersection(X_126,intersection(X_127,identity)) != intersection(X_126,negative_part(X_127))
| negative_part(intersection(X_126,X_127)) != intersection(X_126,intersection(X_127,identity))
| negative_part(intersection(X_126,X_127)) = intersection(X_126,negative_part(X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(intersection(X_126,X_127)),intersection(X_126,intersection(X_127,identity))) ),[1],$fot(intersection(X_126,negative_part(X_127)))]]) ).
cnf(refute_0_701,plain,
( negative_part(intersection(X_126,X_127)) != intersection(X_126,intersection(X_127,identity))
| negative_part(intersection(X_126,X_127)) = intersection(X_126,negative_part(X_127)) ),
inference(resolve,[$cnf( $equal(intersection(X_126,intersection(X_127,identity)),intersection(X_126,negative_part(X_127))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
negative_part(intersection(X_126,X_127)) = intersection(X_126,negative_part(X_127)),
inference(resolve,[$cnf( $equal(negative_part(intersection(X_126,X_127)),intersection(X_126,intersection(X_127,identity))) )],[refute_0_694,refute_0_701]) ).
cnf(refute_0_703,plain,
negative_part(intersection(X_129,inverse(positive_part(X_47)))) = intersection(X_129,negative_part(inverse(positive_part(X_47)))),
inference(subst,[],[refute_0_702:[bind(X_126,$fot(X_129)),bind(X_127,$fot(inverse(positive_part(X_47))))]]) ).
cnf(refute_0_704,plain,
( negative_part(intersection(X_129,inverse(positive_part(X_47)))) != intersection(X_129,negative_part(inverse(positive_part(X_47))))
| negative_part(inverse(positive_part(X_47))) != inverse(positive_part(X_47))
| negative_part(intersection(X_129,inverse(positive_part(X_47)))) = intersection(X_129,inverse(positive_part(X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(intersection(X_129,inverse(positive_part(X_47)))),intersection(X_129,negative_part(inverse(positive_part(X_47))))) ),[1,1],$fot(inverse(positive_part(X_47)))]]) ).
cnf(refute_0_705,plain,
( negative_part(intersection(X_129,inverse(positive_part(X_47)))) != intersection(X_129,negative_part(inverse(positive_part(X_47))))
| negative_part(intersection(X_129,inverse(positive_part(X_47)))) = intersection(X_129,inverse(positive_part(X_47))) ),
inference(resolve,[$cnf( $equal(negative_part(inverse(positive_part(X_47))),inverse(positive_part(X_47))) )],[refute_0_670,refute_0_704]) ).
cnf(refute_0_706,plain,
negative_part(intersection(X_129,inverse(positive_part(X_47)))) = intersection(X_129,inverse(positive_part(X_47))),
inference(resolve,[$cnf( $equal(negative_part(intersection(X_129,inverse(positive_part(X_47)))),intersection(X_129,negative_part(inverse(positive_part(X_47))))) )],[refute_0_703,refute_0_705]) ).
cnf(refute_0_707,plain,
negative_part(intersection(inverse(X),inverse(positive_part(X)))) = intersection(inverse(X),inverse(positive_part(X))),
inference(subst,[],[refute_0_706:[bind(X_129,$fot(inverse(X))),bind(X_47,$fot(X))]]) ).
cnf(refute_0_708,plain,
( intersection(inverse(X),inverse(positive_part(X))) != inverse(positive_part(X))
| negative_part(intersection(inverse(X),inverse(positive_part(X)))) != intersection(inverse(X),inverse(positive_part(X)))
| negative_part(intersection(inverse(X),inverse(positive_part(X)))) = inverse(positive_part(X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(negative_part(intersection(inverse(X),inverse(positive_part(X)))))),bind(Y0,$fot(intersection(inverse(X),inverse(positive_part(X))))),bind(Z0,$fot(inverse(positive_part(X))))]]) ).
cnf(refute_0_709,plain,
( intersection(inverse(X),inverse(positive_part(X))) != inverse(positive_part(X))
| negative_part(intersection(inverse(X),inverse(positive_part(X)))) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(negative_part(intersection(inverse(X),inverse(positive_part(X)))),intersection(inverse(X),inverse(positive_part(X)))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
negative_part(intersection(inverse(X),inverse(positive_part(X)))) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(intersection(inverse(X),inverse(positive_part(X))),inverse(positive_part(X))) )],[refute_0_687,refute_0_709]) ).
cnf(refute_0_711,plain,
intersection(X,negative_part(X_204)) = intersection(negative_part(X_204),X),
inference(subst,[],[intersection_commutative:[bind(Y,$fot(negative_part(X_204)))]]) ).
cnf(refute_0_712,plain,
intersection(identity,intersection(X_127,X_128)) = intersection(intersection(identity,X_127),X_128),
inference(subst,[],[intersection_associative:[bind(X,$fot(identity)),bind(Y,$fot(X_127)),bind(Z,$fot(X_128))]]) ).
cnf(refute_0_713,plain,
negative_part(X_127) = intersection(identity,X_127),
inference(subst,[],[refute_0_130:[bind(X,$fot(X_127))]]) ).
cnf(refute_0_714,plain,
( negative_part(X_127) != intersection(identity,X_127)
| intersection(identity,X_127) = negative_part(X_127) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(X_127))),bind(Y0,$fot(intersection(identity,X_127)))]]) ).
cnf(refute_0_715,plain,
intersection(identity,X_127) = negative_part(X_127),
inference(resolve,[$cnf( $equal(negative_part(X_127),intersection(identity,X_127)) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
( intersection(identity,X_127) != negative_part(X_127)
| intersection(identity,intersection(X_127,X_128)) != intersection(intersection(identity,X_127),X_128)
| intersection(identity,intersection(X_127,X_128)) = intersection(negative_part(X_127),X_128) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(identity,intersection(X_127,X_128)),intersection(intersection(identity,X_127),X_128)) ),[1,0],$fot(negative_part(X_127))]]) ).
cnf(refute_0_717,plain,
( intersection(identity,intersection(X_127,X_128)) != intersection(intersection(identity,X_127),X_128)
| intersection(identity,intersection(X_127,X_128)) = intersection(negative_part(X_127),X_128) ),
inference(resolve,[$cnf( $equal(intersection(identity,X_127),negative_part(X_127)) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
intersection(identity,intersection(X_127,X_128)) = intersection(negative_part(X_127),X_128),
inference(resolve,[$cnf( $equal(intersection(identity,intersection(X_127,X_128)),intersection(intersection(identity,X_127),X_128)) )],[refute_0_712,refute_0_717]) ).
cnf(refute_0_719,plain,
intersection(identity,intersection(X_127,X_128)) = negative_part(intersection(X_127,X_128)),
inference(subst,[],[refute_0_205:[bind(X,$fot(intersection(X_127,X_128)))]]) ).
cnf(refute_0_720,plain,
( intersection(identity,intersection(X_127,X_128)) != intersection(negative_part(X_127),X_128)
| intersection(identity,intersection(X_127,X_128)) != negative_part(intersection(X_127,X_128))
| negative_part(intersection(X_127,X_128)) = intersection(negative_part(X_127),X_128) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(identity,intersection(X_127,X_128)),intersection(negative_part(X_127),X_128)) ),[0],$fot(negative_part(intersection(X_127,X_128)))]]) ).
cnf(refute_0_721,plain,
( intersection(identity,intersection(X_127,X_128)) != intersection(negative_part(X_127),X_128)
| negative_part(intersection(X_127,X_128)) = intersection(negative_part(X_127),X_128) ),
inference(resolve,[$cnf( $equal(intersection(identity,intersection(X_127,X_128)),negative_part(intersection(X_127,X_128))) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
negative_part(intersection(X_127,X_128)) = intersection(negative_part(X_127),X_128),
inference(resolve,[$cnf( $equal(intersection(identity,intersection(X_127,X_128)),intersection(negative_part(X_127),X_128)) )],[refute_0_718,refute_0_721]) ).
cnf(refute_0_723,plain,
negative_part(intersection(X_204,X)) = intersection(negative_part(X_204),X),
inference(subst,[],[refute_0_722:[bind(X_127,$fot(X_204)),bind(X_128,$fot(X))]]) ).
cnf(refute_0_724,plain,
( negative_part(intersection(X_204,X)) != intersection(negative_part(X_204),X)
| intersection(negative_part(X_204),X) = negative_part(intersection(X_204,X)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(intersection(X_204,X)))),bind(Y0,$fot(intersection(negative_part(X_204),X)))]]) ).
cnf(refute_0_725,plain,
intersection(negative_part(X_204),X) = negative_part(intersection(X_204,X)),
inference(resolve,[$cnf( $equal(negative_part(intersection(X_204,X)),intersection(negative_part(X_204),X)) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
( intersection(X,negative_part(X_204)) != intersection(negative_part(X_204),X)
| intersection(negative_part(X_204),X) != negative_part(intersection(X_204,X))
| intersection(X,negative_part(X_204)) = negative_part(intersection(X_204,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(intersection(X,negative_part(X_204)),negative_part(intersection(X_204,X))) ),[0],$fot(intersection(negative_part(X_204),X))]]) ).
cnf(refute_0_727,plain,
( intersection(X,negative_part(X_204)) != intersection(negative_part(X_204),X)
| intersection(X,negative_part(X_204)) = negative_part(intersection(X_204,X)) ),
inference(resolve,[$cnf( $equal(intersection(negative_part(X_204),X),negative_part(intersection(X_204,X))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
intersection(X,negative_part(X_204)) = negative_part(intersection(X_204,X)),
inference(resolve,[$cnf( $equal(intersection(X,negative_part(X_204)),intersection(negative_part(X_204),X)) )],[refute_0_711,refute_0_727]) ).
cnf(refute_0_729,plain,
( negative_part(intersection(X_126,X_127)) != intersection(X_126,negative_part(X_127))
| intersection(X_126,negative_part(X_127)) = negative_part(intersection(X_126,X_127)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(intersection(X_126,X_127)))),bind(Y0,$fot(intersection(X_126,negative_part(X_127))))]]) ).
cnf(refute_0_730,plain,
intersection(X_126,negative_part(X_127)) = negative_part(intersection(X_126,X_127)),
inference(resolve,[$cnf( $equal(negative_part(intersection(X_126,X_127)),intersection(X_126,negative_part(X_127))) )],[refute_0_702,refute_0_729]) ).
cnf(refute_0_731,plain,
intersection(X,negative_part(X_204)) = negative_part(intersection(X,X_204)),
inference(subst,[],[refute_0_730:[bind(X_126,$fot(X)),bind(X_127,$fot(X_204))]]) ).
cnf(refute_0_732,plain,
( intersection(X,negative_part(X_204)) != negative_part(intersection(X,X_204))
| intersection(X,negative_part(X_204)) != negative_part(intersection(X_204,X))
| negative_part(intersection(X,X_204)) = negative_part(intersection(X_204,X)) ),
introduced(tautology,[equality,[$cnf( $equal(intersection(X,negative_part(X_204)),negative_part(intersection(X_204,X))) ),[0],$fot(negative_part(intersection(X,X_204)))]]) ).
cnf(refute_0_733,plain,
( intersection(X,negative_part(X_204)) != negative_part(intersection(X_204,X))
| negative_part(intersection(X,X_204)) = negative_part(intersection(X_204,X)) ),
inference(resolve,[$cnf( $equal(intersection(X,negative_part(X_204)),negative_part(intersection(X,X_204))) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
negative_part(intersection(X,X_204)) = negative_part(intersection(X_204,X)),
inference(resolve,[$cnf( $equal(intersection(X,negative_part(X_204)),negative_part(intersection(X_204,X))) )],[refute_0_728,refute_0_733]) ).
cnf(refute_0_735,plain,
( negative_part(intersection(X,X_204)) != negative_part(intersection(X_204,X))
| negative_part(intersection(X_204,X)) = negative_part(intersection(X,X_204)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(negative_part(intersection(X,X_204)))),bind(Y0,$fot(negative_part(intersection(X_204,X))))]]) ).
cnf(refute_0_736,plain,
negative_part(intersection(X_204,X)) = negative_part(intersection(X,X_204)),
inference(resolve,[$cnf( $equal(negative_part(intersection(X,X_204)),negative_part(intersection(X_204,X))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
negative_part(intersection(inverse(positive_part(X)),inverse(X))) = negative_part(intersection(inverse(X),inverse(positive_part(X)))),
inference(subst,[],[refute_0_736:[bind(X,$fot(inverse(X))),bind(X_204,$fot(inverse(positive_part(X))))]]) ).
cnf(refute_0_738,plain,
( negative_part(intersection(inverse(X),inverse(positive_part(X)))) != inverse(positive_part(X))
| negative_part(intersection(inverse(positive_part(X)),inverse(X))) != negative_part(intersection(inverse(X),inverse(positive_part(X))))
| negative_part(intersection(inverse(positive_part(X)),inverse(X))) = inverse(positive_part(X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(negative_part(intersection(inverse(positive_part(X)),inverse(X))))),bind(Y0,$fot(negative_part(intersection(inverse(X),inverse(positive_part(X)))))),bind(Z0,$fot(inverse(positive_part(X))))]]) ).
cnf(refute_0_739,plain,
( negative_part(intersection(inverse(X),inverse(positive_part(X)))) != inverse(positive_part(X))
| negative_part(intersection(inverse(positive_part(X)),inverse(X))) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(negative_part(intersection(inverse(positive_part(X)),inverse(X))),negative_part(intersection(inverse(X),inverse(positive_part(X))))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
negative_part(intersection(inverse(positive_part(X)),inverse(X))) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(negative_part(intersection(inverse(X),inverse(positive_part(X)))),inverse(positive_part(X))) )],[refute_0_710,refute_0_739]) ).
cnf(refute_0_741,plain,
intersection(inverse(positive_part(X)),negative_part(inverse(X))) = negative_part(intersection(inverse(positive_part(X)),inverse(X))),
inference(subst,[],[refute_0_730:[bind(X_126,$fot(inverse(positive_part(X)))),bind(X_127,$fot(inverse(X)))]]) ).
cnf(refute_0_742,plain,
( intersection(inverse(positive_part(X)),negative_part(inverse(X))) != negative_part(intersection(inverse(positive_part(X)),inverse(X)))
| negative_part(intersection(inverse(positive_part(X)),inverse(X))) != inverse(positive_part(X))
| intersection(inverse(positive_part(X)),negative_part(inverse(X))) = inverse(positive_part(X)) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(intersection(inverse(positive_part(X)),negative_part(inverse(X))))),bind(Y0,$fot(negative_part(intersection(inverse(positive_part(X)),inverse(X))))),bind(Z0,$fot(inverse(positive_part(X))))]]) ).
cnf(refute_0_743,plain,
( negative_part(intersection(inverse(positive_part(X)),inverse(X))) != inverse(positive_part(X))
| intersection(inverse(positive_part(X)),negative_part(inverse(X))) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(intersection(inverse(positive_part(X)),negative_part(inverse(X))),negative_part(intersection(inverse(positive_part(X)),inverse(X)))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
intersection(inverse(positive_part(X)),negative_part(inverse(X))) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(negative_part(intersection(inverse(positive_part(X)),inverse(X))),inverse(positive_part(X))) )],[refute_0_740,refute_0_743]) ).
cnf(refute_0_745,plain,
( intersection(inverse(positive_part(X)),negative_part(inverse(X))) != inverse(positive_part(X))
| negative_part(inverse(X)) != intersection(inverse(positive_part(X)),negative_part(inverse(X)))
| negative_part(inverse(X)) = inverse(positive_part(X)) ),
introduced(tautology,[equality,[$cnf( $equal(negative_part(inverse(X)),intersection(inverse(positive_part(X)),negative_part(inverse(X)))) ),[1],$fot(inverse(positive_part(X)))]]) ).
cnf(refute_0_746,plain,
( negative_part(inverse(X)) != intersection(inverse(positive_part(X)),negative_part(inverse(X)))
| negative_part(inverse(X)) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(intersection(inverse(positive_part(X)),negative_part(inverse(X))),inverse(positive_part(X))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
( multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))) != intersection(inverse(positive_part(X)),negative_part(inverse(X)))
| negative_part(inverse(X)) = inverse(positive_part(X)) ),
inference(resolve,[$cnf( $equal(negative_part(inverse(X)),intersection(inverse(positive_part(X)),negative_part(inverse(X)))) )],[refute_0_610,refute_0_746]) ).
cnf(refute_0_748,plain,
negative_part(inverse(X)) = inverse(positive_part(X)),
inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X)),negative_part(inverse(multiply(negative_part(X),positive_part(inverse(X)))))),intersection(inverse(positive_part(X)),negative_part(inverse(X)))) )],[refute_0_478,refute_0_747]) ).
cnf(refute_0_749,plain,
negative_part(inverse(X_55)) = inverse(positive_part(X_55)),
inference(subst,[],[refute_0_748:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_750,plain,
multiply(X_55,negative_part(inverse(X_55))) = multiply(X_55,negative_part(inverse(X_55))),
introduced(tautology,[refl,[$fot(multiply(X_55,negative_part(inverse(X_55))))]]) ).
cnf(refute_0_751,plain,
( multiply(X_55,negative_part(inverse(X_55))) != multiply(X_55,negative_part(inverse(X_55)))
| negative_part(inverse(X_55)) != inverse(positive_part(X_55))
| multiply(X_55,negative_part(inverse(X_55))) = multiply(X_55,inverse(positive_part(X_55))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,negative_part(inverse(X_55))),multiply(X_55,negative_part(inverse(X_55)))) ),[1,1],$fot(inverse(positive_part(X_55)))]]) ).
cnf(refute_0_752,plain,
( negative_part(inverse(X_55)) != inverse(positive_part(X_55))
| multiply(X_55,negative_part(inverse(X_55))) = multiply(X_55,inverse(positive_part(X_55))) ),
inference(resolve,[$cnf( $equal(multiply(X_55,negative_part(inverse(X_55))),multiply(X_55,negative_part(inverse(X_55)))) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
multiply(X_55,negative_part(inverse(X_55))) = multiply(X_55,inverse(positive_part(X_55))),
inference(resolve,[$cnf( $equal(negative_part(inverse(X_55)),inverse(positive_part(X_55))) )],[refute_0_749,refute_0_752]) ).
cnf(refute_0_754,plain,
( multiply(X_55,inverse(positive_part(X_55))) != inverse(positive_part(inverse(X_55)))
| multiply(X_55,negative_part(inverse(X_55))) != multiply(X_55,inverse(positive_part(X_55)))
| multiply(X_55,negative_part(inverse(X_55))) = inverse(positive_part(inverse(X_55))) ),
inference(subst,[],[refute_0_108:[bind(X0,$fot(multiply(X_55,negative_part(inverse(X_55))))),bind(Y0,$fot(multiply(X_55,inverse(positive_part(X_55))))),bind(Z0,$fot(inverse(positive_part(inverse(X_55)))))]]) ).
cnf(refute_0_755,plain,
( multiply(X_55,inverse(positive_part(X_55))) != inverse(positive_part(inverse(X_55)))
| multiply(X_55,negative_part(inverse(X_55))) = inverse(positive_part(inverse(X_55))) ),
inference(resolve,[$cnf( $equal(multiply(X_55,negative_part(inverse(X_55))),multiply(X_55,inverse(positive_part(X_55)))) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
multiply(X_55,negative_part(inverse(X_55))) = inverse(positive_part(inverse(X_55))),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(positive_part(X_55))),inverse(positive_part(inverse(X_55)))) )],[refute_0_188,refute_0_755]) ).
cnf(refute_0_757,plain,
( multiply(X_55,negative_part(inverse(X_55))) != inverse(positive_part(inverse(X_55)))
| multiply(X_55,negative_part(inverse(X_55))) != negative_part(X_55)
| inverse(positive_part(inverse(X_55))) = negative_part(X_55) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,negative_part(inverse(X_55))),negative_part(X_55)) ),[0],$fot(inverse(positive_part(inverse(X_55))))]]) ).
cnf(refute_0_758,plain,
( multiply(X_55,negative_part(inverse(X_55))) != negative_part(X_55)
| inverse(positive_part(inverse(X_55))) = negative_part(X_55) ),
inference(resolve,[$cnf( $equal(multiply(X_55,negative_part(inverse(X_55))),inverse(positive_part(inverse(X_55)))) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
inverse(positive_part(inverse(X_55))) = negative_part(X_55),
inference(resolve,[$cnf( $equal(multiply(X_55,negative_part(inverse(X_55))),negative_part(X_55)) )],[refute_0_144,refute_0_758]) ).
cnf(refute_0_760,plain,
inverse(positive_part(inverse(X_119))) = negative_part(X_119),
inference(subst,[],[refute_0_759:[bind(X_55,$fot(X_119))]]) ).
cnf(refute_0_761,plain,
multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) = multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))),
introduced(tautology,[refl,[$fot(multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))))]]) ).
cnf(refute_0_762,plain,
( multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) != multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))
| inverse(positive_part(inverse(X_119))) != negative_part(X_119)
| multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) = multiply(positive_part(X_119),negative_part(X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))),multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))) ),[1,1],$fot(negative_part(X_119))]]) ).
cnf(refute_0_763,plain,
( inverse(positive_part(inverse(X_119))) != negative_part(X_119)
| multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) = multiply(positive_part(X_119),negative_part(X_119)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))),multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) = multiply(positive_part(X_119),negative_part(X_119)),
inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X_119))),negative_part(X_119)) )],[refute_0_760,refute_0_763]) ).
cnf(refute_0_765,plain,
( X_119 != multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))
| multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))) != multiply(positive_part(X_119),negative_part(X_119))
| X_119 = multiply(positive_part(X_119),negative_part(X_119)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_119,multiply(positive_part(X_119),negative_part(X_119))) ),[0],$fot(multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))))]]) ).
cnf(refute_0_766,plain,
( X_119 != multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))
| X_119 = multiply(positive_part(X_119),negative_part(X_119)) ),
inference(resolve,[$cnf( $equal(multiply(positive_part(X_119),inverse(positive_part(inverse(X_119)))),multiply(positive_part(X_119),negative_part(X_119))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
X_119 = multiply(positive_part(X_119),negative_part(X_119)),
inference(resolve,[$cnf( $equal(X_119,multiply(positive_part(X_119),inverse(positive_part(inverse(X_119))))) )],[refute_0_114,refute_0_766]) ).
cnf(refute_0_768,plain,
( X_119 != multiply(positive_part(X_119),negative_part(X_119))
| multiply(positive_part(X_119),negative_part(X_119)) = X_119 ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(X_119)),bind(Y0,$fot(multiply(positive_part(X_119),negative_part(X_119))))]]) ).
cnf(refute_0_769,plain,
multiply(positive_part(X_119),negative_part(X_119)) = X_119,
inference(resolve,[$cnf( $equal(X_119,multiply(positive_part(X_119),negative_part(X_119))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
multiply(positive_part(a),negative_part(a)) = a,
inference(subst,[],[refute_0_769:[bind(X_119,$fot(a))]]) ).
cnf(refute_0_771,plain,
( multiply(positive_part(a),negative_part(a)) != a
| a != a
| multiply(positive_part(a),negative_part(a)) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(a),negative_part(a)),a) ),[0],$fot(a)]]) ).
cnf(refute_0_772,plain,
( a != a
| multiply(positive_part(a),negative_part(a)) = a ),
inference(resolve,[$cnf( $equal(multiply(positive_part(a),negative_part(a)),a) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
a != a,
inference(resolve,[$cnf( $equal(multiply(positive_part(a),negative_part(a)),a) )],[refute_0_772,prove_product]) ).
cnf(refute_0_774,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_775,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_774,refute_0_773]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 01:49:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.21/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/1.43
% 1.21/1.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.33/1.52
%------------------------------------------------------------------------------